Analytic derivation of the leading-order gluon distribution function G(x,Q^2) = xg(x,Q^2) from the proton structure function F_2^p(x,Q^2)

Details Analytic derivation of the leading-order gluon distribution function G(x,Q^2) = xg(x,Q^2) from the proton structure function F_2^p(x,Q^2) Analytic derivation of the leading-order gluon distribution function G(x,Q^2) = xg(x,Q^2) from the proton structure function F_2^p(x,Q^2)

2007-10-17

arxiv.org/abs/0710.3212v3

Phys.Rev.D77:094003,2008

Physics

High Energy Physics

High Energy Physics - Phenomenology

5 pages, 1 figure; discussion modified and expanded in methods, results and conclusions; figure modified; version accepted for

Scientific paper

10.1103/PhysRevD.77.094003

We derive a second-order linear differential equation for the leading order gluon distribution function G(x,Q^2) = xg(x,Q^2) which determines G(x,Q^2) directly from the proton structure function F_2^p(x,Q^2). This equation is derived from the leading order DGLAP evolution equation for F_2^p(x,Q^2), and does not require knowledge of either the individual quark distributions or the gluon evolution equation. Given an analytic expression that successfully reproduces the known experimental data for F_2^p(x,Q^2) in a domain x_min<=x<=x_max, Q_min^2<=Q^2<=Q_max^2 of the Bjorken variable x and the virtuality Q^2 in deep inelastic scattering, G(x,Q^2) is uniquely determined in the same domain. We give the general solution and illustrate the method using the recently proposed Froissart bound type parametrization of F_2^p(x,Q^2) of E. L. Berger, M. M. Block and C-I. Tan, PRL 98, 242001, (2007). Existing leading-order gluon distributions based on power-law description of individual parton distributions agree roughly with the new distributions for x>~10^-3 as they should, but are much larger for x<~10^-3.

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