Brian Dorney | USLHC | USA

During my brief time participating in the wide world of High Energy Physics (HEP) I have learned many, many things. But above all, if there is one thing I’ve come to understand, it’s that there will never be enough:

Coffee

While some people may concern themselves with blood alcohol content. I spend my time thinking about blood caffeine content. I’ve become thoroughly addicted as a grad student, and without my daily (or sometimes hourly) “fix,” I doubt I would get anything done.

But caffeine isn’t just my own vice (or at least that’s the addict in me talking), I’ve come to think its a necessary evil within all fields of research. As an example, there are not one, not two, but four coffee pots on my floor of the Physics & Chemistry building; and I’m not even counting the chemistry side (or those that may be found in offices).

The coffee pot that I contribute to is filled twice a day (at least). We go through several containers of half & half every week, along with a tub of say Maxwell House coffee. We rely on everyone to contribute to keep this stream of liquid productivity flowing.

My own coffee mug has become to be known as “The Soup Bowl” among the grad students & professors on my floor. I maintained that it is a coffee mug, however I’ve been fighting a losing battle ever since the start of last spring semester. But whether its a mug for drinking coffee or a bowl for holding chicken noodle soup, I would get a whole lot less done in a day without this beautiful piece of ceramic:

My coffee mug, compared with a "normal" coffee mug

And even though this mug fits a gigantic amount of coffee; I’ve come to think that it’s never enough.

Hours in a Day

While I need coffee to get through the hours of my day, I just really wish there were more of them.

My day begins between 8-10 am (usually depending on when I get home from the night before); I usually end up having to work until as late as 8-9pm (or sometimes even midnight) to accomplish what I need to for the day. I spend my time corresponding with other physicists via email, attending meetings, reading papers, and computer programming. It’s a lot of work, but I enjoy what I do. However, I am of the opinion that the sunrise and sunset should be a bit farther apart.

"Zed, don't you guys ever get any sleep around here?" - Jay, "The twins keep us on Centaurian time, standard thirty-seven hour day. Give it a few months. You'll get used to it... or you'll have a psychotic episode." -Zed (Men In Black, 1997)

Personnel

It’s been my experience that every single analysis in CMS can always benefit from more people becoming involved.

To give you an idea of what tasks are involved in an analysis, here’s a generic outline most conform to:

Define experimental techniques
Perform measurements
Determine backgrounds
Analyze experimental/theoretical uncertainties
Obtain approval (each of the LHC’s Collaborations undergo an internal peer-review process before submitting for publication in an external peer-review journal).

These tasks take time, and above all, they need warm bodies (who sometimes have more in common with Zombies, sans coffee that is).

But HEP is a collaborative science. Within a given experiment (such as CMS or ATLAS) we all work together to make sure research is conducted precisely, and promptly. Each individual within the CMS Collaboration is usually juggling a series of different analyses. The time they invest in each of these analyses varies. However, each researcher usually has one project which is their “pet project,” and occupies the majority of their time.

But needless to say, HEP is a massive undertaking, and it seems like there are never enough Physicists/Grad Students involved.

Data

What’s the difference between one inverse femtobarn (fb^-1) of data, and say ten, or a hundred?? Only a series of discoveries that will forever change our understanding of the universe. You know, nothing major.

Humor aside, the experiments at the LHC have collected over 1 fb^-1 of data this past year. And there have been several times in which we collected more data in a day then we did in all of 2010 (which I find astounding):

Integrated luminosity delivered to/recorded by the CMS Detector per day. Note the 2010 data set consisted of only ~43.3 pb^-1. (Image Courtsey of the CMS Collaboration)

Total integrated luminosity delivered to/recorded by the CMS Detector in 2011. (Image Courtesy of the CMS Collaboration)

But what’s the big deal? Well, one of the rules of thumb in particle physics says: to have a discovery, you need to have a statistical significance of five sigma over your current theory/background. Simply put, the chances that your discovery is a statistical fluke must be less then 0.01%.

While this may seem a bit ad hoc, it is actually necessary. Three sigma effects come and go in particle physics.

But because of this stringent requirement we are always asking for more. We always wish for our colliding beams to have a higher luminosity. We always want the time between crossings of particles in the detector to be minimized. In short, we always want more data, and there is never enough!

Who knows what is on the horizon of tomorrow’s proton collisions. I for one have no idea, but I avidly look forward to the coming “more glorious dawn.”

CPU’s

I’m sure my colleagues have differing opinions on what is and is not needed in high energy physics. But, I adamantly believe there are two things all of us would agree on. We always need more data, and we always need more CPU’s.

Cluster computing is the name of the game. There are rooms at HEP Labs that can usually be heard from “miles away” (or at least a few meters). They literally hum with activity. To me it sounds like raw science. To someone more “normal,” it probably sounds like hundreds of fans all operating at once (which is exactly what it is). These rooms are filled with racks upon racks of computers, all linked in some fashion. Users all over the country/world submit hundreds of thousands of “jobs,” or research tasks, to these clusters. In each of these jobs, a piece of the cluster is given some software a researcher has developed, and use this software to analyze data.

As an example, I perform a relatively small analysis (with respect to the scope of LHC Physics), but I run between 7.5-14K computing jobs a week. Job number is a bit arbitrary though; this is because a user specifies how large each job is. To be a bit more concrete, the size of all the data & simulated samples I need for my work is over 80 terabytes.

So how do I, and other physicists, analyze all this data? With jobs!

And here’s how it works: one of my data sets has roughly 35 million events. If I attempt to process this data all at once, with one computer (even recent jeopardy champion Watson) it will take forever. Instead, I break the task of data analysis up into many many tasks (aka jobs). Each job will analyze 25-50K events. In this manner high energy physics makes use of “parallel-computing,” and save time.

But why do we need this job system, how long would it really take to process that data in one shot? Well assuming a spherical cow, each of my jobs takes ~12 hours. To run over those 35 Million events I mentioned, I need 3836 jobs. So at 12 hours a job, it would take Watson ~5.3 years to process all the data if it was done in one job.

So much for getting my degree in less then a decade (and heaven forbid I make a mistake!).

But the irony of having so many physicists participating in a HEP experiment, is that not everyone will have all of their jobs running at a time. Each cluster has a finite number of CPU’s, and a seemingly infinite amount of jobs submitted to it (continually). What usually happens is a person will have anywhere between 6 to 600 of their jobs running at a time (depending on who else is using the cluster).

So to analyze data, it could take anywhere between a night to a week. And in this regard, I believe we will never have enough CPU’s.

Until next time,

-Brian

Tags: coffee, CPU, data, hours
Posted in Latest Posts | 4 Comments »

In a World Without Color, Why do I believe in Gluons?

Saturday, July 9th, 2011

I’m often asked as a high energy physicist how do we know that the elementary particles exist. One might think such questions are absurd. But, if the scientific method is to stand for anything, then these questions must have merit (and be taken seriously). After all, it is our duty as scientists to take an unbiased skeptical viewpoint; and to report on what is actually observed in nature.

Trust me, I would find a world were Hogwarts Castle actually existed as a school of magic far more interesting. But alas, nature has no room for such things as wands or Horcruxes.

But I thought I’d try to discuss this week how the gluon was “discovered” decades ago. The gluon is represented by the “g” in our “periodic table” of elementary particles:

Experimentally observed members of the Standard Model (Ref. 1)

The gluon is what’s called a “vector boson,” meaning it has spin 1 (in units of planck’s fundamental constant, ℏ). And it is the mediator of the strong nuclear force. The force which is responsible for binding quarks into hadrons and keeping atomic nuclei together. When I say the gluon is a mediator, I mean that when a quark interacts with another quark or anti-quark, it does so by exchanging gluons with the other quark/anti-quark. In fact gluons themselves interact with other gluons by exchanging gluons!!!

But how exactly do the quarks/anti-quarks and gluons interact? Well quarks & gluons (whenever I say quarks, my statement also applies to anti-quarks) carry something called Color Charge. Color is a type of charge (similar to electric charge) in physics. It comes in three types labelled as red, green & blue. Now where as electric charge has a postive and a negtive, color charge has a “color” (i.e. red charge) and an “anti-color” (i.e. anti-red charge). It is this color charge that gives rise to the strong nuclear force, and is what is responsible for the interaction of quarks and gluons with each other. The quantum theory associated with the interactions of quarks and gluons is known as Quantum Chromodynamics (QCD, “Chromo-“ for color!).

However, no particle with a color charge can be directly observed in the universe today. This is due to something called “Color Confinement,” which causes colored particles to form bind together into “white” (all colors present in equal parts), or “colorless” (net color is zero) states. We sometimes call these states “color neutral” or “color singlet” states. Flip Tanedo has written this nice post about Color Confinement if you’d like to know more.

So if an experimentalist cannot directly observe a gluon, how were they discovered? One of the best answers to this question comes from electron-positron colliders, such as the LHC’s predecessor: the Large Electron-Positron Collider (LEP), and this is where our story takes us.

Jet’s in Electron-Positron Collisions

While electrons & positrons do not carry color charge, they can produce colored particles in a collision. The Feynman Diagram for such a process is shown here:

Here an electron and a positron annihilate, emit a virtual photon, which then pair produces a quark and an anti-quark (Image courtesy of Wikipedia, Ref. 2)

Since the quark & anti-quark produced carry color; they must hadronize, or bind together, to form color neutral states. This hadronization process then gives rise to the formation of jets.

If the momentum of the colliding electron and the positron are equal but opposite (the angle between them is 180 degrees), the two jets produced would appear to be “back-to-back.” Meaning that the angle between them is also 180 degrees (For those of you counting, you must look in the center-of-momentum frame).

The reason for this is that momentum must be conserved. If the electron comes in with Y momentum, and the positron comes in from the opposite direction with -Y momentum, then the total momentum of the collision is zero. Then if I sum over all the momentum of all the particles produced in the collision (termed “outgoing” particles), this sum must also equal zero. In this case there are only two outgoing particles, and the angle between them must be 180 degrees!

We call such a collision event a “di-jet event,” because two jets are created. Here’s an example of a Di-Jet Event as seen by the CMS Detector, and would look identical to what is observed in an electron-positron collider.

Di-Jet Event within the CMS Detector, as seen in looking down the beam-pipe in the xy-plane.

The two protrusions of rectangles together with the solid and dotted purple lines represent the two jets in the above image. The black lines represent each jet’s direction. Notice how the angle between them is almost exactly 180 degrees.

Now suppose either the quark or the anti-quark in the above Feynman Diagram was very energetic, and radiated off another particle. QCD tells us that this particle that is radiated is a gluon. The Feynman Diagram for this “gluon radiation” would look like the above diagram, but with one additional “line,” as shown here:

Gluon radiation from an anti-quark in an electron-positron collision (Image courtesy of Wikiepdia, Ref. 2)

We say this Feynman Diagram describes the process e⁺e^– →qqg. Here the anti-quark is shown as radiating a gluon, but the quark could have just as easily radiated a gluon. If the radiated gluon is very energetic, the theory tells us it would have a different direction from the quark and the anti-quark. Thus the gluon would make its own jet!

Now an experimentalist has something to look for! If gluons exist, we should see events in which we have not two, but three jets created in electron-positron collisions. Due to momentum conservation, these three jets should also all lie in the same plane (called “the event plane”); and if the gluon has enough energy, the three jets should be “well separated,” or the angles between the jets are large.

Such electron-positron collision events were observed in the late 1970s/early 1980s at the Positron Electron Tandem Ring Accelerator (PETRA) at the Deutsches Elektronen Synchrotron (DESY). Here are two examples of three jet events observed by the JADE detector (one of the four detectors on PETRA):

A Tri-Jet event observed in the JADE Detector, again looking down the beampipe (Ref. 3)

Another Tri-Jet event observed in the JADE detector (Ref. 4)

From these event displays you can see the grouping of charged & neutral tracks (the solid & dotted lines in the images) in three regions of the JADE detector. Notice how the tracks are clustered, we say they are “collinear.” The reason they are appear collinear is because when a quark/gluon hadronizes, the hardonization process must conserve momentum. The particles produced from hadronization must travel in the same direction as the original quark/gluon. Then because of this collinear behavior the tracks group together to form jets. Notice also how the jets are no longer back-to-back, but are well separated from each other (as expected).

