Summation of Leading Logarithms at Small x

R. D. Ball; S. Forte

Paper

Summation of Leading Logarithms at Small x

Abstract

We show how perturbation theory may be reorganized to give splitting functions which include order by order convergent sums of all leading logarithms of

. This gives a leading twist evolution equation for parton distributions which sums all leading logarithms of

and

, allowing stable perturbative evolution down to arbitrarily small values of

. Perturbative evolution then generates the double scaling rise of

observed at HERA, while in the formal limit

at fixed

the Lipatov

behaviour is eventually reproduced. We are thus able to explain why leading order perturbation theory works so well in the HERA region.