Jet (particle physics)

Last updated March 20, 2024

A jet is a narrow cone of hadrons and other particles produced by the hadronization of quarks and gluons in a particle physics or heavy ion experiment. Particles carrying a color charge, i.e. quarks and gluons, cannot exist in free form because of quantum chromodynamics (QCD) confinement which only allows for colorless states. When protons collide at high energies, their color charged components each carry away some of the color charge. In order to obey confinement, these fragments create other colored objects around them to form colorless hadrons. The ensemble of these objects is called a jet, since the fragments all tend to travel in the same direction, forming a narrow "jet" of particles. Jets are measured in particle detectors and studied in order to determine the properties of the original quarks.

A jet definition includes a jet algorithm and a recombination scheme.^[1] The former defines how some inputs, e.g. particles or detector objects, are grouped into jets, while the latter specifies how a momentum is assigned to a jet. For example, jets can be characterized by the thrust . The jet direction (jet axis) can be defined as the thrust axis. In particle physics experiments, jets are usually built from clusters of energy depositions in the detector calorimeter. When studying simulated processes, the calorimeter jets can be reconstructed based on a simulated detector response. However, in simulated samples, jets can also be reconstructed directly from stable particles emerging from fragmentation processes. Particle-level jets are often referred to as truth-jets. A good jet algorithm usually allows for obtaining similar sets of jets at different levels in the event evolution. Typical jet reconstruction algorithms are, e.g., the anti-k_T algorithm, k_T algorithm, cone algorithm. A typical recombination scheme is the E-scheme, or 4-vector scheme, in which the 4-vector of a jet is defined as the sum of 4-vectors of all its constituents.

In relativistic heavy ion physics, jets are important because the originating hard scattering is a natural probe for the QCD matter created in the collision, and indicate its phase. When the QCD matter undergoes a phase crossover into quark gluon plasma, the energy loss in the medium grows significantly, effectively quenching (reducing the intensity of) the outgoing jet.

Example of jet analysis techniques are:

jet correlation
flavor tagging (e.g., b-tagging)
jet substructure.

The Lund string model is an example of a jet fragmentation model.

Jet production

Jets are produced in QCD hard scattering processes, creating high transverse momentum quarks or gluons, or collectively called partons in the partonic picture.

The probability of creating a certain set of jets is described by the jet production cross section, which is an average of elementary perturbative QCD quark, antiquark, and gluon processes, weighted by the parton distribution functions. For the most frequent jet pair production process, the two particle scattering, the jet production cross section in a hadronic collision is given by

\sigma _{ij\rightarrow k}=\sum _{i,j}\int dx_{1}dx_{2}d{\hat {t}}f_{i}^{1}(x_{1},Q^{2})f_{j}^{2}(x_{2},Q^{2}){\frac {d{\hat {\sigma }}_{ij\rightarrow k}}{d{\hat {t}}}},

with

x, Q²: longitudinal momentum fraction and momentum transfer
${\hat {\sigma }}_{ij\rightarrow k}$ : perturbative QCD cross section for the reaction ij → k
$f_{i}^{a}(x,Q^{2})$ : parton distribution function for finding particle species i in beam a.

Elementary cross sections ${\hat {\sigma }}$ are e.g. calculated to the leading order of perturbation theory in Peskin & Schroeder (1995), section 17.4. A review of various parameterizations of parton distribution functions and the calculation in the context of Monte Carlo event generators is discussed in T. Sjöstrand et al. (2003), section 7.4.1.

Jet fragmentation

Perturbative QCD calculations may have colored partons in the final state, but only the colorless hadrons that are ultimately produced are observed experimentally. Thus, to describe what is observed in a detector as a result of a given process, all outgoing colored partons must first undergo parton showering and then combination of the produced partons into hadrons. The terms fragmentation and hadronization are often used interchangeably in the literature to describe soft QCD radiation, formation of hadrons, or both processes together.

As the parton which was produced in a hard scatter exits the interaction, the strong coupling constant will increase with its separation. This increases the probability for QCD radiation, which is predominantly shallow-angled with respect to the progenitor parton. Thus, one parton will radiate gluons, which will in turn radiate qq pairs and so on, with each new parton nearly collinear with its parent. This can be described by convolving the spinors with fragmentation functions $P_{ji}\!\left({\frac {x}{z}},Q^{2}\right)$ , in a similar manner to the evolution of parton density functions. This is described by a Dokshitzer [ de ]-Gribov-Lipatov-Altarelli-Parisi (DGLAP) type equation

{\frac {\partial }{\partial \ln Q^{2}}}D_{i}^{h}(x,Q^{2})=\sum _{j}\int _{x}^{1}{\frac {dz}{z}}{\frac {\alpha _{S}}{4\pi }}P_{ji}\!\left({\frac {x}{z}},Q^{2}\right)D_{j}^{h}(z,Q^{2})

Parton showering produces partons of successively lower energy, and must therefore exit the region of validity for perturbative QCD. Phenomenological models must then be applied to describe the length of time when showering occurs, and then the combination of colored partons into bound states of colorless hadrons, which is inherently not-perturbative. One example is the Lund String Model, which is implemented in many modern event generators.

