Jet (particle physics)

Last updated May 09, 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 accordance with 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

A gluon is a type of massless elementary particle that mediates the strong interaction between quarks, acting as the exchange particle for the interaction. Gluons are massless vector bosons, thereby having a spin of 1. Through the strong interaction, gluons bind quarks into groups according to quantum chromodynamics (QCD), forming hadrons such as protons and neutrons.

A quark is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly observable matter is composed of up quarks, down quarks and electrons. Owing to a phenomenon known as color confinement, quarks are never found in isolation; they can be found only within hadrons, which include baryons and mesons, or in quark–gluon plasmas. For this reason, much of what is known about quarks has been drawn from observations of hadrons.

In theoretical physics, quantum chromodynamics (QCD) is the study of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years.

The Standard Model of particle physics is the theory describing three of the four known fundamental forces in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy.

In quantum chromodynamics (QCD), color confinement, often simply called confinement, is the phenomenon that color-charged particles cannot be isolated, and therefore cannot be directly observed in normal conditions below the Hagedorn temperature of approximately 2 terakelvin. Quarks and gluons must clump together to form hadrons. The two main types of hadron are the mesons and the baryons. In addition, colorless glueballs formed only of gluons are also consistent with confinement, though difficult to identify experimentally. Quarks and gluons cannot be separated from their parent hadron without producing new hadrons.

Color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics (QCD). Like electric charge, it determines how quarks and gluons interact through the strong force; however, rather than there being only positive and negative charges, there are three "charges", commonly called red, green, and blue. Additionally, there are three "anti-colors", commonly called anti-red, anti-green, and anti-blue. Unlike electric charge, color charge is never observed in nature: in all cases, red, green, and blue or any color and its anti-color combine to form a "color-neutral" system. For example, the three quarks making up any baryon universally have three different color charges, and the two quarks making up any meson universally have opposite color charge.

Hadronization is the process of the formation of hadrons out of quarks and gluons. There are two main branches of hadronization: quark-gluon plasma (QGP) transformation and colour string decay into hadrons. The transformation of quark-gluon plasma into hadrons is studied in lattice QCD numerical simulations, which are explored in relativistic heavy-ion experiments. Quark-gluon plasma hadronization occurred shortly after the Big Bang when the quark–gluon plasma cooled down to the Hagedorn temperature when free quarks and gluons cannot exist. In string breaking new hadrons are forming out of quarks, antiquarks and sometimes gluons, spontaneously created from the vacuum.

Perturbative quantum chromodynamics is a subfield of particle physics in which the theory of strong interactions, Quantum Chromodynamics (QCD), is studied by using the fact that the strong coupling constant $is small in high energy or short distance interactions, thus allowing perturbation theory techniques to be applied. In most circumstances, making testable predictions with QCD is extremely difficult, due to the infinite number of possible topologically-inequivalent interactions. Over short distances, the coupling is small enough that this infinite number of terms can be approximated accurately by a finite number of terms. Although only applicable at high energies, this approach has resulted in the most precise tests of QCD to date.$

In particle physics, the Lund string model is a phenomenological model of hadronization. It treats all but the highest-energy gluons as field lines, which are attracted to each other due to the gluon self-interaction and so form a narrow tube of strong color field. Compared to electric or magnetic field lines, which are spread out because the carrier of the electromagnetic force, the photon, does not interact with itself.

<span class="mw-page-title-main">Drell–Yan process</span> Process in high-energy hadron–hadron scattering

The Drell–Yan process occurs in high energy hadron–hadron scattering. It takes place when a quark of one hadron and an antiquark of another hadron annihilate, creating a virtual photon or Z boson which then decays into a pair of oppositely-charged leptons. Importantly, the energy of the colliding quark-antiquark pair can be almost entirely transformed into the mass of new particles. This process was first suggested by Sidney Drell and Tung-Mow Yan in 1970 to describe the production of lepton–antilepton pairs in high-energy hadron collisions. Experimentally, this process was first observed by J. H. Christenson et al. in proton–uranium collisions at the Alternating Gradient Synchrotron.

In particle physics, the parton model is a model of hadrons, such as protons and neutrons, proposed by Richard Feynman. It is useful for interpreting the cascades of radiation produced from quantum chromodynamics (QCD) processes and interactions in high-energy particle collisions.

In high-energy physics, jet quenching is a phenomenon that can occur in the collision of ultra-high-energy particles. In general, the collision of high-energy particles can produce jets of elementary particles that emerge from these collisions. Collisions of ultra-relativistic heavy-ion particle beams create a hot and dense medium comparable to the conditions in the early universe, and then these jets interact strongly with the medium, leading to a marked reduction of their energy. This energy reduction is called "jet quenching".

The automatic calculation of particle interaction or decay is part of the computational particle physics branch. It refers to computing tools that help calculating the complex particle interactions as studied in high-energy physics, astroparticle physics and cosmology. The goal of the automation is to handle the full sequence of calculations in an automatic (programmed) way: from the Lagrangian expression describing the physics model up to the cross-sections values and to the event generator software.

<span class="mw-page-title-main">Quark–gluon plasma</span> Phase of quantum chromodynamics (QCD)

Quark–gluon plasma is an interacting localized assembly of quarks and gluons at thermal and chemical (abundance) equilibrium. The word plasma signals that free color charges are allowed. In a 1987 summary, Léon van Hove pointed out the equivalence of the three terms: quark gluon plasma, quark matter and a new state of matter. Since the temperature is above the Hagedorn temperature—and thus above the scale of light u,d-quark mass—the pressure exhibits the relativistic Stefan-Boltzmann format governed by temperature to the fourth power and many practically massless quark and gluon constituents. It can be said that QGP emerges to be the new phase of strongly interacting matter which manifests its physical properties in terms of nearly free dynamics of practically massless gluons and quarks. Both quarks and gluons must be present in conditions near chemical (yield) equilibrium with their colour charge open for a new state of matter to be referred to as QGP.

R-hadrons are hypothetical particles composed of a supersymmetric particle and at least one quark.

The photon structure function, in quantum field theory, describes the quark content of the photon. While the photon is a massless boson, through certain processes its energy can be converted into the mass of massive fermions. The function is defined by the process $e + γ \to e +$ hadrons. It is uniquely characterized by the linear increase in the logarithm of the electronic momentum transfer log $Q 2$ and by the approximately linear rise in $x$ , the fraction of the quark momenta within the photon. These characteristics are borne out by the experimental analyses of the photon structure function.

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:

In particle physics, the Cornell potential is an effective method to account for the confinement of quarks in quantum chromodynamics (QCD). It was developed by Estia J. Eichten, Kurt Gottfried, Toichiro Kinoshita, John Kogut, Kenneth Lane and Tung-Mow Yan at Cornell University in the 1970s to explain the masses of quarkonium states and account for the relation between the mass and angular momentum of the hadron. The potential has the form:

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. 97 (2–3). Elsevier BV: 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. 48 (7). American Physical Society (APS): 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

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[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.

[1]