Creating and finding jets
Johannes Hamre Isaksen
The project is based on a script written in C++ which uses PYTHIA to create particle collider events and FastJet to identify the jets in the events. ROOT is used to make and plot a histogram showing the energy spectrum of the jets.
Table of Contents
The Large Hadron Collider at CERN collides protons together at extremely high energies. The proton consists of three valence quarks and additional sea quarks and gluons, which collectively are called partons. In a proton-proton collision some of the partons in the two protons will interact and create new particles. A sketch of one of the many possible events can be seen below.
Fig. 1: Two sea gluons contained in the protons interact and create a top-antitop pair. These will typically decay further and at some point the resulting particles hadronize. Figure from .
The role of the theoretical physicist is to calculate processes like this using Quantum Chromodynamics (QCD). It is a very complicated task, but is made easier by an assumption called a factorization theorem. The point of the factorizaton theorem is to compute the cross section of the hadron-hadron collision from the different underlying parton-parton cross sections. These are generally much easier to compute, and can be done through standard QCD. Symbolically it can be written like in the following way .
As seen from the above equation the cross section for the two protons to go to some collection of hadrons h can be given by the sum of products of the different parts:
- The two parton distribution functions (PDF) fa/p(x,Q2) for the two protons. This describes the probability of finding a parton a with momentum fraction x inside of the proton.
- The hard partonic cross section dσab → c. This gives the cross section for the partons a and b interacting and creating a collection of partons c.
- The fragmentation function Dc → h(z,Q2), which gives the probability of the partons c to evolve and hadronize into a collection of hadrons h with momentum fraction z.
To account for all possible ways to create the hadrons h there is a sum over the initial partons a and b and the resulting collection of hadrons c. The partonic cross section can be calculated perturbatively using QCD, provided that the interaction energy Q2 is big enough. The PDFs and the fragmentation functions are non-perturbative objects, and have to be inferred from experiments. This factorization can be seen graphically in the figure below.
Fig. 2: Factorization theorem illustrated. Figure from .
In some of the collision events the created partons are highly virtual, and will emit partons to reduce its virtuality down to the non-perturbative scale where hadronization happens. In rare cases when the interaction energy Q2 is very big the initial parton will branch into a collection of many particles hitting the detector in a small radius R. This collection of particles is called a jet.
Fig. 3: Picture of a jet. Hadronization happens in the end and is not shown.
Jets are very interesting objects to study, and have been researched heavily both in proton-proton collisions and in heavy ion collisions. For heavy ion physicist jets are especially interesting because they travel through the quark-gluon plasma created in the collision, and is affected by it. This phenomenon is called jet quenching, and is a topic of a lot of research.
1.2. SoftwareThe goal of a theorist working on jets is to come up with models for all of the processes mentioned above, and compare them to the experimental data from CERN. However, since there are so many possible outcomes for each collision event it would be impossible to calculate the cross-sections in the traditional way. To incorporate all the complicated effects and outcomes physicists have developed event generator software, based on Monte-Carlo methods, which simulate collision events. They take into account all the effects mentioned above, both the perturbative partonic cross sections and the non-perturbative PDFs and fragmentation functions. One of the most famous of these event generators is PYTHIA , which is very successful when it comes to comparing its predictions to experimental data.
In some the generated events from PYTHIA there will be jets. Another software called FastJet  has been written to analyze the events to find and identify the jets. There are several jet-finding algorithms, which I will not discuss in detail. They do however typically involve different ways of clustering together particles laying close together in some radius R. FastJet will find the jets and record their properties, like the jet energy pT.
The goal of this project was to write a script to generate many collision events with PYTHIA, find the jet energy spectrum using FastJet and plot it using ROOT. The code that does this can be found
The script is based on the extensive PYTHIA documentation . To run it one has to specify the value of several parameters. As an example I have chosen proton-proton collisions with energy 14 TeV, which is close to the conditions at the LHC. I have chosen to simulate 10000 PYTHIA collisions, which should be enough to get good statistics. It was also chosen to only simulate evens where the partonic interaction energy is bigger than 200 GeV, which is done to create more jets. The jet radius R was chosen to be 0.7, the pseudorapitidy is |η|< 5, and the minimum jet pT was limited to 250 GeV. Running the above code with these conditions created the following energy spectrum.
Fig. 4: Jet energy spectrum based on 10000 collision events of 14 TeV, with minimum interaction energy 200 GeV.
As seen from the jet spectrum in Fig. 4 it is clear that it is far more likely to generate jets with low pT than with high pT. That is especially evident since the y-axis is plotted in log scale. The shape of this plot is generally also seen on experimental jet energy spectrum plots, see for example . Since it is so unlikely to produce high-pT jets the energy spectrum is known in the field of jet physics as the steeply falling spectrum. The shape of this spectrum can be explained by the partonic cross section in the equation above.
In the end the parameters in the code can easily be changed as to fit the conditions in different experiments, and one can compare the jet data from these to the simulated events.
 T. G. McCarthy, "An Introducton to Collider Physics III", http://www.thomasgmccarthy.com/an-introduction-to-collider-physics-iii (read 7th June 2021)
 D. d'Enterria, "Jet quenching," Landolt-Bornstein, vol. 23, p. 471, 2010.
 C. Bierlich et al., "PYTHIA", https://pythia.org/
 Cacciari et al., "FastJet", http://fastjet.fr/
 B. B. Abelevet al., "Charged jet cross sections and properties in proton-proton collisions at √s= 7 TeV," Phys. Rev. D, vol. 91, no. 11, p. 112012, 2015