Quark correlation functions and deep inelastic scattering

It is shown that, when ultraviolet divergences are properly taken into account, the naive relation between deep inelastic structure functions and quark light-cone correlation functions is replaced by a relation to quark correlation functions smeared over distances of order 1/square root of Q2 transverse to the light-cone. The quark and gluon distributions, which - with the definition adopted - are related to the structure functions by a convolution, are shown to be fourier transforms of the smeared correlation functions to all orders in αδ but zeroth order in 1/Q2. The discussion is based on a version of the all orders in αδ proof of factorization of mass singularities which leads to a particularly transparent proof of the evolution equations. The relation to correlation functions allows structure functions to be predicted in models and underwrites quantitative discussions of the distances that control deep inelastic scattering