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Title: 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})

Abstract

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}.

Authors:
 [1];  [2];  [3]
  1. Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208 (United States)
  2. Department of Physics, University of Wisconsin, Madison, Wisconsin 53706 (United States)
  3. Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045 (United States)
Publication Date:
OSTI Identifier:
21250109
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 77; Journal Issue: 9; Other Information: DOI: 10.1103/PhysRevD.77.094003; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DEEP INELASTIC SCATTERING; DIFFERENTIAL EQUATIONS; DISTRIBUTION; DISTRIBUTION FUNCTIONS; EVOLUTION; GLUONS; MATHEMATICAL SOLUTIONS; PROTONS; QUARKS; STRUCTURE FUNCTIONS

Citation Formats

Block, Martin M, Durand, Loyal, and McKay, Douglas W. 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}). United States: N. p., 2008. Web. doi:10.1103/PHYSREVD.77.094003.
Block, Martin M, Durand, Loyal, & McKay, Douglas W. 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}). United States. https://doi.org/10.1103/PHYSREVD.77.094003
Block, Martin M, Durand, Loyal, and McKay, Douglas W. 2008. "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})". United States. https://doi.org/10.1103/PHYSREVD.77.094003.
@article{osti_21250109,
title = {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})},
author = {Block, Martin M and Durand, Loyal and McKay, Douglas W},
abstractNote = {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}.},
doi = {10.1103/PHYSREVD.77.094003},
url = {https://www.osti.gov/biblio/21250109}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 9,
volume = 77,
place = {United States},
year = {Thu May 01 00:00:00 EDT 2008},
month = {Thu May 01 00:00:00 EDT 2008}
}