Thorne, RS; (2001) The running Coupling BFKL Anomalous dimensions and splitting functions. Physical Review D , 64 , Article 074005. 10.1103/PhysRevD.64.074005.

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Abstract

I explicitly calculate the anomalous dimensions and splitting functions governing the Q2 evolution of the parton densities and structure functions which result from the running coupling Balitskiĭ-Fadin-Kuraev-Lipatov (BFKL) equation at leading order; i.e., I perform resummation in powers of ln(1/x) and in powers of β0 simultaneously. This is extended as far as possible to next-to-leading order (NLO). These are expressed in an exact, perturbatively calculable analytic form, up to small power-suppressed contributions which may also be modeled to very good accuracy by analytic expressions. Infrared renormalons, while in principle present in a solution in terms of powers in αs(Q2), are ultimately avoided. The few higher twist contributions which are directly calculable are extremely small. The splitting functions are very different from those obtained from the fixed coupling equation, with weaker powerlike growth ∼x-0.25, which does not set in until extremely small x indeed. The NLO BFKL corrections to the splitting functions are moderate, both for the form of the asymptotic powerlike behavior and more importantly for the range of x relevant for collider physics. Hence, a stable perturbative expansion and predictive power at small x are obtained.

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