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→0
at fixed
Q
2
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.