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Posts Tagged ‘gluons’

Paper vs. Protons (Pt. 2)

Tuesday, August 9th, 2011

Yup, it’s still summer conference season here in the Wonderful World of Physics. My fellow QD bloggers rocked at covering the European Physics Society meeting back in July, so check it out. Aside from the summer conferences, it is also summer school season for plenty of people (like me!). To clarify, I am not talking about repeating a class during the summer. Actually, it is quite the opposite: these are classes that are at most offered once a year and are taught in different countries, depending on the year.

To give you context, graduate students normally run out of courses to take in our second or third of our PhD program; and although the purpose of a PhD is to learn how to conduct research, there will always be an information gap between our courses and our research. There is nothing wrong with that, but sometimes that learning curve is pretty big. In order to alleviate this unavoidable issue, university professors often will teach a one-time-only “topics” course on their research to an audience of three or four students during the regular academic year. Obviously, this is not always sustainable for departments, large or small, because of fixed costs required to teach a course. The solution? Split the cost by inviting a hundred or so students from around the world to a university and cram an entire term’s worth of information into a 1- to 4-week lecture series, which, by the way, are taught by expert faculty from everywhere else in the world. 🙂

To be honest, it is like learning all about black holes & dark matter from the people who coined the names “black holes” & “dark matter.” So not only do graduate students get to learn about the latest & greatest from the people who discovered the latest & greatest, but we also get to hear all the anecdotal triumphs and setbacks that lead to the discoveries.

Fig. 1: Wisconsin’s state capitol in Madison, Wi., taken from one of the bike paths
that wrap around the city’s many lakes. (Photo: Mine)

This brings us to the point of my post. Back in July, I had the great opportunity to attend the 2011 CTEQ Summer School in Madison, Wi., where for 10 days we talked about this equation:

Now, this is not just any ordinary equation, it is arguably the most important equation for any physicist working at the Large Hadron Collider, the Tevatron, or any of the other half-dozen atom smashers on this planet. In fact, this equation is precisely what inspired the name Paper vs. Protons.

Since quantum physics is inherently statistical most calculations result in computing probabilities of things happening. The formula above allows you to compute the probability of what happens when you collide protons, something experimentalists can measure, by simply calculating the probability of something happening when you collide quarks, something undergraduates can do! Physicists love quarks very much because they are elementary particles and are not made of anything smaller, at least that is what we think. Protons are these messy balls of quarks, gluons, photons, virtual particles, elephant-anti-elephant pairs, and are just horrible. Those researchers studying the proton’s structure with something called “lattice QCD” have the eternal gratitude of physicists like me, who only deal with quarks and their kookiness.

Despite being so important the equation only has three parts, which are pretty straightforward. The first part, is that tail end of the second line:

which is just probability of this happening:

Fig. 2: Feynman diagram representing the qq-bar → γ → e+e- process.

If you read Paper vs. Protons (Pt. 1) you might recognize it. This Feynman diagram represents a quark (q) & an antiquark (q with a bar over it) combine to become a photon (that squiggly line in the center), which then decays into an electron (e-) & its antimatter partner, the positron (e+). Believe it or not, the probability of this “qq-bar → γ → e+e-” process happening (or cross section as we call it) is something that advanced college students and lower level graduate students learn to calculate in a standard particle physics course. Trust me when I say that every particle physicist has calculated it, or at the very least a slight variation that involves muons. By coincidence, I actually calculated it (for the nth time) yesterday.

Okay, time for the second part of the equation. To help explain it, I am using a great image (below) from the LHC experiment ALICE. So you & I know that all matter is made from atoms (left). Atoms, in turn, consist of a nucleus of protons & neutrons (center) that are being orbited by electrons (white dots, left). A proton (right) is made up of three quarks (three fuzzy, white dots, right) that bathe in a sea of gluons (red-blue-green fuzziness, right). About 45% of a proton’s energy at the LHC is shared by the three quarks; the remaining 55% of the proton’s energy is shared by the gluons.

Fig. 3: An atom (left), an atom’s nucleus (center), and a free proton (right). (Image: ALICE Expt)

How do we know those numbers? Easy, with something called a “parton distribution function”, or p.d.f. for short! A p.d.f. gives us back the probability of finding, for example, a quark in a proton with 15% of the proton’s energy. Since we want to know the probability of finding a quark (q) in the first proton (with momentum x1) and the probability of finding an anti-quark (q with a bar over its head) in the second proton (with momentum x2) we need to use our p.d.f. (which we will call “f”) twice. Additionally, since the quark and anti-quark can come from either of the two protons we need to use “f” a total of four times. Part 2 of our wonderful equation encapsulates the entire likelihood of finding the quarks we want to smash together:

Now the third (and final!) part is the simple to understand because all it tells us to do is to add: add together all the different ways a quark can share a proton’s energy. For example, a quark could have 5% or 55% of a proton’s energy, and even though either case might be unlikely to happen we still add together the probability of each situation happening. This the third part of our wonderful equation:

Putting everything together, we find that the probability of producing an electron (e-) and a positron (e+) when smashing together two protons is actually just the sum (part 3) of all the different ways (part 2) two quarks can produce an e+e- pair (part 1). Hopefully that made sense.

Though it gets better. When we plug our values into the formula, we get a number. This number is literally what we try to measure that the Large Hadron Collider; this is how we discover new physics! If theory “A” predicts a number and we measure a number that is way different, beyond any statistical uncertainty, it means that theory “A” is wrong. This is the infamous Battle of Paper vs Protons. To date, paper and protons agree with one another. However, at the end of this year, when the LHC shuts down for routine winter maintenance, we will have enough data to know definitively if the paper predictions for the higgs boson match what the protons say. Do you see why I think this equation is so important now? This is equation is how we determine whether or not we have discovered new physics. :p

Happy Colliding.

– richard (@bravelittlemuon)

PS. If you will be at the PreSUSY Summer School at the end of August, be sure to say hi.

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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 5th, 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).

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