Interval arithmetic

Top quark and anti top quark pair decaying into jets, visible as collimated collections of particle tracks, and other fermions in the CDF detector at Tevatron.

A jet is a narrow cone of hadrons and other particles produced by the hadronization of a quark or gluon in a particle physics or heavy ion experiment. Because of QCD confinement, particles carrying a color charge, such as quarks, cannot exist in free form. Therefore they fragment into hadrons before they can be directly detected, becoming jets. These jets must be measured in a particle detector and studied in order to determine the properties of the original quark.

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 the outgoing jet.

Example of jet analysis techniques are:

• jet reconstruction (e.g., k_T algorithm, cone algorithm)
• jet correlation
• flavor tagging (e.g., b-tagging).

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 they ultimately produce 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 originating parton. Thus, one parton will radiate gluons, which will in turn radiate Template:SubatomicParticleTemplate:SubatomicParticle 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-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.

References

• B. Andersson et al., "Parton Fragmentation and String Dynamics", Phys. Rep. 97(2–3), 31–145 (1983).
• S. D. Ellis, D. E. Soper, "Successive Combination Jet Algorithm For Hadron Collisions", Phys. Rev. D48, 3160–3166 (1993).
• 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).

See also

• Dijet event

External links

• The Pythia/Jetset Monte Carlo event generator