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Posts Tagged ‘Summer 2011’

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.


Paper vs. Protons (Pt. 1)

Tuesday, July 19th, 2011

It’s summer conference season! Well actually, it is summer school season for me…. but it is summer nonetheless. Last time, I briefly alluded to the fact that I am attending a 10-day summer school on how exactly physicists turn Feynman diagrams (Fig. 1) into numerical predictions, honest-to-goodness numbers that can be tested with an experiment (Fig. 9). Unfortunately, when I started writing my original post I of course decided to make a few pictures… let’s just say I got a little carried away and I am now dividing my summer school adventures into two parts. It’s also 3 am for me. 🙂

My goal for part 1 of “Paper vs. Protons” is to give an intuitive picture of how we generate electron (e-) & positron (e+) pairs when we physically collide two protons. Hopefully, the images are detailed enough so that you don’t have to read the text to understand what is happening. The words are there mostly for completeness.

Figure 1: A quark (q) & an anti-quark (q-bar) with equal and opposite charges combine and become a photon (γ).
The photon then decays into an electron (e-) & a positron (e+).

My colleague/fellow blogger Flip Tanedo has already done an awesome job describing Feynman diagrams, what they are, how they work, and why physicists love them so much. I do neither him nor Feynman justice when I say that the diagrams are simply ways for anyone (not just physicists!) to intuitively visualize how two or more pieces of matter can interact. The point I want to make with figure 1 (above) is that one way we can produce an electron and a positron pair at the Large Hadron Collider (LHC) is by having a quark from one proton and an anti-quark from another proton smash into each other and become a photon (γ). This photon then travels for a very short amount of time (and I mean very short) before it decays into an electron (e-) and a positron (e+). This process can also happen if we were to replace the photon (γ) with a related particle called the Z boson. You can forget about the Z boson for now, though we will need it for the very end of the post.

At the Large Hadron Collider (LHC), we are colliding protons (left black circle) with other protons (right black circle) in order to look for new physics.

Figure 2. Two protons (black circles) are moments from colliding.

We learned a while back ago that the proton is primarily composed of two up-type quarks and one down-type quark. The proton is also made up of something called “gluons,” they help mediate the Strong nuclear force. Gluons are emitted and absorbed from quarks at such a fantastic rate that the proton is ostensibly made of three quarks tied to one another with rigid rope. The three quarks are represented by the red/blue/green circles and the curly lines are the gluons.

Figure 3: The proton is actually made up quarks (red/green/blue circles), gluons (curly lines),
and virtual particles (black circles).

In the image right above you might have noticed that there are small little black circles, these are virtual particles. Quantum Mechanics and Special Relativity tell us that if we have enough energy, then matter can spontaneously form for a short amount of time. These could be muons (my personal favorite) or even other quarks. So long as matter and antimatter are produced in equal amounts all is well in the universe. Things get interesting when these virtual particles are produced right before two protons collide (below).

Figure 4: Two protons are about to collide right after an anti-quark (magenta circle) and its quark partner (not shown) were produced.

If, for instance, an anti-up quark (the magenta dot in the left circle, above… I did not come up with the color convention but I do like it.) were to form, it could then collide with a u-type quark from an oncoming proton (green circle in right circle, above) and become an photon. Jumping now to the image below, we can imagine the photon being that little black dot in center of the two incoming protons.

Figure 5: Two protons (gray circles) are about to collide resulting in an up quark (green circle, right) & an anti-up quark (magenta dot, left) becoming a photon (black dot, center), and decay into an electron & positron (two outgoing arrows).

If we now zoomed in on the collision (below), we would see the two protons physically overlap when they collide and it is at this moment the quark and its anti-partner combine to become a photon. I have removed the gluons just for clarity. Trust me, they are still there.

Figure 6: Two protons (gray circles) are about to collide resulting in an up quark (green circle, right) & an anti-up quark (magenta dot, left) becoming a photon (black dot, center), and decay into an electron & positron (two outgoing arrows).

Here is where things get messy. Imagine a firework exploding and fragmenting into a bunch of small pieces. Well, that is not too different from when two protons collide; they just kind of explode when they smash into each other while traveling at 99.99999% the speed of light. In the image below I left the q q-bar → e+ e- diagram in order to give you an idea how the protons, or what were formerly known as protons, fragment and decay. The dashed arrows should give you an idea of how they fan out.

Figure 7: Post collisions, the remnants of the two protons begin to fragment and decay.

Okay, let’s zoom all the way out because this is all happening in one of the LHC detectors!

Figure 8: How the q q-bar → e+ e- + fragmenting protons might look in a particle detector. The different colors represent the different layers in a collider detector. The beam travels horizontally through the center of the white region.

So one proton enters from the far left and the other proton comes from the far right. Again, the q q → e+ e- diagram has been left as a reference. After the two protons collide, an electron travels one way (long back arrow) and gets stopped pretty early. In a similar fashion, the positron heads out in the opposite direction from the electron in order to conserve momentum (the other long black arrow). The remaining proton fragments continue to decay and just start spewing out particles. The neatest thing about everything above is that we observe this stuff all the time at the LHC. Sadly, I could not find an event that matched our process perfectly. I did, however, find an real life event (below), seen with the ATLAS detector, where a quark and an anti-quark become a Z boson (Remember? Like a photon but heavier.) which then decays into an electron and positron (yellow lines). The remnants of the protons can be seen in teal.

Figure 9: A real q q-bar → Z → e+ e- from proton collisions at the LHC, seen with the ATLAS detector. Click on image for high-res version. The e- and e+ can be seen in yellow and proton fragments in teal.

I had a blast writing this post, even though I had a few WordPress issues. So what do you think? Cool right?

– richard (@bravelittlemuon)

PS Happy Colliding.