While these images were first reported decades ago, we still observe three jet events today at the LHC and other colliders. Here is an example of a three jet event as recorded by the CMS Detector:

A Tri-Jet event in CMS

But now let’s actually compare some theoretical predictions of QCD to the experimental data seen at PETRA and see if we can come up with a reason to believe in the gluon.

QCD Wins the Day

The MARK-J Collaboration (also one of the detectors at PETRA) decided to investigate three jet events based on two models of the day, the first of which was QCD [4], now a fully formalized theory, which interpreted three jet events as:

e⁺e^– →qqg

In which a gluon is produced in the collision, in addition to the quark and anti-quark. The second model they used was what was called the quark/anti-quark model, or phase-space model [4]. Which interpreted three jet events as simply:

e⁺e^– →qq

In which only a quark and an anti-quark are produced.

To compare their theoretical predictions to the experimental data they looked at how energy was distributed in the detector. They looked to see how well the two predictions matched what was observed by using something called a “normalized chi-squared test” (a test which is still widely used today across all areas of research).

In a normalized chi-squared test, you perform a statistical test between the two “data sets” (in this case one set is the experimental data, the other is the theoretical prediction), from this test you get a “chi-squared” value. If the “chi-squared” value divided by the “number of degrees of freedom” (usually the number of data points available) is equal to one, then we say that the two data sets are well matched. Or, the theoretical prediction has matched the experimental observation. So if one of the two above models (QCD, and the “Phase-Space” model) has a normalized chi-squared value of one or near one when compared with the data, then that is the model that matches nature!

So to make their energy distributions, the MARK-J Collaboration decided to work in a coordinate system defined by three axes [4,5]. The first of which was called the “Thrust” axis, defined as the direction for which the “energy flow” is maximum [4,5]. This basically means the Thrust axis is taken as the direction of the most energetic jet in the event.

The second axis, the “Major” axis, is taken to be perpendicular to the Thrust axis; but with the requirement that the projected energy of the most energetic jet onto the Major axis in is maximized [4,5]. Meaning if I took the dot product between the Major axis and the direction of the most energetic jet, this dot product would always be maximum (but still keep the Major axis and the Thrust axis perpendicular). This additional requirement needs to be specified so that the Major axis is unique (there are an infinite number of perpendicular directions to a given direction).

The third axis, called the “Minor” axis, is then perpendicular to these two. However, it turns out that energy flow along this direction is very close to the minimum energy flow along any axis [4,5].

But let’s not get bogged down in these definitions. All this is doing is setting up a way for us to compare different events all at once; since no two events will have jets oriented in exactly the same way. In addition, these definitions also identify the event plane for each collision event.

So here’s what the energy distributions turned out looking like for all events considered:

Energy distributions in selected three jet events recorded by the MARK-J Collaboration. The black dots are the data points, the dotted line is the theoretical prediction, more details below (Ref. 5).

The angles in the above plots correspond to the where in the energy was deposited within the MARK-J Detector. The distance from the black dots to the center of each graph is proportional to the amount of energy deposited in the detector in this direction [4,5].

Forty events in total were used to make the above distributions [4]. Each event’s jet topologies where re-oriented so they matched the definitions of the Thrust, Major & Minor axes outlined above. From the top diagram labeled as “Thrust-Major” plane we see three “lobes” or clustering of data points. This indicates that the three jet structure, or topology, of these forty events.

By rotating the entire picture along the thrust axis by 90 degrees we end up looking at the “Thrust-Minor” plane, the bottom diagram. Notice how we now only have two clusterings of data points or lobes. This is because we are looking at the event plane edge on. Imagine looking at the Mercedes-Benz symbol. The plane that the three spokes in it is the “Thrust-Major” Plane. Then if I turn it so I can see only the metal rim of the Mercedes symbol, I’m looking in the “Thrust-Minor” plane. So the bottom diagram then illustrates that these events have the jets all lying in a plane, as expected due to momentum conservation.

Now how well did the two theoretical predictions mentioned above match up to the experimental observations?

The “phase space” model (no gluons) was not plotted in the above diagrams. However, the normalized chi-squared value between the experimental data and the “phase space” model was reported as 222/70 [4]; which is nowhere near one! Researchers took this to mean that this theoretical model does not do a good job at describing the observed behavior in nature (and is thus wrong, or missing something).

Now the QCD prediction (with gluons!) is shown as the dotted line in the above diagrams. See how well it matches the experimental data? In fact the normalized chi-squared value between the data and the predictions of QCD was 67/70 [4,5]; now this is close to one! So the predictions of QCD with three jet events being caused by the radiation of an energetic gluon has matched the experimental observation, and given us the proof we needed to believe in gluons!

However, the story of the gluon did not end there. Much more was needed to be done, for example QCD predicts the gluon to have spin 1. These measurements which I have outlined in this post did not measure the spin of the gluon. More work was needed for that; but safe to say by the mid 1980s the gluon was well established as an elementary particle, and we have lived with this knowledge ever since.

Until next time,

-Brian

References

[1] Wikipedia, The Free Encyclopedia, “The Standard Model of Elementary Particles,” http://en.wikipedia.org/wiki/File:Standard_Model_of_Elementary_Particles.svg, July 5^th, 2011.

[2] Wikipedia, The Free Encyclopedia, “Feynmann Diagram Gluon Radiation,” http://en.wikipedia.org/wiki/File:Feynmann_Diagram_Gluon_Radiation.svg, July 5th, 2011.

[3] P. Söding, “On the discovery of the gluon,” The European Physical Journal H, 35 (1), 3-28 (2010).

[4] P. Duinker, “Review of e+e- physics at PETRA,” Rev. Mod. Phys. 54 (2), 325-387 (1982).

[5] D.P. Barber, et. al., “Discovery of Three-Jet Events and a Test of Quantum Chromodynamics at PETRA,” Phys. Rev. Letters, 43 (12), 830-833 (1979).

Tags: DESY, discoveries, event displays, gluons, PETRA, QCD
Posted in Latest Posts | 4 Comments »

To B or not to Bbar: B-Tagging via Track Counting

Friday, June 10th, 2011

So in the last few posts, I’ve been talking about Jets. I’ve also touched on ways to identify a specific type of jet: the b-Jet. Recall, a b-Jet is a jet that is produced as a result of the hadronization of a b or anti-b quark (termed bbar or simply b).

I also outlined some properties of B-Hadrons (see the second link above). So let’s start to put these properties to good use and flesh out one of the standard B-Taggers used by high energy physicists, namely the Track Counting (TC) Algorithm.

(Again, you may click on any of the below images to enlarge them further).

One Track, Two Track, Three Track, Four!?

In my previous post I stated that a B-Hadron will produce roughly five charged particles per decay. These charged particles will then leave a track within the Silicon Tracker of CMS. So if a jet is a b-jet, it will have more high impact parameter tracks then a jet produced from the hadronization of a light quark or gluon.

The Track Counting approach is actually rather simple, physicists require a jet to have at least N tracks (for some integer N). In CMS we take N to usually be 3, but I will explain why in more detail below. However, we don’t use all of a jet’s tracks in the TC Algorithm. We require the tracks used to be of “high quality”.

But what does that mean? How do you judge the “quality” of a track? The answer is information, how much the detector knows about the particle that made that track. This comes about in the form of how many hits a particle left within the silicon tracker as it traveled (these hits are then used to make the track). If the particle left more hits in the tracker it means higher track quality. Here’s an example of two tracks, the one on the left has more then 10 hits in the tracker, while the one on the right has only 5. So, the left track is of higher quality.

: An Example of two tracks left by charged particles recorded by the CMS Detector. The higher quality track (at left) has more hits within the Silicon Tracker (Represented by the blue rectangles).

Here the blue dot at the start of each track represents the location of the primary vertex (the point where the proton-proton collision occurred). The track itself is represented by the green line. The track’s hits in Silicon Tracker of CMS are represented by the blue rectangles (each rectangle is a piece of the Silicon Tracker).

A Measurement of Impact

Now that we have a collection of high quality tracks belonging to a jet, how do I use them to test if the jet is a b-Jet or not? We look at something called the impact parameter, or the distance between the primary vertex and the closest approach to the track. A visualization will help with understanding this:

Visualization of the Impact Parameter (IP, red line) of a track (Image courtesy of Jean-Roch Vlimant, of the CMS Collaboration).

The track is represented by the dotted blue line. And this track belongs to a jet (with a direction given by the green arrow). This Jet direction represents the direction of the jet’s cone within the detector (see the first link above to get an idea of what a jet cone is like in CMS).

The Impact Parameter, is represented by the red line, and is drawn from the primary vertex to the track. Notice how the point where the IP touches the track, a right angle is formed, this is how the point of closest approach is identified. Also, the location where the red line makes a right angle with the track is unique. Meaning, the IP always makes a right angle with the track, and there is only one IP per track.

However, the error on the IP measurement could sometimes be large. To account for this physicists divide the IP by its error, and this new value is called the IP-Significance (IP-Sig).

We also have a sign convention for this IP-Sig value. If the cosine of the angle between the track and the jet axis is positive (marked as θ in above diagram), the IP-Sig is a positive number (the track is said to be “downstream” of the jet axis). If the cosine of this angle is negative, the IP-Sig is negative (and this is said to be “upstream” of the jet axis).

Discriminating against non-b-Jets

The goal of all B-Tagging algorithms is to create what is called a discriminator. A discriminator is some number that is calculated from a jet’s properties. As the value of a jet’s discriminator increases, the likelihood that the jet is a b-Jet also increases. It’s a very simplistic approach, and works beautifully.

In the TC Algorithm, the discriminator is the signed IP-Sig value mentioned above. The reason we use the signed IP-Sig value is best summarized as:

Prompt tracks from the primary vertex have small IP values while tracks from decays of B hadrons have rather large IP values because of the B hadron lifetime [1].

So b-jets will have several tracks with large IP values. But as I mentioned above, we convert these IP values to signed IP-Sig values to minimize the impact of the measurement’s error on our discriminator. In summary, if a jet has many tracks with small signed IP-Sig values, it is most likely not from the hadronization of a b quark/anti-quark. While a jet originating from a b quark/anti-quark will have tracks with large IP values, because they will be “displaced” from the primary vertex.

This again ties back to my previous post which outlined the properties of B Hadrons (second link at the start of this post). And it was these B-Hadron properties that motivated the creation of the TC Algorithm years ago.

But this raises a new question. Each of the high quality tracks within a jet has a signed IP-Sig value, so which of these of these IP-Sig values do we use in B-Tagging?

To answer this we first order all of a jet’s high quality tracks by decreasing IP-Sig value. We then choose to look at the N^th track in this listing for all of our jets under study (remember how I said N was usually 3 above?). The N^thtrack has a signed IP-Sig value greater then some number Y; and thus the jet has a chance X of being b-Jet. As the number Y increases, the chance to be a b-Jet, X, also increases. Here are some plots that will let us get a better understanding of this:

From left to right: signed IP-Sig for all selected tracks, 1st, and 3rd track, in selected jets found in proton-proton collisions recorded by the CMS Detector in 2010 [2].

In the above plots, CMS physicists have plotted the signed IP-Sig values for: (from left to right) all high quality tracks within all jets, the first high quality track within a jet, and the third high quality track within a jet. The x-axis in each case is the value of the signed IP-Sig of the jet’s track(s). The y-axis represents the number of jets found with tracks/a track with that signed IP-Sig value.

The black dots in each of the colored distributions represent the signed IP-Sig values of jets found in actual collision data. Whereas the colored distributions represent the values found in simulation for light jets (blue), c-jets (green), and b-jets (red). Recall that when I say a jet is a light-jet or a c-jet, I mean the jet was created by the hadronization of a light quark/anti-quark (or gluon), or a c quark/anti-quark.

The distributions below the colored distributions represent how well the simulation compares to actual data. If the simulation matches data, the black points there should be at one, or close to one. For the most part, the simulation describes the data well, and we are constantly improving our simulation so that the agreement becomes better and better.

