Investigations into the BFKL Mechanism with a Running QCD Coupling

Details Investigations into the BFKL Mechanism with a Running QCD Coupling Investigations into the BFKL Mechanism with a Running QCD Coupling

1997-11-20

arxiv.org/abs/hep-ph/9711403v1

Phys.Rev. D57 (1998) 5543-5554

Physics

High Energy Physics

High Energy Physics - Phenomenology

24 pages, 10 supplementary files, submitted to Physical Review D

Scientific paper

10.1103/PhysRevD.57.5543

We present approximations of varying degree of sophistication to the integral equations for the (gluon) structure functions of a hadron (``the partonic flux factor'') in a model valid in the Leading Log Approximation with a running coupling constant. The results are all of the BFKL-type, i.e. a power in the Bjorken variable x_B^{-\lambda} with the parameter \lambda determined from the size \alpha_0 of the ``effective'' running coupling \bar{\alpha}\equiv 3\alpha_s/\pi= \alpha_0/\log(k_{\perp}^2) and varying depending upon the treatment of the transverse momentum pole. We also consider the implications for the transverse momentum (k_{\perp}) fluctuations along the emission chains and we obtain an exponential falloff in the relevant \kappa\equiv \log(k_{\perp}^2)-variable, i.e. an inverse power (k_{\perp}^2)^{-(2+\lambda)} with the same parameter \lambda. This is different from the BFKL-result for a fixed coupling, where the distributions are Gaussian in the \kappa-variable with a width as in a Brownian motion determined by ``the length'' of the emission chains, i.e. \log(1/x_B). The results are verified by a realistic Monte Carlo simulation and we provide a simple physics motivation for the change.

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