Summation of Leading Logarithms at Small x

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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 Q², allowing stable perturbative evolution down to arbitrarily small values of x. Perturbative evolution then generates the double scaling rise of F₂ observed at HERA, while in the formal limit x→ 0 at fixed Q² the Lipatov x⁻λ behaviour is eventually reproduced. We are thus able to explain why leading order perturbation theory works so well in the HERA region.