We’ve mentioned jets a few times here on the US LHC blog, so I’d like to go into bit more detail about these funny unavoidable objects in hadron colliders. Fortunately, Cornell recently had a visit from David Krohn, a Simons Fellow at Harvard University who is an expert at jet substructure. With his blessing, I’d like to recap parts of his talk to highlight a few jet basics an mention some of the cutting edge work being done in the field.
Let’s review what we know about quantum chromodynamics (QCD). Protons and neutrons are composite objects built out of quarks which are bound together by gluons. Like electrons and photons in quantum electrodynamics (QED), quarks and gluons are assumed to be “fundamental” particles. Unlike electrons and photons, however, we do not observe individual quarks or gluons in isolation. You can pull an electron off of a Hydrogen atom without much ado, but you cannot pull a quark out of a proton without shattering the proton into a bunch of other very different looking things (things like pions).
The reason is that QCD is very nonperturbative at low energies. QCD hates to have color-charged particles floating around, it wants them to immediately bind into color-neutral composite objects, even if that means producing new particles out of the quantum vacuum to make everything neutral. These color-neutral composite objects are called hadrons. Unfortunately, usually the process of hadronizing a quark involves radiating off other quarks of gluons which themselves hadronize. This process continues until you end up with a messy spray of particles in place of the original colored object. This spray is called a jet. (Every time I write about jets I feel like I have to reference West Side Story.)
As one can see in the image above, the problem is that the nice Feynman diagrams that we know how to calculate do not directly correspond to the actual mess of particles that form the jets which the LHC experiments measure. And it really is mess. One cannot effectively measure every single particle within each jet and even if one could, it is impractically difficult to calculate Feynman diagrams for very large numbers of particles.
Thus we’re stuck having to work with the jets themselves. High energy jets usually correspond to the production of a single high-energy colored particle, so it makes sense to talk about jets as “single objects” even though they’re really a spray of hadrons.
So we’ve accepted the following fact of life for QCD at a particle collider:
Even though our high energy collisions produce ‘fundamental’ particles like quarks and gluons, the only thing we get to observe are jets: messy sprays of hadrons.
Thus one very important task is trying to make the correspondence between the ‘fundamental’ particles in our Feynman diagrams and the hadronic slop that we actually measure. In fact, it’s already very hard to provide a technical definition of a jet. Our detectors can identify most of the “hadronic slop,” but how do we go from this to a measurement of some number of jets?
This process is called clustering and involves developing algorithms to divide hadrons into groups which are each likely to have come from a single high energy colored particle (quarks or gluons). For example, for the simple picture above, one could develop a set of rules that cluster hadrons together by drawing narrow cones around the most energetic directions and defining everything within the cone to be part of the jet:
One can then measure the energy contained within the cone and say that this must equal the energy of the initial particle which produced the jets, and hence we learn something about fundamental object. I’ll note that this kind of “cone algorithms” for jet clustering can be a little crude and there are more sophisticated techniques on the market (“sequential recombination”).
Even though the above cartoon was very nice, you can imagine how things can become complicated. For example, what if the two cones started to approach each other? How would you know if there was one big jet or two narrow jets right next to each other? In fact, this is precisely what happens when you have a highly boosted object decaying into jets.
By “boosted” I mean that the decaying particle has a lot of kinetic energy. This means that even though the particle decays into two colored objects—i.e. two jets—the jets don’t have much time to separate from one another before hitting the detector. Thus instead of two well-separated jets as we saw in the example above, we end up with two jets that overlap:
Now things become very tricky. Here’s a concrete example. At the LHC we expect to produce a lot of top/anti-top pairs (t–t-bar). Each of these tops immediately decays into a b-quark and a W. Thus we have
t, t-bar → b, b-bar, W W
(As an exercise, you can draw a Feynman diagram for top pair production and the subsequent decay.) These Ws are also fairly massive particles and can each decay into either a charged lepton and a neutrino, or a pair of quarks. Leptons are not colored objects and so they do not form jets; thus the charged lepton (typically a muon) is a very nice signal. One promising channel to look for top pair production, then, is the case where one of the Ws decays into a lepton and neutrino and the other decays into two quarks:
t, t-bar → b, b-bar, W W → b, b-bar, q, q-bar, lepton, ν
The neutrino is not detected, and all of the quarks (including the bottoms) turn into jets. We thus can search for top pair production by counting the number of four jet events with a high energy lepton. For this discussion we won’t worry about background events, but suffice it to say that one of the reasons why we require a lepton is to help discriminate against background.
Here’s what such an event might look like:
Here “pT” refers to the energy (momentum perpendicular to the beam) of the top quarks. In the above event the tops have a modest kinetic energy. On the other hand, it might be the case that the tops are highly boosted—for example, they might have come from the decay of a very heavy particle which thus gives them a lot of kinetic energy. In the following simulated event display, the tops have a pT that is ten times larger than the previous event:
Now things are tricky! Instead of four clean jets, it looks like two slightly fat jets. Even though this simulated event actually had the “b, b-bar, q, q-bar, lepton, ν” signal we were looking for, we probably wouldn’t have counted this event because the jets are collimated.