What’s interesting to note is what happens when we look at a jet’s high quality track that has the third highest IP-Sig value. We see that as this value increases positively, the distribution (far right) is completely dominated by b-jets. Whereas in the other two distributions, there is still a reasonable contribution of light jets at all values of signed IP-Sig.

This far right distribution is known as the Track Counting High Purity (TCHP) Algorithm. And CMS Physicists use this algorithm to search for b-Jets in many different research areas; from top quark physics, precision QCD measurements, to supersymmetric searches, this algorithm is one of the major tools employed by high energy physicists as a whole.

Because of B-Hadron properties, physicists have come up with a way to identify b-Jets, require the jet to have tracks with high IP-Sig values.

Recall that this TC Algorithm made use of the fact that B-Hadrons decay into many charged particles, and the long life-time of B-Hadrons. This long-lifetime ensures that particles produced by decaying B-Hadrons will have tracks with large IP values (this then translates into large IP-Sig values). All of these things are illustrated in the three distributions shown above.

Until next time,

-Brian

References:

[1] CMS Collaboration, “Performance of track and vertex reconstruction and b-tagging studies with CMS in pp collisions at sqrt(s) = 7 TeV,” Proceedings of Science, Kruger National Park, Mpumalanga, South Africa, December 2010.

[2] CMS Collaboration, “Commissioning of b-jet identification with pp collisions at sqrt(s) = 7 TeV,” CMS Physics Analysis Summary, CMS-PAS-BTV-10-001, http://cdsweb.cern.ch/record/1279144?ln=en.

Tags: B-Physics, B-Tagging, CMS, Track Counting
Posted in Latest Posts | 6 Comments »

Anatomy of a Jet in CMS

Wednesday, June 1st, 2011

We talk often about Jets here at US LHC. We talk about ways to identify them, their structure, and we even mention some crazy phenomenon involving them. But one thing we don’t always talk about is what a jet looks like. And this is what I would like to show today, in gory detail. So this post is about pictures, lots and lots of pictures.

We can’t see jets with our eyes. The particles that make up a jet are just to small. But using a device as large as the CMS detector, we can take a “snap-shot” of a jet created in a proton-proton collision at the LHC. So it behooves us to start with a brief illustration of CMS.

(Clicking on any of the images below allows you to blow them up in another window, just in case you need a bigger picture)

The CMS Detector

It’s a gigantic cylinder, twenty-one meters long and fifteen meters in diameter! For comparison, the average height of all American women & men over 20 years old is 1.62 & 1.76 meters (5′ 4″, 5′ 9″), respectively. But being gigantic isn’t the only thing CMS has in common with an ogre, CMS also has layers; and each layer is a different sub-detector responsible for identifying a different class of particles.

But Here’s computer generated image of CMS, with a cut-away section showing some of these layers:

: Cut away view of CMS, Hadronic & Electromagnetic Calorimeters not shown. The camera guide in the bottom right shows CMS’s coordinate axis, (x,y,z) for (red,green,blue).

The blue disks and red rectangles on the outside of the detector are part of CMS’s muon chambers (the sub-detector responsible for picking up muons).

The inner cylinder represents CMS’s silicon tracker, this sub-detector is a rather complex instrument. Its made of silicon strips, and is essentially a giant CCD camera (with over ten million pixels). The silicon tracker is responsible for reconstructing the trajectories of charged particles as they pass through CMS; this is done by basically playing a giant game of connect the dots. A close-up of the silicon tracker is shown here:

: Close-up of the silicon tracker

The green and yellow portions are the silicon tracker. The grey/silver part is what’s called the silicon pixel detector. It is less then an inch away from where the proton-proton collisions occur in CMS, and thus the closest detection element.

While not shown in the image above, CMS’s calorimeters and superconducting magnet are located between the silicon tracker and the muon system. They can be seen in this interactive applet on particle detection, of which I’ve taken a screenshot of and shown below:

The calorimeters are responsible for measuring the energy and momentum of charged & neutral particles (the tracker plans a role in this as well). They are critical to jet identification & reconstruction…without them we would not be able to do any jet physics in CMS.

Basically what happens is calorimeters are designed so that a particle loses all of its energy as it travels through the calorimeter. From the energy deposited, and the location of where the deposit occurs we can determine the direction and momentum of charged particles (again, the tracker also plays a role in this).

CMS has two types of calorimeters: an electromagnetic calorimeter (ECAL) for detecting electrons and photons; and a hadronic calorimeter (HCAL) for detecting heavy particles that can pass through the ECAL. The HCAL is also the only place in CMS where we can detect neutral particles with non-zero mass (such as a neutron).

I should mention that neutrino’s escape detection, and we have to infer their presence by looking for “missing energy.”

But now that I’ve introduced you to CMS, let’s get down to business and talk about Jets.

Jets in CMS

I use jets extensively in my own research and its sometimes hard to get a handle on what a jet really is. I like to think of it like a shotgun blast of particles slamming into the detector. Jets arise from the hadronization of colored particles, and because of this they are made up of many particles. Jets can be made of leptons, hadrons and even bosons (specifically the photon). These particles are usually collimated in a given direction, and you can kinda draw a cone around them (like a shotgun blast!).

For this reason in CMS we like to think of jets as cones, like in this image:

: A jet cone in CMS

This is a jet cone created in a single proton-proton collision recorded by CMS detector in 2010. In this image I’ve turned the silicon tracker’s graphics off, along with everything else that happened in this event (it can get really messy anyway). A zoom in of this jet cone can be seen here:

: Zoom in of the jet cone

Now this jet cone may look small in comparison to the entire CMS Detector; but don’t be fooled, I choose a very energetic jet for this post. This jet’s component of momentum in the xy-plane (green & red axis above) is 115 GeV/c. Most jets created in proton-proton collisions have xy-momentum components of less then 30 GeV/c. In fact, if you plot the number of jets detected against their xy-momentum components, you get a distribution that looks similar to an decaying exponential. So, 115 GeV/c jet is rather energetic.

But what makes up this jet!? Simple answer A LOT! This one jet shown above is made up of over 20 different particles, all of which are conveniently hidden at the moment. So let’s go about fleshing this jet out, piece by piece.

Jet Anatomy

So what did CMS see as this jet hit the detector? Let’s start with the silicon tracker:

: A jet & its tracks in CMS

So here I’ve turned off the view of the muon chambers, and just shown the jet cone and the tracks (the green lines) reconstructed in the silicon tracker.

A few things to note, the green lines appear to be coming from the same point in space (for the most part). This point is called the primary vertex, its the point at which the proton-proton collision actually occurred. Another interesting feature is that these tracks go outside of the jet’s cone! What’s up with that!?

Well the answer is two-fold. First, these tracks where made by charged particles; and thus their trajectories are bent in the presebce of CMS’s magnetic field. In other words, we forced the tracks to go outside the jet cone by having a superconducting magnet in our detector (this allows us to make more precise momentum measurements). Second, treating jets as cones is just a model (which works well). It often happens that these tracks are indeed all inside the cone, but I purposefully chose a jet with tracks that had large curvature for this demonstration.

In fact, jets are created by using different algorithms; and not all algorithms use a cone geometry! There are many different algorithms that you can use, they all have subtle differences…but that is really a story for another day. I just want to show you what makes up a jet, and what it looks like to the detector.

So this is all the information that the silicon tracker gave us about the jet. It’s time to ask the calorimeters what they saw, starting with ECAL:

: A Jet, its tracks, and its energy deposits in CMS’s electromagnetic calorimeter

These yellow-ish squares represent the energy deposited in ECAL. How far these squares protrude from that wire-frame represents how much energy has been deposited (for those of you who are keeping track, the scale is 10 GeV per meter). I’ll show some images illustrating this protrusion later on; right now I want to talk about the relation between the tracks, the jet cone and these ECAL energy deposits.

It looks like the jet cone is centered on the bulk of the energy deposits in ECAL. We actually intended this to happen because of something called clustering. We group pieces of the calorimeters (both ECAL & HCAL) into clusters, and then clusters into superclusters. And it is these clusters/superclusters that we go to when beginning to construct a jet.

It also looks like some of the tracks in our silicon tracker match up with these ECAL energy deposits. But, there are clearly some energy deposits that don’t match up to any track! What has happened here!?

The answer, is photons and other neutral particles!

The silicon tracker is incapable of detecting particles without an electric charge (like the photon). But the ECAL was designed specifically to capture electrons & photons (which is why it is called the electromagnetic calorimeter). Adding “photon candidates” to the picture gives us this result:

: A Jet, its tracks, its “photon candidates”, and its energy deposits in CMS’s electromagnetic calorimeter

These dotted purple-ish lines are the trajectories of the “photon candidates” in this jet. I say candidates because they might not actually be photons. To be an actual photon the candidate must past very stringent quality requirements which only a real photon will satisfy. I haven’t enforced any quality requirements here, so all bets are off (remember I’m just trying to show what made up this jet!).

Again all these photon candidates appear to be coming from the primary vertex, most of them are within the jet’s cone (not all); and almost every photon candidate is linked to an energy deposit in the ECAL. These photon candidates are also linked to ECAL energy deposits that are not linked to tracks identified by the silicon tracker.

But we still have some ECAL deposits that are clearly not linked to either tracks identified by the silicon tracker or photon candidates! We need to bring up the rest of the neutral particles:

: A Jet, its tracks, its “photon candidates”, its neutral hadrons, and its energy deposits in CMS’s electromagnetic calorimeter

The dotted blue lines are the “neutral hadron candidates” within this jet. Similar observations as before can be made. But since neither a photon or a neutral hadron leaves a track in the silicon tracker, how do I distinguish between them? This is were HCAL comes into play.

: A Jet, its tracks, its “photon candidates”, its neutral hadrons, and its energy deposits in CMS’s hadronic calorimeter

Now I’ve turned off the energy deposits in ECAL and turned on the deposits in HCAL (teal rectangles). I’ve also drawn a crude circle around one of the jet’s photon candidates. It clearly has no HCAL energy deposit around it, but all the dotted blue lines are linked to HCAL deposits. Now we can clearly see the difference between neutral hadrons and photon candidates; one has energy deposited in HCAL, the other doesn’t.

It might be interesting to note that some photon candidates appear to have HCAL deposits. There are two reasons for this: 1) the photon candidate isn’t a real photon (it would fail the quality requirements I mentioned above), or 2) there is a nearby hadronic particle that is actually responsible for the HCAL energy deposit.

Now Let’s add the charged hadrons into the picture as well:

: A Jet, its tracks, its “photon candidates”, its neutral hadrons, its charged hadrons, and its energy deposits in CMS’s hadronic calorimeter

These bright blue lines represent the trajectories of charged hadrons. Notice that they are also coincident with the tracks in the silicon tracker (as they should be!). These charged hadrons also link to energy deposits in HCAL. In addition, they also have a chance of depositing energy in ECAL as well:

: A Jet and its components in CMS

I’ve turned the ECAL deposits back on in the image above.

Notice the ECAL and HCAL deposits are stacked on top of each other (with ECAL appearing first). We like to do this because this gives us the full idea of the direction of energy deposition in the CMS detector. Let’s turn our view around so we can see the differences in this jet’s energy deposition:

: A jet’s calorimeter deposits in CMS (also note the curvature of the jet’s tracks!!)

: Rotated view of a jet’s calorimeter deposits in CMS

: Final view of a jet’s calorimeter deposits in CMS

So from these views we can see the amount of energy deposited around the jet’s cone.

Again, height above the wire frame corresponds to the amount of total energy deposited in a region. In some cases this energy was deposited in both the ECAL (yellow-ish rectangles) and the HCAL (teal rectangles). The height of these different rectangles corresponds to the amount of energy deposited in their respective calorimeters.

I’ve also now colored all of the jet’s constituents blue, this now is the complete jet, its a spray of particles that goes along a specific direction (shown by the black shaded cone).

For those of you wondering, this is a specific type of jet called an anti-kT particle flow jet. The algorithm, anti-kT particle flow, used to “reconstruct” this jet made use of the energy deposited in the calorimeters, the tracks in the silicon tracker, and the primary vertex (for determining tracks of neutral particles).

Some algorithms make use of only the calorimeters and the primary vertex (these are called calo-jets). But discussing the different jet algorithms is a story for another day.

