NLO BFKL equation, running coupling, and renormalization scales - art. no.054031

I examine the solution of the BFKL equation with NLO corrections relevant f or deep inelastic scattering. Particular emphasis is placed on the part pla yed by the running of the coupling. It is shown that the solution factorize s into a part describing the evolution in Q(2), and a constant part describ ing the input distribution. The latter is infrared dominated, being describ ed by a coupling which grows as x decreases, and thus being contaminated by infrared renormalons. Hence, for this part we agree with previous assertio ns that predictive power breaks down for small enough x at any Q(2). Howeve r, the former is ultraviolet dominated, being described by a coupling which falls like 1/(ln(Q(2)/Lambda(2))+A[<(alpha)over bar>(s)(Q(2))ln(1/x)](1/2) ) with decreasing x, and thus is perturbatively calculable at all x. Theref ore, although the BFKL equation is unable to predict the input for a struct ure function for small I, it is able to predict its evolution in Q(2), as w e would expect from the factorization theory. The evolution at small x has no true powerlike behavior due to the fall of the coupling, but does have s ignificant differences from that predicted from a standard NLO in cu, treat ment Application of the resummed splitting functions with the appropriate c oupling constant to an analysis of data, i.e., a global fit, is very succes sful. [S0556-2821(99)07213-6].