Ioffe-time distribution of quarks in the photon

Abstract

We have analysed the Ioffe-time distribution of quarks in virtual photons using Operator Product Expansion of the correlation function that determines the matrix element of the corresponding quark string operator. The distribution for a transversally polarised photon admits a spectral representation which can be continued to the on-shell region $p^2 =0$. The resulting model Ioffe-time distribution turns out to be larger than parametrisations of the available $F_2^{\gamma}$ data. This result is linked to the slope of the quark distribution at the origin, which comes out too large as well.