Infrared and collinear safety

A jet algorithm is infrared safe if it yields the same set of jets after modifying an event to add a soft radiation. Similarly, a jet algorithm is collinear safe if the final set of jets is not changed after introducing a collinear splitting of one of the inputs. There are several reasons why a jet algorithm must fulfill these two requirements. Experimentally, jets are useful if they carry information about the seed parton. When produced, the seed parton is expected to undergo a parton shower, which may include a series of nearly-collinear splittings before the hadronization starts. Furthermore, the jet algorithm must be robust when it comes to fluctuations in the detector response. Theoretically, If a jet algorithm is not infrared and collinear safe, it can not be guaranteed that a finite cross-section can be obtained at any order of perturbation theory.

Related Research Articles

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<span class="mw-page-title-main">Three-jet event</span> Phenomenon in particle physics

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The light-front quantization of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to a relativistic description of bound systems in terms of quantum-mechanical wave functions. The quantization is based on the choice of light-front coordinates, where $plays the role of time and the corresponding spatial coordinate is . Here, is the ordinary time, is a Cartesian coordinate, and is the speed of light. The other two Cartesian coordinates, and, are untouched and often called transverse or perpendicular, denoted by symbols of the type . The choice of the frame of reference where the time and -axis are defined can be left unspecified in an exactly soluble relativistic theory, but in practical calculations some choices may be more suitable than others. The basic formalism is discussed elsewhere.$

In high energy particle physics, specifically in hadron-beam scattering experiments, transverse momentum distributions (TMDs) are the distributions of the hadron's quark or gluon momenta that are perpendicular to the momentum transfer between the beam and the hadron. Specifically, they are probability distributions to find inside the hadron a parton with a transverse momentum $and longitudinal momentum fraction . TMDs provide information on the confined motion of quarks and gluons inside the hadron and complement the information on the hadron structure provided by parton distribution functions (PDFs) and generalized parton distributions (GPDs). In all, TMDs and PDFs provide the information of the momentum distribution of the quarks, and the GPDs, the information on their spatial distribution.$

In quantum field theory, a sum rule is a relation between a static quantity and an integral over a dynamical quantity. Therefore, they have a form such as:

References

↑ Salam, Gavin P. (2010-06-01). "Towards jetography". The European Physical Journal C. 67 (3): 637–686. arXiv: 0906.1833 . Bibcode:2010EPJC...67..637S. doi:10.1140/epjc/s10052-010-1314-6. ISSN 1434-6052. S2CID 119184431.

Andersson, B.; Gustafson, G.; Ingelman, G.; Sjöstrand, T. (1983). "Parton fragmentation and string dynamics". Physics Reports. Elsevier BV. 97 (2–3): 31–145. Bibcode:1983PhR....97...31A. doi:10.1016/0370-1573(83)90080-7. ISSN 0370-1573.
Ellis, Stephen D.; Soper, Davison E. (1993-10-01). "Successive combination jet algorithm for hadron collisions". Physical Review D. American Physical Society (APS). 48 (7): 3160–3166. arXiv: hep-ph/9305266 . Bibcode:1993PhRvD..48.3160E. doi:10.1103/physrevd.48.3160. ISSN 0556-2821. S2CID 2667115.
M. Gyulassy et al., "Jet Quenching and Radiative Energy Loss in Dense Nuclear Matter", in R.C. Hwa & X.-N. Wang (eds.), Quark Gluon Plasma 3 (World Scientific, Singapore, 2003).
J. E. Huth et al., in E. L. Berger (ed.), Proceedings of Research Directions For The Decade: Snowmass 1990, (World Scientific, Singapore, 1992), 134. (Preprint at Fermilab Library Server)
M. E. Peskin, D. V. Schroeder, "An Introduction to Quantum Field Theory" (Westview, Boulder, CO, 1995).
T. Sjöstrand et al., "Pythia 6.3 Physics and Manual", Report LU TP 03-38 (2003).
G. Sterman, "QCD and Jets", Report YITP-SB-04-59 (2004).

External links

The Pythia/Jetset Monte Carlo event generator
The FastJet jet clustering program

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[1] Salam, Gavin P. (2010-06-01). "Towards jetography". The European Physical Journal C. 67 (3): 637–686. arXiv: 0906.1833 . Bibcode:2010EPJC...67..637S. doi:10.1140/epjc/s10052-010-1314-6. ISSN 1434-6052. S2CID 119184431.

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