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In particle physics, the parton model was proposed by Richard Feynman in 1969^[1] as a way to analyze high-energy hadron collisions. 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.^[2] 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.

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 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. The ordinary parton distribution functions are recovered when the generalized parton distributions are integrated over the extra variables. Generalized parton distributions hope to describe more accurately the low-momentum details of collider processes.

1. ^ R. P. Feynman, Proceedings of the 3rd Topical Conference on High Energy Collision of Hadrons, Stony Brook, N. Y. (1969)
2. ^ J. D. Bjorken and E. A. Paschos, Inelastic Electron-Proton and γ-Proton Scattering and the Structure of the Nucleon, Phys. Rev. 185, 1975-1982 (1969). doi:10.1103/PhysRev.185.1975

• 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).

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

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