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:
-
- 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)
- 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}
}