All Order Running Coupling BFKL Evolution from GLAP (and vice-versa)

Details All Order Running Coupling BFKL Evolution from GLAP (and vice-versa) All Order Running Coupling BFKL Evolution from GLAP (and vice-versa)

2006-01-06

arxiv.org/abs/hep-ph/0601049v2

Nucl.Phys.B742:158-175,2006

Physics

High Energy Physics

High Energy Physics - Phenomenology

Scientific paper

10.1016/j.nuclphysb.2006.02.020

We present a systematic formalism for the derivation of the kernel of the BFKL equation from that of the GLAP equation and conversely to any given order, with full inclusion of the running of the coupling. The running coupling is treated as an operator, reducing the inclusion of running coupling effects and their factorization to a purely algebraic problem. We show how the GLAP anomalous dimensions which resum large logs of x can be derived from the running-coupling BFKL kernel order by order, thereby obtaining a constructive all-order proof of small x factorization. We check this result by explicitly calculating the running coupling contributions to GLAP anomalous dimensions up to next-to-next-to leading order. We finally derive an explicit expression for BFKL kernels which resum large logs of Q^2 up to next-to-leading order from the corresponding GLAP kernels, thus making possible a consistent collinear improvement of the BFKL equation up to the same order.

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