Fracture functions in different kinematic regions and their factorizations

Fracture functions are parton distributions of a hadron in the presence of an almost collinear particle observed in the final state. They are important ingredients in QCD factorization for processes where a particle is produced diffractively. We take the production of a Drell-Yan lepton pair and a diffractively produced photon in hadron collisions to discuss this. Through explicit one-loop calculations , we show that both the transverse momentum dependent and the integrated fracture functions can be factorized with twist-2 parton distribution functions and fragmentation functions in different kinematic regions. The complete perturbative coefficients are obtained. Evolution equations for these fracture functions are also derived.