Exclusive photoproduction of a di-meson pair with large invariant mass

TL;DR

This paper develops a theoretical framework for exclusive di-meson photoproduction, calculating amplitudes and cross sections for 26 channels, highlighting their potential for probing quark GPDs at JLab energies.

Contribution

It provides a fully-automated leading-order calculation of di-meson production amplitudes, addresses pole regularisation, and proposes a kinematic consistency resolution.

Findings

Calculated cross sections at JLab energies show high statistics potential.

Identified processes sensitive to chiral-odd GPDs.

Demonstrated the importance of proper pole treatment in amplitude calculations.

Abstract

The exclusive photoproduction of a pair of light mesons is studied within the framework of collinear factorisation. The amplitude factorises into a process-dependent perturbatively calculable hard part, a generalised parton distribution (GPD) and two distribution amplitudes (DAs). We focus on the production of any combination of $\rho$ and $\pi$ mesons (of any charge and polarisation) that do not involve neutral $C=+$ exchanges with the nucleon. This gives a total of 26 distinct channels, which are sensitive to quark GPDs only. We calculate the amplitude for these di-meson processes at leading order in $\alpha_s$ and at leading twist, in a fully-automated way. Depending on the choice of mesons in the final state, some of these processes are sensitive to chiral-odd (helicity-flip) GPDs. Particular attention is given to the treatment of poles in the 3-dimensional convolution integral of the momentum fractions connecting the hard part with the different non-perturbative components. These poles are regularised by usual Feynman $i \epsilon$ factors, but lead to numerical instabilities if not dealt with properly. We also discuss in detail the construction of the phase space. Importantly, we propose a resolution for the inconsistency of the kinematics of the hard part of the process, where hadron masses and other soft scales are neglected, with the rest of the process. As a proof of concept, we explicitly evaluate the cross section, for a subset of processes whose amplitudes have been constructed, at energies typical of the CLAS12 experiment at JLab. Our results indicate that exclusive di-meson photoproduction processes have very good statistics, which can be a factor of up to a hundred more than the exclusive photon-meson photoproduction process. Therefore, the family of processes that we study here represents a great opportunity for GPD extraction.