Solving the high energy evolution equation including running coupling corrections

被引:189
作者
Albacete, Javier L. [1 ]
Kovchegov, Yuri V. [1 ]
机构
[1] Ohio State Univ, Dept Phys, Columbus, OH 43210 USA
来源
PHYSICAL REVIEW D | 2007年 / 75卷 / 12期
关键词
D O I
10.1103/PhysRevD.75.125021
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We study the solution of the nonlinear Balitsky-Kovchegov evolution equation with the recently calculated running coupling corrections [I. I. Balitsky, Phys. Rev. D 75, 014001 (2007). and Y. Kovchegov and H. Weigert, Nucl. Phys. A784, 188 (2007).]. Performing a numerical solution we confirm the earlier result of Albacete et al. [Phys. Rev. D 71, 014003 (2005).] (obtained by exploring several possible scales for the running coupling) that the high energy evolution with the running coupling leads to a universal scaling behavior for the dipole-nucleus scattering amplitude, which is independent of the initial conditions. It is important to stress that the running coupling corrections calculated recently significantly change the shape of the scaling function as compared to the fixed coupling case, in particular, leading to a considerable increase in the anomalous dimension and to a slow-down of the evolution with rapidity. We then concentrate on elucidating the differences between the two recent calculations of the running coupling corrections. We explain that the difference is due to an extra contribution to the evolution kernel, referred to as the subtraction term, which arises when running coupling corrections are included. These subtraction terms were neglected in both recent calculations. We evaluate numerically the subtraction terms for both calculations, and demonstrate that when the subtraction terms are added back to the evolution kernels obtained in the two works the resulting dipole amplitudes agree with each other. We then use the complete running coupling kernel including the subtraction term to find the numerical solution of the resulting full nonlinear evolution equation with the running coupling corrections. Again the scaling regime is recovered at very large rapidity with the scaling function unaltered by the subtraction term.
引用
收藏
页数:17
相关论文
共 56 条
[1]   Numerical analysis of the Balitsky-Kovchegov equation with running coupling: Dependence of the saturation scale on nuclear size and rapidity [J].
Albacete, JL ;
Armesto, N ;
Milhano, JG ;
Salgado, CA ;
Wiedemann, UA .
PHYSICAL REVIEW D, 2005, 71 (01) :014003-1
[2]   Energy dependence of the Cronin effect from nonlinear QCD evolution [J].
Albacete, JL ;
Armesto, N ;
Kovner, A ;
Salgado, CA ;
Wiedemann, UA .
PHYSICAL REVIEW LETTERS, 2004, 92 (08)
[3]   Nuclear size and rapidity dependence of the saturation scale from QCD evolution and experimental data [J].
Albacete, JL ;
Armesto, N ;
Milhano, JG ;
Salgado, CA ;
Wiedemann, UA .
EUROPEAN PHYSICAL JOURNAL C, 2005, 43 (1-4) :353-360
[4]   Parton densities and dipole cross-sections at small x in large nuclei [J].
Armesto, N ;
Braun, MA .
EUROPEAN PHYSICAL JOURNAL C, 2001, 20 (03) :517-522
[5]   Relating high-energy lepton-hadron, proton-nucleus, and nucleus-nucleus collisions through geometric scaling [J].
Armesto, N ;
Salgado, CA ;
Wiedemann, UA .
PHYSICAL REVIEW LETTERS, 2005, 94 (02)
[6]  
BALITSKII YY, 1978, SOV J NUCL PHYS+, V28, P822
[7]   Factorization and high-energy effective action [J].
Balitsky, I .
PHYSICAL REVIEW D, 1999, 60 (01)
[8]   Operator expansion for high-energy scattering [J].
Balitsky, I .
NUCLEAR PHYSICS B, 1996, 463 (01) :99-157
[9]  
BALITSKY I, HEPPH9706411 ARXIV
[10]   Quark contribution to the small-x evolution of color dipole [J].
Balitsky, Ian .
PHYSICAL REVIEW D, 2007, 75 (01)