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Posts Tagged ‘PreSUSY’

What If It’s Not The Higgs?

Sunday, August 21st, 2011

Updated: Monday, 2011 August 29, to clarify shape of angular distribution plots.

It’s the $10 billion question: If experimentalists do discover a bump at the Large Hadron Collider, does it have to be the infamous higgs boson? Not. One. Bit. Plainly and simply, if the ATLAS & CMS collaborations find something at the end of this year it will take a little more data to know we are definitely dealing with a higgs boson. Okay, I suppose I should back up a little an add some context. 🙂

The Standard Model of Particle Physics (or SM for short) is the name for the very well established theory that explains how almost everything in the Universe works, from a physics perspective at least. The fundamental particles that make up the SM, and hence our Universe, are shown in figure 1 and you can learn all about them by clicking on the hyperlink a sentence back. Additionally, this short Guardian article does a great job explaining fermions & bosons.

Fig 1. The Standard Model is composed of elementary particles, which are the fundamental building blocks of the Universe, and rules dictating how the particles interact. The fundamental building blocks are known as fermions and the particles which mediate interactions between fermions are called bosons. (Image: AAAS)

As great as the Standard Model is, it is not perfect. In fact, the best way to describe the theory is to say that it is incomplete. Three phenomena that are not fully explained, among many, are: (1) how do fermions (blue & green boxes in figure 1) obtain their mass; (2) why is there so little antimatter (or so much matter) in the Universe; and (3) how does gravity work at the nanoscopic scale? These are pretty big questions and over the years theorists have come up with some pretty good ideas.

The leading explanation for how fermions (blue & green boxes in figure 1) have mass is called the Higgs Mechanism and it predicts that there should be a new particle called the higgs boson (red box at bottom of figure 1). Physicist believe that the Higgs Mechanism may explain the fermion masses is because this same mechanism very accurately predicts the masses for the other bosons (red boxes in figure 1). It is worth nothing that when using the Higgs Mechanism to explain the masses of the bosons, no new particle is predicted.

Unfortunately, the leading explanations for the huge disparity between matter & antimatter, as well as a theory of gravity at the quantum level, have not been as successful. Interestingly, all three types of  theories (the Higgs Mechanism, matter/antimatter, and quantum gravity) generally predict the existence of a new boson, namely, the higgs boson, the Z’ boson (pronounced: zee prime), and the graviton. A key property that distinguishes each type of boson from the others is the intrinsic angular momentum they each carry. The higgs boson does not carry any, so we call it a “spin 0” boson; the Z’ boson carries a specific amount, so it is called a “spin 1” boson; and the graviton carries precisely twice as much angular momenta as the Z’ boson, so the graviton is called a “spin 2” boson. This will be really important in a few paragraphs but quickly let’s jump back to the higgs story.

Fig 2. Feynman Diagrams representing a higgs boson (left), Z’ boson (center), and graviton (right)
decaying into a b quark (b) & anti-b quark (b).

In July, at the European Physics Society conference, the CDF & DZero Experiments, associated with the Tevatron Collider in Illinois, USA, and the CMS & ATLAS Experiments, associated with the Large Hadron Collider, in Geneva, Switzerland, reported their latest results in the search for the higgs boson. The surprising news was that it might have been found but we will not know for sure until the end of 2011/beginning of 2012.

This brings us all the way back to our $10/€7 billion question: If the experiments have found something, how do we know that it is the higgs boson and not a Z’ boson or a graviton? Now I want to be clear: It is insanely unlikely that the new discovery is a Z’ or a graviton, if there is a new discovery at all. If something has been been discovered, chances are it is the higgs boson but how do we know?

Now, here is where awesome things happen.

The Solution.

In all three cases, the predicted boson can decay into a b quark (b) & anti-b quark (b) pair, which you can see in the Feynman diagrams in figure 2. Thanks to the Law of Conservation of Momentum, we can calculate the angle between each quark and the boson. Thanks to the well-constructed detectors at the Large Hadron Collider and the Tevatron, we can measure the angle between each quark and the boson. The point is that the angular distribution (the number of quarks observed per angle)  is different for spin 0 (higgs), spin 1 (Z’), and spin 2 (graviton) bosons!

To show this, I decided to use a computer program to simulate how we expect angular distributions for a higgs → bb, a Z’→ bb, and a graviton → bb to look. Below are three pairs of plots: the ones to the left show the percentage of b (or b) quarks we expect at a particular angle, with respect to the decaying boson; the ones on the right show the percentage of quarks we expect at the cosine (yes, the trigonometric cosine) of the particular angle.

 

Figure 3. The angular distribution (left) and cosine of the angular distribution (right) for the higgs (spin-0) boson, mH = 140 GeV/c2. 50K* events generated using PYTHIA MSUB(3).

Figure 4. The angular distribution (left) and cosine of the angular distribution (right) for a Z’ (spin-1) boson, mZ’ = 140 GeV/c2. 50K* events generated using PYTHIA MSUB(141).

Figure 5. The angular distribution (left) and cosine of the angular distribution (right) for a graviton (spin-2) boson, mG = 140 GeV/c2. 40K* events generated using PYTHIA MSUB(391), i.e., RS Graviton.

