Numerical analysis of the Balitsky-Kovchegov equation with running coupling: Dependence of the saturation scale on nuclear size and rapidity
- Departamento de Fisica, Modulo C2, Planta baja, Campus de Rabanales, Universidad de Cordoba, 14071 Cordoba (Spain)
- Department of Physics, CERN, Theory Division, CH-1211 Geneva 23 (Switzerland)
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.
- OSTI ID:
- 20705700
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 71, Issue 1; Other Information: DOI: 10.1103/PhysRevD.71.014003; (c) 2005 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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