Remember how I said that the scale of those calorimeter deposits was 10 GeV per meter. Let’s put that into perspective now:

: The complete jet recorded by CMS, note the intense curvature of some of the jet’s tracks!

Remember the diameter of CMS is 15 meters, so from the primary vertex to the edge of the red muon system (near my coordinate axis guide at the bottom right) is 7.5 meters. Hopefully, this gives you an idea of the amount of energy deposited in each of the calorimeter clusters.

So this is what a jet looks like! All in all this jet had 29 different particles that were used in its construction.

So when we talk about Jets here at US LHC (and the rest of Quantum Diaries) I hope you will have a much better idea of what a jet really is.

Until next time,

-Brian

For some further reading on Jets, I suggest taking a look at these older posts:

My previous post, and this one by Matthew Tamsett, both on Jet Identification
This post by Flip Tanedo, on Jet Structure
This post by Christine Nattrass, on Jet Quenching

Tags: CMS, event displays, Jets
Posted in Latest Posts | 7 Comments »

High Energy Physics Software and You!

Monday, May 23rd, 2011

Since deciding to become a high energy physicist I’ve had a much harder time answering a question often asked of scientists, “What’s the practical application.” After all, High Energy Physics is, for the most part, a basic science; meaning its long term goals are to increase our understanding of the natural world. Whereas in applied science (such as hydrogen fuel cell research) there is usually a targeted application from the get go (i.e. hydrogen powered automobiles).

When asked what’s the practical application of my research, I have a tough time answering. After all, I study experimental Quantum Chromodynamics; and a “practical application” such as the light bulb (application of electromagnetism) or the transistor (quantum mechanics) may not arise in my lifetime. But what I can say is the technologies developed to perform my research have a noticeable impact on our society (much like the benefits of the Space Program).

I thought today it might be interesting to talk about one such technology….namely the software used by high energy physicists.

Now each experiment at the LHC has its own unique software and computing environment (this is by design). I can’t speak for the other experiments, but researchers within the CMS Collaboration have created something called CMSSW (or the CMS Software frameWork). This software framework uses C++ plugins in a python based environment to analyze all experimental data taken by the CMS detector, and all simulated data created by the CMS Collaboration. However, to use CMSSW (and the software of the other LHC experiments) you must be a member of the collaboration.

But rather then discussing CMSSW, I would like to discuss something common to all LHC experiments (and available to the general public), ROOT. It is this “practical application” that I’d like to bring your attention to.

(Readers less experienced with programming languages may want to see the “Coding” section of one of my older posts for some background info).

What is ROOT?

ROOT is a object oriented software framework that uses a C++ interpreter to write scripts/macros for data analysis. There are many pre-defined classes and methods available in ROOT; these are designed to enable a user to quickly & efficiently access large amounts of data, and perform analysis. ROOT has both a command line interface and a graphical user interface, so modifications can be made either “on the fly” or by re-running a script/macro.

ROOT is very powerful, and it is possible to incorporate other libraries (such as the C++ Standard Template Library & others) into ROOT scripts/programs.

But, programming jargon aside, what can you actually do with ROOT? Simple answer: lots.

ROOT is perfect for creating graphics, namely graphs & plots of interesting data. But it can also be used to perform more useful tasks, such as numeric integration or differentiation. ROOT also has several aspects from linear algebra built in (so you can do matrix multiplication/addition with it). ROOT even enables a user to perform high level custom curve fits.

In fact, in some ways ROOT is very similar to programs like Mathematica & MATLAB.

However, ROOT has a distinct advantage over these products, its free. ROOT can be downloaded by anyone; and has a rather detailed User’s Guide, and set of Tutorials/HowTo’s that can show new users how to perform a specific task.

But, enough boasting, let’s show some examples so you can get a feel for what ROOT can do! I’m going to show some simple commands and their outputs, if you’d like to try them out yourself feel free. My goal with this post is to get you interested in ROOT, not necessarily show you how to use it (guides such as that already exist! See links above!).

Example: Visualization

Suppose I was interested in observing the jet topology (or how the jets appear in space) in a particular proton-proton collision event. There are several ways I could do this. The first of which is to make what’s called a “lego plot.” In a lego plot, I place the jet in space based on its angular coordinates; the polar angle, θ, and the azimuthal angle, Φ; and then each point is “weighted” by its momentum component in the xy-plane (termed p_T). To see how these angles & the xy-plane are defined in CMS, see the diagram below:

But in high energy physics θ is not very useful; instead we use a related variable called η, which is proportional to θ (η = 0 is still on the positive z-axis).

So in a lego plot I take all the jets in my event, and I plot them by their eta & phi values. This is very simple to do in ROOT, and for this task I’m going to make a two dimensional histogram:

TH2D *LegoPlot = new TH2D(“LegoPlot”,”Jet Topology”);

LegoPlot->Fill( Jet.eta(), Jet.phi(), Jet.pt() );

Where the first line creates an instance of a two dimensional histogram object, and the second line stores the jet’s η, Φ, & p_T as an (x,y) point; but let’s call this an (η,φ) point instead. This is literally all I need to type. Of course this is just for one jet, I could put the second line within a loop structure so that I could enter all my jets in my event.

To visualize this output, I simply need to type:

LegoPlot->Draw(“lego2”);

Where “lego2” is an option of the Draw command. The output of this command is then:

Three Jet Event in CMS

Here ROOT will automatically open up a new window, and draw the plot for us…it even gave us some statistics regarding the plot (upper right corner).

And all this was done with one line of code!

But, unfortunately the plot isn’t labeled, so we can’t make sense of it quiet yet. We could use the graphical interface to add a label, or we can use the command line approach. The GUI is great, but if I have to make this plot over and over again from multiple data files; I’m going to get really tired of using the GUI each time. So instead, I could use the command line interface and write a script to have ROOT do this for me. The commands I would use are:

LegoPlot->SetXTitle(“#eta”);

LegoPlot->SetYTitle(“#phi (Radians)”);

LegoPlot->SetZTitle(“p_{T} (GeV/c)”);

Then upon running my script ROOT would automatically add these titles to the plot.

The use of “#” signs in the above lines let ROOT know that I don’t just want the axis to say “eta” but that I want the axis to display the symbol “η.” The underscore with the {} brackets inform ROOT that I also want a subscript (superscripts are done with ^{ …text….} ). So with a few lines of code in the ROOT framework I have not only stored data, but shown it graphically.

I never had to compile anything, and I didn’t need to spend time building my GUI!

The final plot result is shown here:

Thee Jet Event in CMS, with Labels!

But this η-Φ plot really hasn’t helped me visualize the jets in 3D; after all CMS is a giant Cylinder. The above plot would be if I took a pair of scissors to the cylinder (starting at the x-axis) and cut down a line parallel to the z-axis. This would then “un-roll” the cylinder into the flat plane above.

But what if I wanted to view this plot in actual “η-Φ” space? Well ROOT can do that too, and in one line of code!

LegoPlot->Draw(“psrlego2”)

The familiar “lego2” is still there, but now I’ve added “psr” to the options of the draw command. ROOT understands psr to mean 3D pseudorapidity coordinates. The output of this options is shown here:

Three Jet Event in CMS, in eta-phi space

Again, in a simple command I’ve been able to do some very intense plotting. Of course these are just a few brief examples. I am by no means trying to give an all inclusive guide to how to use ROOT. As I’ve mentioned, those already exist (see the user’s guide, tutorials & how-to’s I’ve linked above).

Example: Curve Fitting

I think one of the most challenging things in all of science is curve fitting. The reason I believe it is challenging is two-fold: first, you have to know what kind of curves would do well in describing your data; second, curve-fitting software is usually very expensive!

However, as I mentioned, ROOT is free! And can perform very powerful curve-fitting techniques very simply.

Suppose I’ve made a histogram of an observable, and kept track of the number of counts per each value of my observable (this is my measurement). Let’s say it looks like this:

Now let’s say I’m interested fitting a curve to this data. Ordinary office programs such as Open Office Spreadsheet or Microsoft Excel have the ability to do simple fits such as polynomials, or simple exponentials. But beyond a correlation coefficient, I’m not going to get much out of a fit from one of those programs. I also don’t really get much functionality from them either.

Let me elaborate further on that part. The above graph, it has a horizontal asymptote at one. Let’s say I want to incorporate this behavior into my fit. Well I happen to know that the function:

Has this asymptotic behavior. This is a relatively simple function, but I couldn’t use the “out-of-the box” Microsoft Excel for this fit.

But, the above function is just to simplistic, it doesn’t allow for any “shifts” or changes in the data from that expression. Instead, let’s toss in a few parameters, called A & B; these parameters will give us some more flexibility in our fitting procedure:

This is again simplistic, but staying simple is usually a good rule of thumb in science.

But we’ve settled on a function to fit to our data. How do we implement it in ROOT? Again, it is very simplistic, we use the function class already available in the ROOT framework:

TF1 *func = new TF1(“func”,”1.0 – exp( [0] * x [1] )”, 0, 40);

Here, I’ve setup a new function. The first word in quotes is my function’s name, “func.” The second set of quotes is the mathematical expression I want the function to use; with [0] and [1] being our parameters A & B. Then the last two numbers are the range of the x-variable that the function will be defined for.

This should immediately illustrate the power of ROOT. In one line, I can tell ROOT symbolically what mathematical expression I want it to use for fitting. I can construct any function imaginable, with any number of parameters, just by typing it out to ROOT. ROOT will even recognize trigonometric functions, along with others. I can even construct numeric functions (but this takes more code then one line).

Now to perform the fit I just tell the histogram above (call it “Histo”) that I want to fit a function to it. This is done by:

Histo->Fit(func,””,””,3,40);

The quotes in the above expression tell ROOT how to perform the fit. Right now there’s nothing in the quotes, so ROOT will just use its default fitting method (chi-squared minimization), in the range of x equals 3 to 40.

Executing this command causes ROOT to perform the fit and spit back the values for my parameters A & B along with their errors:

Fit Output

Here the parameters [0] and [1] are labeled as “p0” and “p1.” There is a column for their values (“VALUE”), and a column for their errors (“ERROR”). Up at the top I can see that the fit converged, and that ROOT took 86 attempts/iterations in its fitting process.

The “Histo->Fit….” command will also plot the original histogram with the fit overlaid, as shown here:

Result of Fit

ROOT has also the fit parameters in the statistics box. From the Χ²/ndf we see that the fit wasn’t a very good fit mathematically; but we weren’t really trying here either. With a better fit function, and selecting a more advanced fitting procedure we can get Χ²/ndf ~ 1.0 (exactly what we want to have!).

In Closing

My goal with this post was to illustrate a product that has come about because of High Energy Physics research, and show that it could be beneficial for the rest of society. Hopefully this will spark your interest in ROOT for science/engineering/mathematics applications. There is an extensive ROOT community and support system that you may turn to if you decide to learn ROOT and encounter problems/questions.

I would highly recommend ROOT for any of our readers who are students with technical majors (at all levels).

Until next time,

-Brian

Tags: CMS, ROOT, software
Posted in Latest Posts | 5 Comments »

To B or not to Bbar: b-Jet Identification

Thursday, May 12th, 2011

Well its been longer then usual since my last post. This past weekend was commencement at my host institution; and I spent it with my friends who graduated with their Master’s degrees (myself included) and family who came down to visit.

But today I’d like to talk about something that is crucial to my own research, B-Tagging. Or, the experimental tools we (as high energy physicists) use to identify b-jets. Here b stands for the “beauty” or “bottom” quark; these are two interchangeable terms for the same particle.

Importance of B-Tagging

But first, what’s the big deal about B-Tagging?

Well, many current Standard Model physics process under study at the LHC have a b and an anti-b quark (termed bbar or simply b) in the final state.

To understand what “final state” means, let’s look at an example. Suppose in a proton-proton collision a top quark, t, and an anti-top quark, t, are produced (this is called top-quark pair, tt, production). Well the top quark decays to a W boson, and another quark, q, ~10% of the time [1]. i.e.

t → W ⁺ q → l⁺v q

Here: the W⁺ boson has decayed leptonically into a lepton, l, a neutrino, v; and a quark, q. The quark may be either a d, s, or b quark. The case for anti-top quark decay, t, is shown here:

t → W ^– q → l^–v q

Where q = d, s, or b.

