Exclusive processes in position space and the pion distribution amplitude

TL;DR

This paper proposes a novel lattice QCD approach using position-space current correlators to access pion distribution amplitudes, avoiding renormalization issues and providing a new perspective on hard exclusive reactions.

Contribution

It introduces a method to compute hadronic light-cone distribution amplitudes via position-space correlators, bypassing renormalization challenges and connecting to continuum perturbation theory.

Findings

Calculated correlation function of electromagnetic currents to NNLO with twist-4 corrections.

Argued the method is competitive with traditional lattice moment calculations.

Provides new insights into the space-time structure of exclusive processes.

Abstract

We suggest to carry out lattice calculations of current correlators in position space, sandwiched between the vacuum and a hadron state (e.g. pion), in order to access hadronic light-cone distribution amplitudes (DAs). In this way the renormalization problem for composite lattice operators is avoided altogether, and the connection to the DA is done using perturbation theory in the continuum. As an example, the correlation function of two electromagnetic currents is calculated to the next-to-next-to-leading order accuracy in perturbation theory and including the twist-4 corrections. We argue that this strategy is fully competitive with direct lattice measurements of the moments of the DA, defined as matrix elements of local operators, and offers new insight in the space-time picture of hard exclusive reactions.