Factorisation in Deeply Virtual Compton Scattering: Local OPE Formalism and Structure Functions

We give a complete treatment of factorisation of Deeply Virtual Compton Scattering (DVCS) in the generalised Bjorken limit, using the local Operator Product Expansion (OPE). The method allows a straightforward proof that, at leading twist, the DVCS amplitude factorises into an integral over coefficient functions and Skewed Parton Distribution Functions (SPDFs). The integral is well defined for on-shell final state photon if the Wilson coefficients satisfy a certain factorisation condition, which we derive. We also show that it enables a simple proof that soft singularities either cancel out or, in the case where the final state photon is on shell, are integrable. This confirms the argument of Collins and Freund. Further, we repeat the tree-level calculation of twist-three contributions to DVCS off a scalar target, where factorisation was found to be violated. We propose a new definition of the structure functions and calculate the coefficient functions, which are such that factorisation works.