Investigations into the BFKL Mechanism with a Running QCD Coupling

Abstract

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^{-λ} with the parameter λdetermined from the size α_0 of the ``effective'' running coupling \barα\equiv 3α_s/π= α_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 κ\equiv \log(k_{\perp}^2)-variable, i.e. an inverse power (k_{\perp}^2)^{-(2+λ)} with the same parameter λ. This is different from the BFKL-result for a fixed coupling, where the distributions are Gaussian in the κ-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.