Analytic derivation of the leading-order gluon distribution function G(x,Q{sup 2})=xg(x,Q{sup 2}) from the proton structure function F{sub 2}{sup p}(x,Q{sup 2})
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208 (United States)
- Department of Physics, University of Wisconsin, Madison, Wisconsin 53706 (United States)
- Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045 (United States)
We derive a second-order linear differential equation for the leading-order gluon distribution function G(x,Q{sup 2})=xg(x,Q{sup 2}) which determines G(x,Q{sup 2}) directly from the proton structure function F{sub 2}{sup p}(x,Q{sup 2}). This equation is derived from the leading-order evolution equation for F{sub 2}{sup p}(x,Q{sup 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{sub 2}{sup p}(x,Q{sup 2}) in a domain x{sub min}(Q{sup 2}){<=}x{<=}x{sub max}(Q{sup 2}), Q{sub min}{sup 2}{<=}Q{sup 2}{<=}Q{sub max}{sup 2} of the Bjorken variable x and the virtuality Q{sup 2} in deep inelastic scattering, G(x,Q{sup 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{sub 2}{sup p}(x,Q{sup 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 > or approx. 10{sup -3} as they should, but are much larger for x < or approx. 10{sup -3}.
- OSTI ID:
- 21250109
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 77, Issue 9; Other Information: DOI: 10.1103/PhysRevD.77.094003; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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