Jet (particle physics)

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 d x_1 d x_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 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 -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. == See also ==