Then the final state for this event is two oppositely charged leptons, two neutrinos, a quark, and an anti-quark (These quarks will turn into jets as they cannot exist freely, more information on this below). But when looking for top-quark pair production events in a collider, it’s easiest to find them if you look for events containing two b-jets along with the charge leptons and neutrinos.

In addition to top-quark pair production, the Higgs Boson is theorized to decay into a bb final state; which in turn form two b-jets (see one of my older posts here, or one of Flip Tanedo’s posts here for more details regarding the Higgs Boson).

But b-jets don’t just don’t come from Standard Model processes, many new physics searches (such as supersymmetric searches) have bb final states.

With this in mind, it is of paramount importance to be able to find and identify b-jets. But to do this we first need to understand the properties of the b quark itself; or more importantly b-Hadrons as these are what we actually observe.

Beautiful Hadrons

B-Hadrons are rather unique in elementary particle physics. They offer us a chance to study so much; we are able to use them to investigate topics from Quantum Chromodynamics, to CP-Violation, and even physics beyond the Standard Model. Simply put, B-Hadrons have got it going on!

They are very heavy particles, with rest masses of approximately 5-10 GeV/c²; or roughly five to ten times the proton’s rest mass [2].

B-Hadrons are also very “long lived” particles, with mean life-times of approximately 1.6 pico-seconds, or 1.6·10^-12 seconds. For comparison, the π⁰ meson has a lifetime of roughly 8·10^-17 seconds [2]; and the top quark has an even shorter lifetime of ~10^-23 seconds. So B-Hadrons are very long lived indeed. In fact, because of this long life-time a B-Hadron has a cτ of approximately 480-500 micro-meters (τ being the proper time, or the B-Hadron’s mean life-time; and c is the speed of light). Putting this into more tangible terms, a B-Hadron will travel roughly half a millimeter before it decays. For comparison, the π⁰ meson has a cτ of only 25 nano-meters (2.5·10^-8meters).

In addition to their long life-time and large mass, a B-Hadron will produce five charged particles per decay (on average)! In comparison a Δ⁺⁺ (a light baryon made of u quarks) will produce only 3 charge particles per decay; and a π⁺ (a light meson made of a u and d) will produce merely a single charged particle per decay.

Also, when a B-Hadrons decays, there is a 10% chance that a lepton will be produced during the decay process.

In summary, B-Hadrons have:

Large mass
A long life-time
Large cτ
High number of charged particles per decay
Chance of leptonic decay

But what does this have to do with B-Tagging? For this we must ask ourselves how these properties listed above would show themselves within our detectors.

Experimental Signatures: B-Tagging

Hadrons will exist in clustered collimated groups within a detector, known as jets. Thus we say jets are due to “hadronic activity.”

But what causes this clustering/jet structure to occure? Well when protons collide in the LHC, a quark or gluon may “escape” the proton it was originally found in. But quarks/gluons cannot exist freely in nature! Thus quarks/anti-quarks use some of their kinetic energy to pull other quarks/antiquarks out of the vacuum to form hadrons (this is called hadronization, see one of Flip’s old posts here for more info). And gluons “split” into a quark an anti-quark pair. The produce quark and anti-quark in this “gluon-splitting” will then in turn undergo hadronization process.

But this all occurs within a jet!

So these B-Hadrons that we have been talking about are going to be found within jets. So b-jets must have B-Hadrons inside them (hence the name)!

Now here is where our B-Hadron properties start to come into play.

Since a B-Hadron has a long lifetime, and travels some distance before decaying, we are able to look for what’s called a secondary vertex (SV). A SV is a spot that new particles spew from because of the decay of a heavier particle (creating tracks if these new particles have an electric charge). So if a jet has a SV it is much more likely to be a b-jet.

To get an idea what an SV might look like in our detectors take a look at this image uploaded by Anna Phan. Here a B-Hadron (B_s) has decayed into a charmed hadron (D⁺) and a muon (μ); the charmed hadron has then decayed into three other particles (hence a total of five charged particles were produced due to the B-Hadron’s decay!).

Notice how these particles are collimated and clustered together, i.e. this is a jet; and in this case it is a b-jet!

Also, because many charged particles are produced by a decaying B-Hadron, a jet that has a large number of tracks within it is more likely to be a b-jet. So these four tracks that are produced after the SV (image I linked above) gave experimentalists in the LHCb Collaboration the ability to determine that this was a b-jet. Had this jet come from say, a pion or a Δ⁺⁺, there may have only been one or two tracks, and it would not be tagged as a b-jet (and rightly so!).

Finally, this picture has also shown the B-Hadron having a lepton (the muon) in its decay chain. As a result, experimentalists look for jets that have nearby leptons when looking for b-jets.

So in summary, we as experimentalists in our B-Tagging efforts combine as much of this information as possible when searching for b-jets. When we want to determine if a jet is a b-jet, we look to see if it has one or more of the following things:

A secondary vertex
A large number of tracks within them
A nearby lepton

So from our list of B-Hadron properties we were able to construct a list of what to look for when attempting to perform B-Tagging.

But that wraps up our discussion for today. There are many more levels to this then I’ve illustrated here. If you are interested in more details, simply post below and I’ll try to answer your questions!

One last piece of information, creating the tools to perform B-Tagging is not something that one person alone can do. For example, CMS has a very large staff of researchers (over 100) who focus directly on developing techniques these techniques that I spoke on briefly. Needless to say, without the researchers who develop these B-Tagging techniques, my own research would be impossible!

But until next time,

-Brian

References

[1] Particle Data Group, http://pdg.lbl.gov/2010/tables/rpp2010-sum-quarks.pdf, May 11^th 2011.

[2] Particle Data Group, http://pdg.lbl.gov/2010/tables/rpp2010-sum-mesons.pdf, Math 11^th 2011.

Tags: B-Physics, CMS, Jets
Posted in Latest Posts | 15 Comments »

A Day in the Life: Cross-Sections

Sunday, May 1st, 2011

Hello again!

I thought I might take some time to describe what an experimental particle physicist actually does on a day-to-day basis.

I remember when I was an undergraduate studying physics, I found particle physics so fascinating. It was this high tech world that seemed so glamorous. But, at the time, I had no idea what a particle physicist did! Big shiny detectors, and billion dollar machines were all that I knew about!

But, now that I’ve spent two years in the field, perhaps I can give you an idea of what happens “behind the scenes.” I’m going to talk about cross-sections, and how we go about finding them.

(If you are unfamiliar with what a cross-section is, then take a look at these nice posts by Aidan Randle-Conde and Seth Zenz found here, and here, respectively.)

The Bane of My Existence: Coding

So one of the things I’ve gotten far better at over the years has been computer programming. Sadly, I purposefully avoided almost all computer-programming classes during my undergraduate studies. This was a horrifically stupid idea in retrospect. And if anyone reading this is interested in pursuing a career in a math, science, or an engineering related discipline; my suggestion to you is learn to code before you’re expected to. It will do wonders for your career.

Moving on though, long gone are the days were particle physics experiments relied on photographic plates and cloud chambers. Nowadays our detectors record everything electronically.

The detectors spit out an electric signal. Then we perform what is called “reconstruction” on these signals (using computer algorithms), to make physics objects (observable particles, like photons, electrons, muons, jets, etc…).

Now, if you are a computer programmer, you might know where I’m going with this discussion. If not a bit of some background info is required. There is something called object-oriented programming (OOP). In OOP you make what is called a class. A class is like a template, which you use make objects.

Imagine I own a factory that makes cars. Somewhere in my factory are the blue prints for the cars I produce. Well a blueprint is what a class is in OOP. Each blueprint is a template for a car, just as each class is a template for an object. So we see that in this analogy, a car represents an object.

Now classes have what are called methods and data members. On the blueprint for the 2012 Ford Mustang there is a data member for the car’s color, and there is a method for what type of transmission the car will be manufactured with. So data members store information (car’s color), and methods perform actions on objects (manufacture with transmission type X).

But what do classes and methods have to do with High Energy Physics? Well, physicists use classes present in an OOP language to store and analyze our data. In CMS we use two OOP languages to accomplish this; they are python and C++; and we make our own custom classes to store our data.

So what types of classes do we have? Well, there are classes for all physics objects (electron, a muon, a jet, etc…), detector pieces, and various other things. In fact we’ve created an entire software framework to perform our research.

But, lets take the electron class as an example. Because of these classes, all electrons in our data have the same structure. The way they are accessed is the same regardless of the electron; and all the information about a particular electron is stored/retrieved in the same way (via the methods & data members of the electron class).

This is a very good thing, because a physicist may have to look at hundreds of thousands of electrons in the course of their research; so having a standardized way to access information is beneficial.

So in summary, to do research and analyze data we write code, and we run our analysis code on super-computing clusters around the world.

Event Selection

Okay, now we know we need to write code to get anywhere, but what do we do from there?

Well we need to decide on what type of physics we want to study. And how to find that physics in the data.

In 2010, the CMS detector recorded 43 inverse picobarns of data. Now, there are approximately 7 * 10¹⁰ (or 70 billion) proton-proton collisions in one inverse pico-barn. This makes for a total of 3 trillion recorded proton-proton collision events for 2010.

That’s a lot of data…and not all of it is going to be useful to a physicist. But as they say, one person’s trash is another’s treasure.

For example, in my own analysis I look for low energy muons inside jets because this helps me find b-Jets in an event. But an electro-weak physicist looking for W or Z’s decaying to muons is going to think the events that I use are garbage. My muons are low energy whereas an electro-weak physicist needs high energy muons. My muons are within jets whereas an electroweak physicist needs muons that are isolated (nothing else around them). So while my data is perfect for the physics I’m trying to do, it is worthless to an electroweak physicist.

With this in mind we as physicists make checklists of what an event needs for it to be considered useful. This type of checklist is called a pre-selection, and it will include what type of data acquisition trigger was used; and a list of physics objects that must be present (and restrictions on them) in the event.

After an event has been tagged as being possibly useful to us, we investigate it further using another checklist, called a full event-selection.

For example, I might be interested in studying B-Physics, and I want to look at the correlations between two B-Hadrons produced in an event.

My pre-selection check-list for this might be:

Jets detected by the High Level Trigger
Presence of a Secondary Vertex in the event

My Event Selection Checklist might then be:

The most energetic jet in the event must have an energy above threshold X
The invariant mass of the secondary vertex must be above some value Y.

In case you are wondering, a secondary vertex is a point at which a heavy particle decayed within the detector, this occurs away from the primary vertex (point at which the protons collided). The invariant mass of the secondary vertex is found by summing the invariant masses of all of the products that the heavy particle decayed into.

So in summary, we make checklists of what we are looking for; and then implement this into our computer code.

Efficiencies

Finally we need to measure the efficiency of our selection process, or what percent of events that are created do we actually select. We use a combination of real collision data and simulated data to make this estimation. Then our efficiency is a measure of everything from the detectors ability to record the collision, our reconstruction process, and up to our specific selection techniques listed above.

The reason we need to measure this efficiency is that we are, more often then not, interested in performing inclusive measurements in physics. Meaning, I want to study every single proton-proton collision that could give insight into my physics process of interest (i.e all events in which two B-Hadrons were produced).

The problem is, I could never possibly study all such collisions. For one, we are colliding protons every 50 nano-seconds at the LHC currently. We design our trigger system to only capture the most interesting events, and this sometimes causes us to purposefully drop a few here and there. But this is a story for another time, and Aidan has done a good job describing this already in this post.

Anyway, so we convert our measurements back to this “inclusive” case. This conversion allows us to say, “well if we were able to record all possible events, this is what our results would look like.”

But how is this accomplished? Well, one way to do this is restrict ourselves to the point of which our data acquisition triggers have an efficiency of greater then 99%.

Courtesy of the CMS Collaboration

Here is a plot that shows the efficiency to record an event via several single jet triggers available in CMS. Three triggers are plotted here, they each have a minimum energy/momentum threshold to detect a jet.