Thanks to the Law of Conservation of Angular Momentum, the intrinsic angular momenta held by the spin 0 (higgs), spin 1 (Z’), and spin 2 (graviton) force the quarks to decay preferentially at some angles and almost forbid other angles. Consequentially, the angular distribution for the higgs boson (spin 0) will give one giant hump around 90°; for the Z’ boson will have two humps at 60° and 120°; and the graviton (spin 2) will have three humps at 30°, 90°, and 150°. Similarly in the cosine distribution: the spin-0 higgs boson has no defining peak; the spin-1 Z’ boson has two peaks; and the spin-2 graviton has three peaks!

In other words, if it smells like a higgs, looks like a higgs, spins like a higgs, then my money is on the higgs.

A Few Words About The Plots

I have been asked by a reader if I could comment a bit on the shape and apparent symmetry in the angular distribution plots, both of which are extremely well understood. When writing the post, I admittedly glossed over these really important features because I was pressed to finish the post before traveling down to Chicago for a short summer school/conference, so I am really excited that I was asked about this.

At the Large Hadron Collider, we collide protons head-on. Since the protons are nicely aligned (thanks to the amazing people who actually operate the collider), we can consistently and uniformly label the direction through which the protons travel. In our case, let’s have a proton that come from the left be proton A and a proton that comes from the right be proton B. With this convention, proton A is traveling along what I call the “z-axis”; if proton A were to shoot vertically up toward the top of this page it would be traveling along the “x-axis”; and if it were to travel out of the computer screen toward you, the reader, the proton would be traveling in the “y direction” (or along the “y-axis”). The angle between the z-axis and the x-axis (or z-axis and the y-axis) is called θ (pronounced: theta). You can take a look at figure 6 for a nice little cartoon of the coordinate system I just described to you.

Figure 6: A coordinate system in which proton A (pA) is traveling along the z-axis and proton B (pB) in the negative z direction. The angle θ is measure as the angle between the z-axis and the x-axis, or equally, between the z-axis and the y-axis.

When the quarks (spin 1/2) inside a proton collide to become a higgs (spin 0), Z’ (spin 1), or graviton (spin 2), angular momentum must always be conserved. The simplest way for a quark in proton A and a quark in proton B to make a higgs boson is for the quarks to spin opposite directions, while still traveling along the z-axis, so that their spins cancel out, i.e., spin 1/2 – spin 1/2 = spin 0. This means that the higgs boson (spin 0) does not have any angular momentum constraints when decaying into two b-quarks and thus the cosine of the angle between the two b-quarks should be roughly flat and uniform. This is a little hard to see in figure 3 (right) because, as my colleague pointed out, the resolution in my plots are too small. (Thanks, Zhen!)

Turning to the Z’ boson (spin 1) case, protons A & B can generate a spin 1 particle most easily when their quarks, again while traveling along the z-axis, are spinning in the same direction, i.e., spin 1/2 + spin 1/2 = spin 1. Consequentially, the spin 1 Z’ boson and its decay products, unlike the higgs boson (spin 0), are required to conserve 1 unit of angular momentum. This happens most prominently when the two b-quarks (1) push against each other in opposite directions or (2) travel in the same direction. Therefore, the cosine of the angle made by the b-quarks is dominantly -1 or +1. If we allow for quantum mechanical fluctuations, caused by Heisenberg’s Uncertainty Principle, then we should also expect b-quarks to sometimes decay with a cosine greater than -1 and less than +1. See figure 4 (right).

The spin 2 graviton can similarly be explained but with a key difference. The spin 2 graviton is special because like the Z’ boson (spin 1) it can have 1 unit of angular momentum, but unlike Z’ boson (spin 1) it can also have 2 units of angular momenta. To produce a graviton with 2 units of angular momenta, rarer processes that involve the W & Z bosons (red W & Z in figure 1) must occur. This allows the final-state b-quarks to decay with a cosine of 0, which explains the slight enhancement in figure 5 (right).

It is worth noting that the reason why I have been discussing the cosine of the angle between the the quarks and not the angle itself is because the cosine is what we physicists calculate and measure. The cosine of an angle, or equally sine of an angle, amplify subtle differences between particle interactions and can at times be easier to calculate & measure.

The final thing I want to say about the angular distributions is probably the coolest thing ever, better than figuring out the spin of a particle. Back in the 1920s, when Quantum Mechanics was first proposed, people were unsure about a keystone of the theory, namely the simultaneous particle and wave nature of matter. We know bosons definitely behave like particles because they can collide and decay. That wavy/oscillatory behavior you see in the plots are exactly that: wavy/oscillatory behavior. No classical object will decay into particles with a continuous distribution; no classical has ever been found to do so nor do we expect to find one, at least according to our laws of classical physics. This wave/particle/warticle behavior is a purely quantum physics effect and would be an indicator that Quantum Mechanics is correct at the energy scale being probed by the Large Hadron Collider. 🙂

 

Happy Colliding.

– richard (@bravelittlemuon)

PS I apologize if some things are a little unclear or confusing. I traveling this weekend and have not had time to fully edit this post. If you have a question or want me to clarify something, please, feel free to write a comment.

PPS If you are going to be at the PreSUSY Summer School in Chicago next week, feel free to say hi!

*A note on the plots: I simulated several tens of thousands of events for clarity. According to my calculations, it would take four centuries to generate 40,000 gravitons, assuming the parameters I chose. In reality, the physicists can make the same determination as we did with fewer than four years worth of data.

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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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