Skewed parton distributions and the scale dependence of the transverse size parameter

We discuss the scale dependence of a skewed parton distribution of the pion obtained from a generalized light-cone wave function overlap formula. Using a simple ansatz for the transverse momentum dependence of the light-cone wave function and restricting ourselves to the case of a zero skewedness parameter the skewed parton distribution can be expressed through an ordinary parton distribution multiplied by an exponential function. Matching the generalized and ordinary DGLAP evolution equations of the skewed and ordinary parton distributions, respectively , we derive a constraint for the scale dependence of the transverse size parameter which describes the width of the pion wave function in transverse momentum space. This constraint has implications for the Fock state probability and valence quark distribution. We apply our results to the pion form factor. Skewed parton distributions (SPDs) provide a link between exclusive and inclusive quantities of QCD [1, 2, 3]. Among some of their well known properties is their relation to ordinary parton distributions and hadronic form factors via so-called reduction formulas. Moreover, their evolution behaviour has been investigated and generalized DGLAP evolution equations have been derived. Only few is known, however, about their particular form and so for applications to physical processes one has to resort to specific models. The authors of [4] discussed SPDs in the context of soft contributions to large angle Compton scattering and form factors and proposed a generalized Drell-Yan overlap formula [5] for SPDs in terms of light-cone wave functions (LCWFs). It was shown that in a special kine-matical region, where the plus component of the momentum transfer and consequently the 1