INVESTIGATIONS INTO THE BFKL MECHANISM WITH A RUNNING QCD COUPLING

We present approximations of varying degree of sophistication to the i ntegral equations for the (gluon) structure functions of a hadron (''t he partonic flux factor'') in a model valid in the leading log approxi mation with a running coupling constant. The results are all of the BF KL 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 <(alpha)over bar>=3 alpha(s)/pi =alpha(0)/ln(k(perp endicular to)(2)) and varying depending upon the treatment of the tran sverse momentum pole, we also consider the implications for the transv erse momentum (k(perpendicular to)) fluctuations along the emission ch ains and we obtain an exponential falloff in the relevant kappa=ln(k(p erpendicular to)(2)) variable, i.e., an inverse power (k(perpendicular to)(2))(-(2+lambda)) with the same parameter lambda. This is differen t from the BFKL result for a fixed coupling, where the distributions a re Gaussian in the kappa variable with a width as in a Brownian motion determined by ''the length'' of the emission chains, i.e., In(1/x(B)) . The results are verified by a realistic Monte Carlo simulation and w e provide a simple physics motivation for the change.