Analytic derivation of the leading-order gluon distribution function G(x,Q2)=xg(x,Q2) from the proton structure function F2p(x,Q2)

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 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)(Q(2))<= x <= x(max)(Q(2)), 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 [Phys. Rev. Lett. 98, 242001 (2007)]. Existing leading-order gluon distributions based on power-law descriptions of individual parton distributions agree roughly with the new distributions for x greater than or similar to 10(-3) as they should, but are much larger for x less than or similar to 10(-3).