Structure functions from the Compton amplitude

Abstract

We have initiated a program to compute the Compton amplitude from lattice QCD with the Feynman-Hellman method. This amplitude is related to the structure function via a Fredholm integral equation of the first kind. It is known that these types of equations are inherently ill--posed - they are, e.g., extremely sensitive to perturbations of the system. We discuss two methods which are candidates to handle these problems: the model free inversion based on singular value decomposition and one Bayesian type approach. We apply the Bayesian method to currently available lattice data for the Compton amplitude.

arXiv comment7 pages, 5 figures, poster presented at the 37th International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China