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 $x$. This gives a leading twist evolution equation for parton distributions which sums all leading logarithms of $x$ and $Q^2$, allowing stable perturbative evolution down to arbitrarily small values of $x$. Perturbative evolution then generates the double scaling rise of $F_2$ observed at HERA, while in the formal limit $x\to 0$ at fixed $Q^2$ the Lipatov $x^{-\lambda }$ behaviour is eventually reproduced. We are thus able to explain why leading order perturbation theory works so well in the HERA region.

21 pages, TeX with harvmac, 3 figures in compressed postscript. Final published version (several minor corrections)

References in corpus (2)

• Double Asymptotic Scaling at HERA
• A Direct Test of Perturbative QCD at Small x

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