An x-Space Analysis of Evolution Equations: Soffer's Inequality and the Non-forward Evolution

Details An x-Space Analysis of Evolution Equations: Soffer's Inequality and the Non-forward Evolution An x-Space Analysis of Evolution Equations: Soffer's Inequality and the Non-forward Evolution

2003-03-06

arxiv.org/abs/hep-ph/0303050v1

JHEP 0311 (2003) 059

Physics

High Energy Physics

High Energy Physics - Phenomenology

26 pages, 11 figures

Scientific paper

10.1088/1126-6708/2003/11/059

We analize the use of algorithms based in x-space for the solution of renormalization group equations of DGLAP-type and test their consistency by studying bounds among partons distributions - in our specific case Soffer's inequality and the perturbative behaviour of the nucleon tensor charge - to next-to-leading order in QCD . A discussion of the perturbative resummation implicit in these expansions using Mellin moments is included. We also comment on the (kinetic) proof of positivity of the evolution of $h_1$, using a kinetic analogy and illustrate the extension of the algorithm to the evolution of generalized parton distributions. We prove positivity of the non-forward evolution in a special case and illustrate a Fokker-Planck approximation to it.

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