As an example, if in a proton-proton collision, a jet is produced with a momentum of 50 GeV/c; then this event will be recorded:

99% of the time by the trigger represented by the green line
50% of the time by the trigger represented by the blue line
0% of the time by the trigger represented by the red line (The Jet’s momentum isn’t high enough for that trigger!).

So by playing with the jet energy thresholds in our Event Selection above, I can ensure that my detector will inclusively record all events in this region of phase space (99% or higher chance to record an event).

But as I said earlier this is just one way we can transform our measurements into inclusive measurements. There are usually other steps that must also be done to get back to the inclusive case.

Experimental Cross-Section

Now that I’ve selected my events and physics objects within those events; and determined the efficiency of this process, I’m ready to make my measurement.

This part of the process takes much less time then our previous two steps. In fact, it may take months for physicists to write our analysis code, and become confident in our selection techniques (rigorous investigation is required for this part).

Then, to determine an inclusive cross-section with respect to some quantity (say the angle between two B-Hadrons), I make a histogram.

The angle between two B-Hadrons can be between 0 and 180 degrees. So the x-axis of this histogram is in degrees, and is binned into different regions. The y-axis is then counts, or number of times I observed a B-Hadron pair with angle φ between them.

Next, I need to divide by the number of counts in each bin of my histogram by three things:

The integrated luminosity of my data sample (see Aidan’s post “What the L!?”), this makes the Y-Axis go from counts to units of inverse barn (or more appropriately, inverse picobarn).
My selection efficiency, this takes my measurement to the inclusive case
The width of each bin, this puts my cross-section purely in units of inverse barn (rather then inverse barn times degrees)

And finally, I’m left with a cross-section:

: Image Courtesy of the CMS Collaboration. Here the data points are shown in black, and the theoretical prediction is shown in green.

I’m now left with the differential scattering cross-section, for the production of 2 B-Hadrons, with respect to the angle between the two B-Hadrons.

Three cross-sections are actually plotted here. Each of them corresponds to one of the triggers in our efficiency graph above. The researchers who made this plot also multiplied two of the distributions by a factor of 2 and a factor of 4 (as shown in the legend). This was done so the three curves wouldn’t fall on top of each other, and other scientists could interpret the data in an easier fashion.

This plot tells us that, at LHC Energies, B-Hadron pairs are more likely to be produced with small angles between them (the data points near the zero region on the x-axis are higher then the other points). This is because a process called gluon splitting (a gluon splits into a quark and anti-quark) occurs more often then other processes. Due to conservation of momentum, the angle between the quark/anti-quark that the gluon split into is very small. But this is also a lengthy discussion for another time!

But that’s how we experimentally measure cross-sections, from start to finish. We need to: write computer code, make a checklists of what we are looking for, determine the efficiency of our selection technique, and then make our measurement.

So hopefully this gives you an idea as to what an experimental particle physicists actually does on a day to day basis. This is by no means all we do, measuring cross-sections is only one part of the research being done at the LHC. I could not hope to, in a single post, cover all of our research activities.

Until next time,

-Brian

Tags: CMS, Cross-Sections, life at the lab
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The CERN Accelerator Complex

Sunday, April 24th, 2011

With all the buzz this past week regarding the breaking of the world instantaneous luminosity record, I thought it might be interesting for our readers to get an idea of how we as physicists achieved this goal.

Namely, how do we accelerate particles?

(This may be a review for some of our veteran readers due to this older post by Regina)

The Physics of Acceleration

Firstly, physicists rely on a principle many of us learn in our introductory physics courses, the Lorentz Force Law. This result, from classical electromagnetism, states that a charged particle in the presence of external electric and/or magnetic fields will experience a force. The direction and magnitude (how strong) of the force depends on the sign of the particle’s electric charge and its velocity (or direction its moving, and with what speed).

So how does this relate to accelerators? Accelerators use radio frequency cavities to accelerate particles. A cavity has several conductors that are hooked up to an alternating current source. Between conductors there is empty space, but this space is spanned by a uniform electric field. This field will accelerate a particle in a specific direction (again, depending on the sign of the particle’s electric charge). The trick is to flip this current source such that as a charged particle goes through a succession of cavities it continues to accelerate, rather than be slowed down at various points.

A cool Java Applet that will help you visualize this acceleration process via radio frequency cavities can be found here, courtesy of CERN.

Now that’s the electric field portion of the Lorentz Force Law, what about the magnetic? Well, magnetic fields are closed circular loops, as you get farther and farther away from their source the radii of these loops continually increases. Whereas electric fields are straight lines that extend out to infinity (and never intersect) in all directions from their source. This makes the physics of magnetic fields very different from that of electric fields. We can use magnetic fields to bend the track (or path) of charged particles. A nice demonstration of this can be found here (or any of the other thousands of hits I got for Googling “Cathode Ray Tube + YouTube”).

Imagine, if you will, a beam of light; you can focus the beam (make it smaller) by using a glass lens, you can also change the direction of the beam using a simple mirror. Now, the LHC ring uses what are called dipole and quadropole magnets to steer and focus the beam. If you combine the effects of these magnets you can make what is called a magnetic lens, or more broadly termed “Magnetic Optics.” In fact, the LHC’s magnetic optics currently focus the beam to a diameter of ~90 micro-meters (the diameter of a human hair is ~100 micro-meters, although it varies from person to person, and where on the body the hair is taken from). However, the magnetic optics system was designed to focus the beam to a diameter of ~33 micro-meters.

In fact, the LHC uses 1232 dipole magnets, and 506 quadrupole magnets. These magnets have a peak magnetic field of 8.3 Tesla, or 100,000 times stronger than Earth’s magnetic field. An example of the typical magnetic field emitted by the dipole magnets of the LHC ring is shown here [1]:

Image courtesy of CERN

The colored portions of the diagram indicate the magnetic flux, or the amount of magnetic field passing through a given area. Whereas the arrows indicate the direction of the magnetic field. The two circles (in blue) in the center of the diagram indicate the beam pipes for beams one and two. Notice how the arrows (direction of the magnetic field) point in opposite directions! This allows CERN Accelerator physicists to control two counter-rotating beams of protons in the same beam pipe (Excellent Question John Wells)!

Thus, accelerator physicists at CERN use electric fields to accelerate the LHC proton/lead-ion beams and the magnetic fields to steer and squeeze these beams (Also, these “magnetic optics” systems are responsible for “Lumi Leveling” discussed by Anna Phan earlier this week).

However, this isn’t the complete story, things like length contraction, and synchrotron radiation affect the acceleration process, and design of our accelerators. But these are stories best left for another time.

The Accelerator Complex

But where does this process start? Well, to answer this let’s start off with the schematic of this system:

Image courtesy of CERN

One of our readers (thanks GP!) has given us this helpful link that visualizes the acceleration process at the LHC (however, when this video was made, the LHC was going to be operating at design specifications…but more on that later).

A proton’s journey starts in a tank of research grade hydrogen gas (impurities are measured in parts per million, or parts per billion). We first take molecular hydrogen (a diatomic molecule for those of you keeping track) and break it down into atomic hydrogen (individual atoms). Next, we strip hydrogen’s lone electron from the atom (0:00 in the video linked above). We are now left with a sample of pure protons. These protons are then passed into the LINear ACcelerator 2 (LINAC2, 0:50 in the video linked above), which is the tiny purple line in the bottom middle of the above figure.

The LINAC 2 then accelerates these protons to an energy of 50 MeV, or to a 31.4% percent of the speed of light [2]. The “M” stands for mega-, or times one million. The “eV” stands for electron-volts, which is the conventional unit of high energy physics. But what is an electron-volt, and how does it relate to everyday life? Well, for that answer, Christine Nattrass has done such a good job comparing the electron-volt to a chocolate bar, that any description I could give pales in comparison to hers.

Moving right along, now thanks to special relativity, we know that as objects approach the speed of light, they “gain mass.” This is because energy and mass are equivalent currencies in physics. An object at rest has a specific mass, and a specific energy. But when the object is in motion, it has a kinetic energy associated with it. The faster the object is moving, the more kinetic energy, and thus the more mass it has. At 31.4% the speed of light, a proton’s mass is ~1.05 times its rest mass (or the proton’s mass when it is not moving).

So this is a cruel fact of nature. As objects increase in speed, it becomes increasingly more difficult to accelerate them further! This is a direct result of Newton’s Second Law. If a force is applied to a light object (one with little mass) it will accelerate very rapidly; however, the same force applied to a massive object will cause a very small acceleration.

Now at an energy of 50 MeV, travelling at 31.4% the speed of light, and with a mass of 1.05 times its rest mass, the protons are injected into the Proton Synchrotron (PS) Booster (1:07 in the video). This is the ellipse, labeled BOOSTER, in the diagram above. The PS Booster then accelerates the protons to an energy of 1.4 GeV (where the “G” stands for giga- or a billion times!), and a velocity that is 91.6% the speed of light [2]. The proton’s mass is now ~2.49 times its rest mass.

The PS Booster then feeds into the Proton Synchrotron (labeled as PS above, see 2:03 in video), which was CERN’s first synchrotron (and was brought online in November of 1959). The PS then further accelerates the protons to an energy of 25 GeV, and a velocity that is 99.93% the speed of light [2]. The proton’s mass is now ~26.73 times its rest mass! Wait, WHAT!?

At 31.4% the speed of light, the proton’s mass has barely changed from its rest mass. Then at 91.6% the speed of light (roughly three times the previous speed), the proton’s mass was only two and a half times its rest mass. Now, we increased speed by barely 8%, and the proton’s mass was increase by a factor of 10!?

This comes back to the statement earlier, objects become increasingly more difficult to accelerate the faster they are moving. But this is clearly a non-linear affect. To get an idea of what this looks like mathematically, take a look at this link here [3]. In this plot, the Y-axis is in multiples of rest mass (or Energy), and the x-axis is velocity, in multiples of the speed of light, c. The red line is this relativistic effect that we are seeing, as we go from ~91% to 99% the speed of light, the mass increases gigantically!

But back to the proton’s journey, the PS injects the protons into the Super Proton Synchrotron (names in high energy physics are either very generic, and bland, or very outlandish, e.g. matter can be charming). The Super Proton Synchrotron (SPS, also labeled as such in above diagram, 3:10 in video above) came online in 1976, and it was in 1983 that the W and Z bosons (mediators of the weak nuclear force) were discovered when the SPS was colliding protons with anti-protons. In today’s world however, the SPS accelerates protons to an energy of 450 GeV, with a velocity of 99.9998% the speed of light [2]. The mass of the proton is now ~500 times its rest mass.

The SPS then injects the proton beams directly into the Large Hadron Collider. This occurs at 3:35 in video linked above, however, when this video was recorded the LHC was operating at design energy, with each proton having an energy of 7 TeV (“T” for tera-, a million million times). However, presently the LHC accelerates the proton to half of the design energy, and a velocity of 99.9999964% the speed of light. The protons are then made to collide in the heart of the detectors. At this point the protons have a mass that is ~3730 times their rest mass!

So, the breaking of the world instantaneous luminosity record was not the result of one single instrument, but the combined might of CERN’s full accelerator complex, and in no small part by the magnetic optics systems in these accelerators (I realize I haven’t gone into much detail regarding this, my goal was simply to introduce you to the acceleration process that our beams undergo before collisions).

Until next time,

-Brian

References:

[1] CERN, “LHC Design Report,” https://ab-div.web.cern.ch/ab-div/Publications/LHC-DesignReport.html

[2] CERN, “CERN faq: The LHC Guide,” http://cdsweb.cern.ch/record/1165534/files/CERN-Brochure-2009-003-Eng.pdf

[3] School of Physics, University of Southern Wales, Sydney Australia, http://www.phys.unsw.edu.au/einsteinlight/jw/module5_equations.htm

Tags: accelerator, luminosity
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First CMS Results on WW Production and Higgs Search

Sunday, April 17th, 2011

For all our electro-weak enthusiasts, this past week has been a very exciting time. The CMS Collaboration has just published our first study measuring the W⁺W^– production cross section at 7 TeV. This study, titled “Measurement of W⁺W^– Production and Search for the Higgs Boson in pp Collisions at sqrt(s) = 7 TeV,” is available on arXiv.org and has been accepted for publication by Physics Letters B (a peer-review journal for those who are wondering).

