Investigations into the BFKL Mechanism with a Running QCD Coupling
B. Andersson, G. Gustafson and H. Kharraziha.
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.
lu_tp_97_29, November 97
submitted to Physical Review D