Partonic structure from the Compton amplitude
The partonic and electromagnetic structure of the proton has been studied extensively over the past few decades. There is now extensive knowledge of the longitudinal momentum distributions of quarks and gluons in the proton. Nevertheless, there are gaps in the experimental coverage and it is hence highly desired to have robust results from numerical simulations in lattice QCD — in addition to establishing that QCD does predict the correct distributions. To date, most studies of partonic structure in lattice QCD have been limited to the lowest couple of moments of longitudinal momentum fraction. Here we present a method to directly study the Compton amplitude in the unphysical region (below inelastic particle production) using lattice QCD. Through a dispersion relation, this Compton amplitude is related to weighted integrals of the parton distribution functions. By providing multiple integrals, this technique is demonstrated to have the ability to provide information on the shape of the corresponding parton distribution. A proof-of-principle numerical calculation will also be presented.
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