But before we delve into the paper proper, let’s take a moment and ask ourselves: “Why study W⁺W^–production at all?”

For this answer, let’s take a page out of one of Flip Tanedo’s posts, “An Idiosyncratic Introduction to the Higgs,” and study the Higg’s Branching Ratios (or the percent of Higgs particles decaying by method X out of all possible decays Y). Now one question you might be asking is: “Do particles really decay in more then one way?”

The answer is, yes. The name of the game is that heavy particles always decay into lighter particles, unless a conservation law prevents it. And particles will decay by different methods based on probability; it’s all random and up to chance. However, some decay methods for a particle are more likely then others. Looking at the plot of the Branching Ratio for the Higgs boson (which I took from Flip), the curves that are above everything else in the plot represent the decay methods that are more likely then the others (So the Branching Ratio is also a statement about probability!).

The Higgs, being a theoretically massive particle (since we have yet to observe it in a collider), can decay in numerous ways. In the plot below, the possible ways the Higgs can decay are:

A quark an anti-quark (b and the b with a bar over it; c and the c with a bar over it).
Two W bosons (with opposite electric charged because the Higgs has zero electric charge).
Two tau (ττ) leptons (with opposite electric charge).
Two gluons (the gg symbol).
Two Z bosons (the Z is also electrically neutral).
Two photons (γγ)
A Z and a photon

But, since the Higgs hasn’t been found yet experimentally, physicists are unsure of its actual mass (and thus what it will decay into). The theory does give us clues though (as do other experiments, more on this later).

But how do particle physicists look for a new particle? One way to find them is to search for peaks in a mass distribution.

Now since energy and mass are related, the more energetic an object is, the more mass it has. This doesn’t really matter in our everyday lives, because the increase is very, very small; but if you’re a sub-atomic particle (or an atomic scale particle) it matters a lot! As an example, when protons are accelerated in the LHC, they become several thousand times more massive to when they are at rest!

But how do you make a mass distribution? Well, physicists take two objects (say a W⁺W^–, or a μ⁺μ^–) and look at the sum of their masses. On the x-axis you plot the mass of the pair, and on the y-axis you plot the number of times you found a pair with that mass value. Here is an example of what you would get for a pair of muons (μ⁺μ^–):

Courtsey of the CMS Collaboration, arXiv:1012.5545v1, 26 Dec 2010

So in this plot of “Events” vs. “Muon Pair (μ⁺μ^–) Mass” (read Y vs. X), we see three peaks! These peaks correspond to three different mesons (a meson is a class of particles made up of a quark and anti-quark); in order they are the Υ(1S), Υ(2S), and Υ(3S). Sadly in particle physics we started to run out of symbols. It is common now to name particles based on how the quarks bind together to form the particle, hence the (1S), (2S) and (3S) after the symbol “Υ”. These represent three different “bound-states” (and thus three different particles) of the quarks making up the Upsilon (“Υ”).

Anyway…

Now back to our Branching Ratio plot above. Notice how the W⁺W^–line is above all the other lines for masses greater than ~130 GeV/c². This means that the Higgs has a higher probability of decaying into a W⁺W^– pair for this region (mass > 130 GeV/c²)! Therefore, if you’re an experimentalist looking to find the Higgs, one of the best places to look is in events with a W⁺W^–pair coming out of the proton-proton collision!!!

Perhaps its also interesting to take a look at the current constraints placed on the Higgs mass. The LHC’s ancestor, the Large Electron Positron (LEP) Collider, has placed a lower limit on the Standard Model (SM) Higgs Boson mass of 114.4 GeV/c² with a 95% Confidence Level (C.L.). Previous precision electroweak measurements have constrained the SM Higgs mass to be less than 185 GeV/c² (95% C.L.). And the US’s Tevatron Collider has excluded the mass range of 158-175 GeV/c² (95% C.L.). In summary, the current unexplored regions of the SM Higgs mass are 114.4-158 GeV/c² and 175-185 GeV/c². Or more precisely, if the SM Higgs boson does exist, then it will most likely have a mass between 114.4-158 GeV/c² or 175-185 GeV/c^2, and for some portions of these ranges the Higgs will decay over 90% of the time to a W⁺W^– Pair!!!

As a note on book keeping, this study used all of the data collected by the CMS Detector in 2010!

So, what did my colleagues in the electro-weak sector of CMS look for? Since a W will decay into a charged lepton and the corresponding lepton-neutrino, (i.e. W^± → l^±v_l); CMS Physicists looked for events containing e⁺e^–, μ⁺μ^–, e⁺μ- (or e^–μ⁺) pairs which have a large component of their momentum in the plane perpendicular to the two proton beams. In addition, CMS Physicists also looked for events containing large missing transverse energy.

Since two neutrinos are present in these W⁺W^–events; and the CMS Detector cannot detect neutrinos directly (they just interact too weakly!), physicists must infer their presence by looking for this “missing transverse energy”.

But what is missing transverse energy? To measure missing transverse energy, we look at the energy coming out in all directions in the transverse plane, the plane perpendicular to the beam pipe where the protons collide. If the energy going out in one direction does not balance the energy going out in the opposite direction, we know that a particle escaped detection.

Or more simply, Ta-da, a neutrino went that-a-way. This is also how we would detect other particles that do not interact with matter in an ordinary way.

Now that’s the basics of Event Selection, the full details can be found in section 3 of the paper (and if anyone has any questions I will try to answer them!), but let’s move on for now.

CMS Researchers found 13 events total, in which a W⁺W^–pair was produced (this is in agreement with simulation, where 13.5 events where found). Now, let’s take a moment to ponder this. Researchers looked at all of the data from 2010, and only found 13 events! This shows that W⁺W^–production is an incredibly rare process!

Now, for some results! Experimentalists have found the W⁺W^– production cross-section at a center of mass energy of 7 TeV in proton-proton collisions to be σ = 41.1 ± 15.3 ± 5.8 ± 4.5 pico-barn (pb, for an idea of what a barn is, see this post by Ken Bloom). The uncertainties listed on this cross-section value are due to statistical, systematic, and luminosity factors, respectively.

So what!? Well, this is in agreement with the theoretical prediction given by the Standard Model (SM) at Next-to-Leading Order (NLO). The SM prediction was 43.0 ± 2.0 pb.

So our theory is correct! It matches the experimental data!

Also, to reduce uncertainties, CMS Physicists also took the ratio of the W⁺W^– to W^±production cross sections. In this case, the uncertainty in the proton beam’s luminosity cancels out. The experimental ratio of these two cross sections was found to be 4.46 ± 1.66 ± 0.64 ·10^-4(uncertainties are again due to statistical & systematic factors, respectively), whereas the theoretical value of this ratio was given to be 4.45 ± 0.30 · 10^-4. Now this is even better agreement! Which is why experimentalists choose to compare these two ratios instead.

Now onto the “Glorious Higgs!” The process we are now interested in is:

H → W⁺W^– → 2l 2v_l

Where: l is a lepton, and v_lis the corresponding neutrino.

CMS Physicists modified the event selection slightly for this. The theory tells us when the Higgs decays into a W⁺W^–pair the angle between the two outgoing oppositely charged (electric) leptons is very small (close to zero degrees), whereas when we are just looking at background processes (such as pure W⁺W^–production, top quark events, ect…) the angle is very large (close to 180 degrees). So experimentalists made a measurement of the angle between these two leptons to get an idea if a Higgs boson had decayed into a W⁺W^–pair, shown here:

So in this plot we have our 13 selected W⁺W^–events, they are the black experimental data points (and their uncertainties), the colored portions are the theoretical predictions given by the SM for various known processes.

Now for our Higgs search, W⁺W^–is a background (shown in brown)! Our other backgrounds being:

Dark Blue: production of a Z boson plus jets (hadronic activity).
Pink: top quark pair production or single top quark with a W boson production
Green: di-boson production, like WZ, or ZZ, or γZ, etc…
Light Blue: W plus jets (hadronic activity).

Now if we assume the Higgs Boson has a mass of 160 GeV/c² then the theoretical prediction of the angle between the two charged leptons in our events is shown as the solid black line (which has a peak near zero, the angle between the outgoing leptons is small for Higgs production). So from this plot, we see that we haven’t found any evidence that a Higgs Boson with a mass of 160 GeV/c² has been found (i.e. there are not a lot of points near the peak in the black solid line).

But that was just one value for the Higgs mass. What about the others? As particle physicists we need to look at all possible ranges for the mass of the Higgs. CMS Physicists decided to look at a large range, of 120-600 GeV/c². This is shown here:

So this is a very colorful plot, but what does it mean?

The Y-Axis is the Higgs production cross section multiplied by the Higgs Branching Ratio to W⁺W^–pairs. The X-axis is the Higgs Mass. The blue line is experimental observation. This is the region of the “phase-space” we where able to see with this study. The “phase-space” is the possible ways something can happen. When you’re playing Monopoly, and you roll two dice, the most likely outcome for the sum of the dice roll is 7. This has a large phase space….you can make 7 with a (1,6), or (2,5) or (3,4) on each dice. Whereas having both dice add to 12 has a very small phase space, this only happens when each die comes up 6.

So the blue line represents how much of the phase space we were able to see. The green and yellow lines are the 95% C.L. bands on the blue lines.

The solid red line near the bottom of the graph is the theoretical prediction given by the current Standard Model for how the Higgs boson’s “phase space” may behave. Notice the experimental blue line, and the theoretical red line are nowhere near each other! Since we didn’t see many data points in the Higgs (160 GeV/c²) region in the graph of the angle between our two charged leptons above, it shouldn’t shock us that the blue line is nowhere near the solid red line (at 160 GeV/c²). But this doesn’t mean that there was anything wrong with the experiment. On the contrary, what this means is that CMS Physicists did not have conclusive evidence to say whether or not the Higgs will or will not decay into a W⁺W^–pair (based on a statistically significant dataset).

So the current theory (the Standard Model) tells us that the Higgs can decay into a W⁺W^– pair; but with the current data CMS Physicists where unable to prove or disprove the Standard Model’s theoretical prediction.

But, the final line is, what I think, the most interesting. This is the red portion with the criss-crossing pattern around it (second item on the legend in the above graph).

Currently in the Standard Model there are three generations of quarks that have been experimentally confirmed. Theorists have often wondered if this is the full story. Meaning, could a possible 4th generation of quarks/leptons exist and we just haven’t seen them yet? This criss-crossing red line gives the phase space for how the Higgs would decay if this 4th generation did exist.

Now notice the blue line is underneath the criss-crossed red line for a Higgs mass of 144-207 GeV/c²when you assume there is a 4th generation of quarks/leptons.

The fact that the blue line is under the criss-crossed red line means that we were conclusively able to probe this portion of the phase space for the 4th generation hypothesis. Since we did not see any conclusive evidence (again, reference angle between our charged leptons in the graph above) of Higgs decaying into a W⁺W^– pair for the mass region of 144-207 GeV/c², we were able to make a definitive statement:

If the Standard Model has a 4th Generation of Quarks/Leptons, and the Higgs boson has a mass between 144-207 GeV/c², the it does not decay to a W⁺W^–pair.

But the jury is still out on the current three generation cases. We weren’t able to probe that region of the phase space (blue line nowhere near solid red line). As is often the case in all fields of science, we need more data.

Until next time,

-Brian

(I would like to thank Kathryn Grim for her helpful advice regarding the presentation of this material)

Tags: CMS, Electroweak, first results, Higgs
Posted in Uncategorized | 5 Comments »

Keeping up with CMS

Friday, April 8th, 2011

In the fast pace world of particle physics its sometimes hard (even for those of us actively involved in it) to keep up with current events. However, Lucas Taylor (the Project Manager of “CMS Centers Worldwide”), has designed a system that helps students, faculty members, post-docs and other researchers to stay active with the day-to-day dealings of the CMS Collaboration without the need to always be on site at CERN. This system, is actually more like a series of locations. They are called CMS Centers and there are in fact 49 of them worldwide! And when the LHC sent its first proton beam around its circumference on Sept. 10th 2008, the world’s largest press conference for a scientific event (since first moon landing) took place in the CERN’s very own CMS Center [1]. In total, 37 media organizations came to the center for the first LHC Beam [1].

