The Small x Behaviour of Altarelli-Parisi Splitting Functions

Details The Small x Behaviour of Altarelli-Parisi Splitting Functions The Small x Behaviour of Altarelli-Parisi Splitting Functions

1999-06-02

arxiv.org/abs/hep-ph/9906222v2

Phys.Lett. B465 (1999) 271-281

Physics

High Energy Physics

High Energy Physics - Phenomenology

TeX with harvmac, 15 pages, 5 figures in postscript. Final version, to be published in Phys. Lett. B. A few minor typos correc

Scientific paper

10.1016/S0370-2693(99)01013-8

We extract the small x asymptotic behaviour of the Altarelli-Parisi splitting functions from their expansion in leading logarithms of 1/x. We show in particular that the nominally next-to-leading correction extracted from the Fadin-Lipatov kernel is enhanced asymptotically by an extra ln 1\x over the leading order. We discuss the origin of this problem, its dependence on the choice of factorization scheme, and its all-order generalization. We derive necessary conditions which must be fulfilled in order to obtain a well behaved perturbative expansion, and show that they may be satisfied by a suitable reorganization of the original series.

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