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Posts Tagged ‘pdf’

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.