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Title: Numerical analysis of the Balitsky-Kovchegov equation with running coupling: Dependence of the saturation scale on nuclear size and rapidity

Abstract

We study the effects of including a running coupling constant in high-density QCD evolution. For fixed coupling constant, QCD evolution preserves the initial dependence of the saturation momentum Q{sub s} on the nuclear size A and results in an exponential dependence on rapidity Y, Q{sub s}{sup 2}(Y)=Q{sub s}{sup 2}(Y{sub 0})exp[{alpha}{sub s}d(Y-Y{sub 0})]. For the running coupling case, we rederive analytical estimates for the A and Y dependences of the saturation scale and test them numerically. The A dependence of Q{sub s} vanishes {proportional_to}1/{radical}(Y) for large A and Y. The Y dependence is reduced to Q{sub s}{sup 2}(Y){proportional_to}exp({delta}{sup '}{radical}(Y+X)), where we find numerically {delta}{sup '}{approx_equal}3.2. We study the behavior of the gluon distribution at large transverse momentum, characterizing it by an anomalous dimension 1-{gamma}, which we define in a fixed region of small dipole sizes. In contrast to previous analytical work, we find a marked difference between the fixed coupling ({gamma}{approx_equal}0.65) and running coupling ({gamma}{approx}0.85) results. Our numerical findings show that both a scaling function depending only on the variable rQ{sub s} and the perturbative double-leading-logarithmic expression provide equally good descriptions of the numerical solutions for very small r values below the so-called scaling window.

Authors:
 [1];  [2]; ; ;  [3];  [3];  [4]
  1. Departamento de Fisica, Modulo C2, Planta baja, Campus de Rabanales, Universidad de Cordoba, 14071 Cordoba (Spain)
  2. (Switzerland)
  3. Department of Physics, CERN, Theory Division, CH-1211 Geneva 23 (Switzerland)
  4. (IST), CENTRA, Avenida Rovisco Pais, P-1049-001 Lisbon (Portugal)
Publication Date:
OSTI Identifier:
20705700
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 71; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevD.71.014003; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANOMALOUS DIMENSION; COUPLING; COUPLING CONSTANTS; DIPOLES; DISTRIBUTION; EVOLUTION; FIELD EQUATIONS; GLUONS; NUCLEAR RADII; NUMERICAL ANALYSIS; NUMERICAL SOLUTION; PARTICLE RAPIDITY; QUANTUM CHROMODYNAMICS; TRANSVERSE MOMENTUM

Citation Formats

Albacete, J.L., Department of Physics, CERN, Theory Division, CH-1211 Geneva 23, Armesto, N., Salgado, C.A., Wiedemann, U.A., Milhano, J.G., and Instituto Superior Tecnico. Numerical analysis of the Balitsky-Kovchegov equation with running coupling: Dependence of the saturation scale on nuclear size and rapidity. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.71.014003.
Albacete, J.L., Department of Physics, CERN, Theory Division, CH-1211 Geneva 23, Armesto, N., Salgado, C.A., Wiedemann, U.A., Milhano, J.G., & Instituto Superior Tecnico. Numerical analysis of the Balitsky-Kovchegov equation with running coupling: Dependence of the saturation scale on nuclear size and rapidity. United States. doi:10.1103/PhysRevD.71.014003.
Albacete, J.L., Department of Physics, CERN, Theory Division, CH-1211 Geneva 23, Armesto, N., Salgado, C.A., Wiedemann, U.A., Milhano, J.G., and Instituto Superior Tecnico. Sat . "Numerical analysis of the Balitsky-Kovchegov equation with running coupling: Dependence of the saturation scale on nuclear size and rapidity". United States. doi:10.1103/PhysRevD.71.014003.
@article{osti_20705700,
title = {Numerical analysis of the Balitsky-Kovchegov equation with running coupling: Dependence of the saturation scale on nuclear size and rapidity},
author = {Albacete, J.L. and Department of Physics, CERN, Theory Division, CH-1211 Geneva 23 and Armesto, N. and Salgado, C.A. and Wiedemann, U.A. and Milhano, J.G. and Instituto Superior Tecnico},
abstractNote = {We study the effects of including a running coupling constant in high-density QCD evolution. For fixed coupling constant, QCD evolution preserves the initial dependence of the saturation momentum Q{sub s} on the nuclear size A and results in an exponential dependence on rapidity Y, Q{sub s}{sup 2}(Y)=Q{sub s}{sup 2}(Y{sub 0})exp[{alpha}{sub s}d(Y-Y{sub 0})]. For the running coupling case, we rederive analytical estimates for the A and Y dependences of the saturation scale and test them numerically. The A dependence of Q{sub s} vanishes {proportional_to}1/{radical}(Y) for large A and Y. The Y dependence is reduced to Q{sub s}{sup 2}(Y){proportional_to}exp({delta}{sup '}{radical}(Y+X)), where we find numerically {delta}{sup '}{approx_equal}3.2. We study the behavior of the gluon distribution at large transverse momentum, characterizing it by an anomalous dimension 1-{gamma}, which we define in a fixed region of small dipole sizes. In contrast to previous analytical work, we find a marked difference between the fixed coupling ({gamma}{approx_equal}0.65) and running coupling ({gamma}{approx}0.85) results. Our numerical findings show that both a scaling function depending only on the variable rQ{sub s} and the perturbative double-leading-logarithmic expression provide equally good descriptions of the numerical solutions for very small r values below the so-called scaling window.},
doi = {10.1103/PhysRevD.71.014003},
journal = {Physical Review. D, Particles Fields},
number = 1,
volume = 71,
place = {United States},
year = {Sat Jan 01 00:00:00 EST 2005},
month = {Sat Jan 01 00:00:00 EST 2005}
}