Parton (particle physics)

In particle physics, the parton model was proposed by Richard Feynman in 1969 as a way to analyze high-energy hadron collisions. It was later recognized that partons describe the same objects now more commonly referred to as quarks and gluons.

Model

A particle scattering off a parton in a hadron at low and high energies. At low energies, the scattering particle only sees the valence partons. At higher energies, the scattering particles also detects the sea partons.

In this model, a hadron (for example, a proton) is composed of a number of point-like constituents, termed "partons". Additionally, the hadron is in a reference frame where it has infinite momentum — a valid approximation at high energies. Thus, parton motion is slowed by time dilation, and the hadron charge distribution is Lorentz-contracted, so incoming particles will be scattered "instantaneously and incoherently". The parton model was immediately applied to electron-proton deep inelastic scattering by Bjorken and Paschos. Later, with the experimental observation of Bjorken scaling, the validation of the quark model, and the confirmation of asymptotic freedom in quantum chromodynamics, partons were matched to quarks and gluons. The parton model remains a justifiable approximation at high energies, and others have extended the theory over the years.

An interesting fact about partons is that a parton is defined with respect to a physical scale (as probed by the inverse of the momentum transfer). For instance, a quark parton at one length scale can turn out to be a superposition of a quark parton state with a quark parton and a gluon parton state together with other states with more partons at a smaller length scale. Similarly, a gluon parton at one scale can resolve into a superposition of a gluon parton state, a gluon parton and quark-antiquark partons state and other multiparton states. Because of this, the number of partons in a hadron actually goes up with momentum transfer! At low energies (i.e. large length scales), a baryon contains three valence partons (quarks) and a meson contains two valence partons (a quark and an antiquark parton). At higher energies however, we have sea partons (nonvalence partons) in addition to valence partons.

Terminology

Feynman preferred to call quarks partons and Gell-Mann prefers to call partons quarks. In modern usage, the term "parton" is often used to mean "a quark or a gluon", in just the same way as "nucleon" refers to a proton or a neutron.

Parton distribution functions

The CTEQ6 parton distribution functions in the MS renormalization scheme and Q = 2 GeV for gluons (red), up (green), down (blue), and strange (violet) quarks. Plotted is the product of longitudinal momentum fraction x and the distribution functions f versus x.

The parton distribution functions are the probability density for finding a particle with a certain longitudinal momentum fraction x at momentum transfer Q². Because of the inherent non-perturbative effect in a QCD binding state, parton distribution functions cannot be obtained by perturbative QCD. Due to the limitations in present lattice QCD calculations, the known parton distribution functions are obtained by using experimental data.

Experimentally determined parton distribution functions are available from various groups worldwide. The major unpolarized data sets are:

• CTEQ, from the CTEQ Collaboration
• GRV, from M. Glück, E. Reya, and A. Vogt
• MRST, from A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne

Generalized parton distributions (GPDs) are a more recent approach to better understand hadron structure by representing the parton distributions as functions of more variables, such as the transverse momentum and spin of the parton. Early names included "non-forward", "non-diagonal" or "skewed" parton distributions. They are accessed through exclusive processes for which all particles are detected in the final state. Ordinary parton distribution functions are recovered by setting to zero (forward limit) the extra variables in the generalized parton distributions. Other rules show that the electric form factor, the magnetic form factor, or even the form factors associated to the energy-momentum tensor are also included in the GPDs. A full 3-dimensional image of partons inside hadrons can be obtained from GPDs.

References

Parton distribution functions

• CTEQ Collaboration, S. Kretzer et al., "CTEQ6 Parton Distributions with Heavy Quark Mass Effects", Phys. Rev. D69, 114005 (2004).
• M. Glück, E. Reya, A. Vogt, "Dynamical Parton Distributions Revisited", Eur. Phys. J. C5, 461–470 (1998).
• A. D. Martin et al., "Parton distributions incorporating QED contributions", Eur. Phys. J. C39, 155 161 (2005).
• X. Ji, "Generalized Parton Distributions", Annu. Rev. Nucl. Part. Sci. 54, 413-50 (2004).

External links

• Parton distribution functions – from HEPDATA: The Durham HEP Databases
• CTEQ6 parton distribution functions