Quantum Diaries

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.