# Tracking the Jets to Monte Carlo

Article: Calculating Track-Based Observables for the LHC
Authors: Hsi-Ming Chang, Massimiliano Procura, Jesse Thaler, and Wouter J. Waalewijn
Reference: arXiv:1303.6637 [hep-ph]

With the LHC churning out hordes of data by the picosecond, theorists often have to work closely with experimentalists to test various theories, devise models, etc. In order to make sure they’re developing the right kinds of tools to test their ideas, theorists have to understand how experimentalists analyze their data.

One very simple example that’s relevant to the LHC involves the reconstruction of jets. Experimentalists often reconstruct jets from only the charged particles (such as $\pi^{\pm}$) they see in the detector while theorists generally do calculations where jets have both charged and neutral particles (such as $\pi^0$, see my previous ParticleBites for a more general intro to jets). In order to compare predictions with experiment, someone is going to have to compromise. The concept of Track-Based Observables is an interesting example of a way of attacking the more general problem of connecting the blackboard with accelerator.

Before diving into the details, let’s briefly look at the basics of how theorists and experimentalists make predictions about these trouble-making collimated sprays of radiation.

Experiment: For experimentalists, jets are collections of clustered signatures left on the detector. These signatures generally come from calorimetry (i.e. measure the energy deposits) and/or from tracking where the trajectories (i.e. the kinematics) of final state particles are measured. At the LHC, where luminosities are absurdly high, a phenomenon known as “pileup” becomes an increasingly aggravating contaminant in the data. In short, pile-up is caused by the fact that the LHC isn’t just shooting a single proton at another proton in the beam, its shooting bunches of protons at each other. Of course while this makes the likelihood of a direct proton-proton collision more likely, it also causes confusion when looking at the mess of final state particles. How do you know which tracks of particles came from a given collision? It turns out that since measuring particle tracks gives you the kinematic properties of particles, those particles are much easier to deal with. However, neutral particles aren’t detected via tracking at the LHC, only via calorimetry. Thus, to make their lives significantly easier, experimentalists can simply do their analyses and reconstruct jets using purely the charged particles.

Theory: The notion of ignoring charged particles in the name of convenience doesn’t immediately jive with theorists. When using standard Quantum Field Theoretic (QFT) techniques to make predictions about jets, theorists have to turn back the clock on the zoo of final state particles that experimentalists analyze. For most sane theorists, calculations that involve 1 particle splitting into 2 is about all we generally tackle using perturbative QFT. Depending on the circumstances, calculating things at this stage is usually said to be a “next-to-leading order” or NLO calculation when one is using perturbation theory to describe strong interactions. This is because there is a factor of the strong coupling constant $\alpha_s$ multiplying this piece of whatever expression you’re dealing with. Luckily, it turns out that in QCD, this is largely all you need most of the time to make decent predictions. The tricky part is then turning a prediction about 1 particle splitting into 2 into a prediction about those particles splitting into 4 then 8 and so on, i.e. a fully hadronized and realistic event. For this, theorists generally employ hadronization “models” that are found by fitting to data or events simulated by Monte Carlo event generators. But how do you do this fitting? How can you properly separate physics into non-perturbative and perturbative pieces in a way that makes sense?

The popular way of handling the tricky task of connecting NLO calculations with fully hadronized events is by using factorization theorems. What factorization theorems do, in short, is to compartmentalize analytic calculations into pieces involving physics happening at widely separated energy scales. Using perturbative techniques, we calculate relevant processes happening in each regime separately, and then combine those pieces as dictated by the factorization theorem to come up with a full answer. This oftentimes involves splitting up an observable into a perturbatively calculable piece and a non-perturbative piece that must be obtained via a fit to data or a Monte Carlo simulation.

Warning: These theorems are, in all but a few cases, not rigorously defined although there are many examples where factorization theorems can be shown to be true up to small power corrections in some parameter. This is often where the power of effective field theories is used. We’ll address this important and complex issue in future bites.
Where do track-based observables fit into all of this? Once we have a factorization theorem, we have to make sure that we encapsulate the physics in a systematic way that doesn’t have infinities popping up all over the place (as often happens when theorists aren’t careful). The authors of arXiv:1303.6637 define track functions that are combined with perturbatively calculable pieces via a factorization theorem they discuss to make an observable cross-section. To find the track functions, they fit their NLO analytic distributions for the fraction of the total jet energy carried by the jet’s charged particles to simulations done by PYTHIA.

As can be seen in Figure 2, the authors then make predictions for a totally different observable using track functions combined with their analytic calculations and compare them to events generated entirely in PYTHIA, achieving very good results. Let’s take a second to appreciate how powerful an idea this is. By writing down the foundation for track functions, the authors have laid the groundwork for a host of track-based observables that focus specifically on probing the charged particles within a jet. However, the real impact is that these track functions are that they can be applied to any quarks/gluons that are undergoing fragmentation in any process. When these are eventually extracted from data at the LHC, phenomenologists will be able to perform analytic calculations and then, using track functions, make precision predictions about track-based observables that experimentalists can then use to more easily extract information about the structure of jets.