The major centers are located at:

CERN in Geneva, Switzerland
Fermi National Accelerator Laboratory (FNAL) in Batavia, Illinois, USA
DESY (Deutsches Elektronen Synchrotron, or the German Electron Synchrotron) in Hamberg, Germany

However these are just three of the many centers worldwide. A complete map is shown here:

Current map of current CMS Centers worldwide, courtesy of CERN

But what kind of information is available at a CMS Center? And more importantly, do you actually have to go to one to see this information? Certain information is available to the general public (which is what I will show here), but most of the information is only available at an actual center. My own host institution has a CMS Center, if you look on the above map you’ll see it listed in Melbourne, Florida.

At a CMS Center one of the things that can be seen is what’s called the LHC Page 1, which the general public can view here. I’ll show a frozen image of this page below, and walk you through what type of information can be found on this page.

LHC Page 1, Courtesy of the CERN CMS Center

A: Shows the target beam energy (if any) of the current experimental requirements
B: Shows what’s happening in with the Collider’s twin proton beams, here they are testing the injection system (hence the “Injection Probe Beam”), basically the LHC is fed beams of particles from the CERN accelerator complex, which does the job of taking particles (in this case protons) up to a small percent of the speed of light. Then the LHC takes over accelerating particles to ~99.9999% the speed of light.
C: Shows an axis representing the beam’s intensity, in this still this is the black line in the central chart (and can also be viewed above at the BCT TI1 & TC2 listings). The beam intensity is also known as the luminosity. This is how many particles are travelling through a unit area (in cm^2) per unit time. So the beam intensity/luminosity is 1.10e9 (cm^2 · s^-1) in this image.
D: Shows any comments relevant to the current state of the accelerator
E: Shows a plot of the current beam energy, with respect to time. The energy unit is GeV, or giga electron volts. An electron volt is the amount of energy it takes to move one electron, through a potential difference of one volt…and a giga electron volt is 100,000,000 eV.

Another thing that can be seen at a CMS Center is what’s called CMS Page 1, which may also be viewed by the general public at this link (sometimes this link switches between CMS Page 1 and CMS DAQ Page that I’ll talk about in a little bit). I’ll show another freeze frame of this image, and try and walk you through some of the information that can be shown on this page.

CMS Page 1, Courtesy of the CERN CMS Center

A: Shows the intensity (or luminosity) of both beams that are colliding within the CMS Detector (currently this is very low, the highest we achieved in 2010 was of the order of 10^32, twenty orders of magnitude higher than what is currently shown here!)
B: Shows the beam energy
C: Shows the current status of the CMS Detector, Running means CMS is taking data…this will sometimes read “Offline” when we are not taking data…but this lets you know whether or not the detector is operating
D: Shows a plot of integrated luminosity in units of 1/nb (nb read, “nano-barn”). A barn, is a unit of cross-sectional area. One barn corresponds to an area of 10^-24 cm^2. (You may make “you couldn’t hit the broad side of a barn” reference now!). When we are colliding proton beams for experimental studies relating to physics analysis the plot will show “Delivered” and “Recorded” integrated luminosities. “Delivered” corresponds to what the Large Hadron Collider is giving the detector, and “Recorded” corresponds to how much of what was delivered was written to our tape drives as useful data.
E: Shows comments made by the shift leader at point 5 (the CMS Control Room) that are relevant to the current experimental study.
F: Shows a readout of all of the CMS Detector’s sub systems, the Detector is like an onion (and also an Ogre), it has layers. These layers are (starting from the top):

1. CSC: Cathode Strip Chambers, these are part of the Detector’s (very impressive) Muon Detection system. The staple of our name, Compact Muon Solenoid.
2. DT: Drift Tubes, these are also part of the Muon Detection system.
3. ECAL: Electromagnetic Calorimeter, these are scintillating lead tungstate (PbWO4) crystals. They have a short characteristic radiation length, and are responsible for photon & electron detection.
4. ES: Electromagnetic PreShower, this system causes cascades of of particles to form in the detector (also known as a shower). This is specifically designed to shower high energy electrons and photons into the ECAL.
5. HCAL: Hadronic Calorimeter, these are “towers” (or stacks) of brass scintillating plates. They are responsible for picking up heavy particles (bayrons and mesons) and neutral particles that do not leave a signal anywhere else in the detector. They are very dense material and have a sufficient nuclear interaction length to do the job.
6. PIXEL: Silicon Pixel Detector, this is a very advanced detector made up of silicon pixel strips, located only centimeters from the proton-proton collision. This is the closest detector element to the interaction point (aka collision point), and gives us very good momentum resolution, and track impact parameter measurements.
7. RPC: Resistive Plate Chambers, are the last element of the muon detection system.
8. TRACKER: Silicon Strip Tracking Detector, this is also a very advanced detector, it encompasses the Pixel Detector, and is the second closest detection element to the beam pipe. We use this to make precision momentum measurements, secondary decay vertices, and track impact parameter measurements. If you combine the entire tracker (both Pixel and Silicon Strip) has over 10^7 channels that are readout by the Detector’s electronics!!!!
9. CASTOR: Castor is a forward element of the Hadronic detection system. It is a little ways away from the rest of the detector down the beam pipe in both directions. CASTOR is responsible for picking up neutral particles that come out at very small scattering angles, almost co-linear with the beam pipe.
10. TRG: Trigger System, responsible for selecting events to record.
11. DAQ: Data Acquisition System
12. DQM: Data Quality Monitoring System (this ensures that the data we are recording is good data!)
13. SCAL: I’m actually not sure what this is unfortunately 🙁
14. HFLUMI: This is part of the Forward Hadron Calorimeter, this sits at both ends of the detector, and trys to capture heavy hadrons and neutral particles at low scattering angles to the beam pipe.
15. Fill/Run Number & Lumi Section: This is how we label events so that we can investigate them individually later.
16. Physics Bit Set: This is a list of technical triggers that give information about the detector, and records this to the data when it is taken.
17. Magnet: it usually operates near 4T (largest of its kind in the world!)

An interactive cartoon of many of these systems and how particles interact with them can be found here.

Another bit of information most CMS Centers will show is the CMS DAQ. And this too is available to the public at this link. Here’s another free-frame so we can walk through what information is available on this page as well.

CMS DAQ Page, Courtesy of CERN CMS Center

A: Shows a basic summary of the DAQ System. Here we have; the beam setup, the run number, the rate of level 1 triggers accepting events (basically how many events our level1 trigger accepts in a second), the size of the event (in kilobytes), the acceptance rate of final events (events that have been accepted by both the level 1 trigger and the high level trigger), and the percent of the high level trigger (HLT) computing power we are using.
B: This image will vary from time to time, sometimes it shows a tiny version of CMS Page 1, LHC Page 1, or a live event display! (See below for more details on that).
C: Shows the status of all the detector elements while the data is being taken.
D: Shows the status of the current data streams.
E: Shows the a plot of; our trigger rate (in green), or CPU performance (in pink), and the number of events accepted and stored (the white shaded region, this region gets larger and larger while we take data, hence the increasing trend).
F: And my favorite, a tiny little statement that says “Physics On,” as if we could turn it Off!

These aren’t the only things that a CMS Center will show. The CMS Center at my host institution has 5 displays in total, so we run 5 displays at a time. However, the CMS Center at CERN has 25 consoles in total, with six monitors per console [2], so that’s 150 screens in total!!!! A CMS Center may also show the status of each individual channel in the detector’s subsystems, the status of the calorimeters; and possibly even the status of the supercomputing farms available. This and much more…but for this, you must go to the Center to observe this information! So if you ever have the opportunity, I highly recommend it. I myself have seen the Center at FNAL on the night of September 10th, 2008, and it was awe-inspiring to say the least. FNAL’s CMS Center is also a remote operations ceneter (ROC). Scientists at Fermi may remotely monitor (and control) various aspects of the CMS Detector at the ROC. This allows them to be part of the action without needing to be present at CERN.

The final thing that may usually be seen at a CMS Center (and is also available to the general public) is the live event feed coming right off of the detector (basically the proton-proton collisions as they happen!!!!!). I personally think this is one of the most inspiring views available from CMS. It let’s you see the “mini-big-bang’s” in action. When two protons collide in CMS, they literally explode into hundreds of pieces, and these pieces are picked up by our detector (if they interact with matter in an ordinary way).

We use a program called “Fireworks Event Display” to visualize the signal the CMS Detector picks up, and to see what’s actually happening “on-line” in the collisions. Its best to view this page when the collider is performing 7 TeV Collisions (we aren’t just yet, but will be soon), so check on this link in the near future to see some very interesting events (that could possibly change the face of modern physics as we know it!!!). The link for the live feed is here. It updates every few minutes with a new event (or if its a particularly interesting event, it will stay on the screen for some time to give it the needed “publicity”).

You can find some previous event displays on the public page of the CMS Collaboration. Here is a sample, I’ll briefly explain the various elements we are looking at:

A Proton Proton Collision Event at 7 TeV, Courtesy of CERN and the CMS Collaboration

Here we have several things going on:

The yellow curved lines are what are called tracks, they are caused by charged particles hitting the Pixel Tracker and the Silicon Strip Tracker. From each hit on pixel or a strip, we can reconstruct the charged particles path as shown above.
The red “rectangles” are hits in the Electromagnetic Calorimeter. These are predominately made by photons and electrons.
The blue “rectangles” are hits in the Hadronic Calorimeter. These are caused by “heavy” particles (like baryons and mesons) that interact strongly with the nuclei of the brass scintillating plates of HCAL. These particles may also be neutral, and HCAL is how we detect these neutral particles.
In the lower right plot, the outermost rectangles that form a ring are the muon detection system of CMS, these are the farthest from the proton-proton collision in the entire detector.
A 3D View of the detector (Left)
A view of the Rho-Z plane, in cylindrical coordinates (Top Right)
A view of the Rho-Phi plane, in cylindrical coordinates (Bottom Right)

Sometimes more “Physics Objects” are shown in event displays; like jets, muons, and MET’s. Jets are conic depositions of energy in the calorimeters in a collimated line. Jets are due to hadronic activity, when quarks are formed in the collision (or release from the exploding protons), they must hadronize immediately into bound states due to color confinement. This process is observed in Jets in the calorimeter. Muons are the heavier brother of the electron, and they will transverse the entire detector (and sometimes the entire atmosphere) before decaying into lighter particles. MET’s are what’s called Missing Transverse Energy. In an event, we sum up all the momentum vectors that we observe. We orient our coordinate axis so that the z-axis is along the beam pipe. The colliding protons have equal and opposite momentum, only in the z-direction. So all the momentum vectors in the xy-plane (perpendicular to the detector) must sum to zero. If it doesn’t its an indication that a particle (like a neutrino) has escaped detection, and went in the direction necessary to balance the momentum vectors in the transverse plane to zero.

You can find more images of real proton-proton collision events here.

And finally some pictures of the CERN CMS Center, the FNAL CMS Center, and my host institution’s (Florida Institute of Technology) CMS Center are shown below.

The CMS Center at CERN [1]:

The CMS Center At FNAL [2]:

And at the Florida Institute of Technology:

CMS Center at the Florida Institute of Technology, showing myself and fellow graduate student, Rob Lucia, hard at work. (Photo taken by Dr. Igor Vodopiyanov)

Well that’s all for now, but hopefully you’ve found this informative. Now you too can be part of the action by checking the links above to see in real-time what’s happening at Point 5 and with CMS and the Large Hadron Collider.

-Brian

References:

[1] Lucas Taylor, “How to create a CMS Centre @ My Institute,” April 8th 2011, https://cms-docdb.cern.ch/cgi-bin/DocDB/RetrieveFile?docid=2527&filename=CMS-Centres-Worldwide-1-5-A5.pdf

[2] Lucas Taylor et al., “CMS centres for control, monitoring, offline operations and prompt analysis,” J. Phys.: Conf. Ser. 119 072029 doi: 10.1088/1742-6596/119/7/072029.

For more information on the FNAL CMS Center please see: http://cms.fnal.gov/index.shtml

Tags: CMS, CMS Centers, event displays
Posted in Uncategorized | 2 Comments »

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