There are other ways that jets tend to be miscounted. For example, if a jet (or anything really) is pointed in the direction of the beam, then it is not detected. This is why it’s something of an art to identify the kinds of signals that one should look for at a hadron collider. One will often find searches where the event selection criteria requires “at least” some number of jets (rather than a fixed number) with some restriction on the minimum jet energy.
One thing you might say is that even though the boosted top pair seemed to only produce two jets, shouldn’t there be some relic that they’re actually two small jets rather than one big jet? There has been a lot of recent progress in this field.
The main point is that one can hope to use the “internal radiation distribution” to determine whether a “spray of hadrons” contains a single jet or more than one jets. As you can see from the plots above, this is an art that is similar to reading tea leaves. (… and I only say that with the slightest hint of sarcasm!)
[For experts: the reason why the QCD jets look so different are the Alterelli-Parisi splitting functions: quarks and gluons really want to emit soft, collinear stuff.]
There’s now a bit of an industry for developing ways to quantify the likelihood that a jet is really a jet (rather than two jets). This process is called jet substructure. Typically one defines an algorithm that takes detector data and spits out a number called a jet shape variable that tells you something about the internal distribution of hadrons within the jet. The hope is that some of these variables will be reliable and efficient enough to help us squeeze as much useful information as we can out of each of our events. There also seems to be a rule in physics that the longer you let theorists play with an idea, the more likely it is that they’ll give it a silly name. One recent example is the “N-subjettiness” variable.
In addition to substructure, there has also been recent progress in the field of jet superstructure, where one looks at correlations between two or more jets. The basic idea boils down to something very intuitive. We know that the Hydrogen atom is composed of a proton and an electron. As a whole, the Hydrogen atom is electrically neutral so it doesn’t emit an electric field. (Of course, this isn’t quite true; there is a dipole field which comes from the fact that the atom is actually composed of smaller things which are charged.) The point, however, is that far away from the atom, it looks like a neutral object so we wouldn’t expect it to emit an electric field.
We can say the same thing about color-charged particles. We already know that quarks and gluons want to recombine into color-neutral objects. Before this happens, however, we have high energy collisions with quarks flying all over the place trying to figure out how to become color neutral. Focusing on this time scale, we can imagine that certain intermediate configurations of quarks might already be color neutral and hence would be less likely to emit gluons (since gluons are the color-field). On the other hand, other intermediate configurations might be color-charged, and so would be more likely to emit gluons. This ends up changing the distribution of jet slop.
Here’s a nice example from one of the first papers in this line of work. Consider the production of a Higgs boson through “quark fusion,” i.e. a quark and an antiquark combining into a Higgs boson. We already started to discuss the Higgs in a recent post, where we made two important points: (1) once we produce a Higgs, it is important to figure out how it decays, and (2) once we identify a decay channel, we also have to account for the background (non-Higgs events that contribute to that signal).
One nice decay channel for the Higgs is b b-bar. The reason is that bottom quark jets have a distinct signature—you can often see that the b quark traveled a small distance in the detector before it started showering into more quarks and gluons. Thus the signal we’re looking for is two b-jets. There’s a background for this: instead of qq-bar → Higgs → b-jets, you could also have qq-bar → gluon → b-jets.
The gluon-mediated background is typically very large, so we would like to find a clever way to remove these background events from our data. It turns out that jet superstructure may be able to help out. The difference between the Higgs → b-jets decay versus the gluon → b-jets decay is that the gluon is color-charged. Thus when the gluon decays, the two b-quarks are also color-charged. On the other hand, the Higgs is color-neutral, so that the two b-quarks are also color neutral.
One can draw this heuristically as “color lines” which represent which quarks have the same color charge. In the image below, the first diagram represents the case where an intermediate Higgs is produced, while the second diagram represents an intermediate gluon.
For the intermediate Higgs, the two b-jets must have the same color (one is red, the other is anti-red) so that the combined object is color neutral. For the intermediate gluon, the color lines of the two b-jets are tied up to the remnants of the protons (the thick lines at the top and bottom). The result is that the hadronic spray that makes up the jets tend to be pulled together for the Higgs decays, while pushed apart for the gluon decays. This is shown heuristically below, where again we should understand the plot as being a cylindrical cross section of the detector:
One can thus define a jet superstructure variable (called ‘pull‘) to quantify how much two jets are pulled together or pushed apart. The hope is that this variable can be used to discriminate between signal and background and give us better statistics for our searches for new particles.
Anyway, that’s just a sample of the types of neat things that people have been working on to improve the amount of information we can get out of each event at hadron colliders like the LHC. I’d like to thank David Krohn, once again, for a great talk and very fun discussions. For experts, let me make one more plug for his workshop next month: Boost 2011.