Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states

TL;DR

This paper validates a formalism relating finite-volume lattice QCD matrix elements to infinite-volume observables, focusing on conserved currents and bound states, with implications for accurately extracting physical quantities like the deuteron's scalar charge.

Contribution

It provides non-trivial consistency checks for the formalism and derives finite-volume corrections, demonstrating their importance in practical lattice QCD calculations.

Findings

Finite-volume matrix element of conserved charge equals total charge, volume-independent.

Leading finite-volume corrections are significant for bound states like the deuteron.

Applying the formalism allows for reliable extraction of infinite-volume observables from lattice data.

Abstract

Recently, a framework has been developed to study form factors of two-hadron states probed by an external current. The method is based on relating finite-volume matrix elements, computed using numerical lattice QCD, to the corresponding infinite-volume observables. As the formalism is complicated, it is important to provide non-trivial checks on the final results and also to explore limiting cases in which more straightforward predications may be extracted. In this work we provide examples on both fronts. First, we show that, in the case of a conserved vector current, the formalism ensures that the finite-volume matrix element of the conserved charge is volume-independent and equal to the total charge of the two-particle state. Second, we study the implications for a two-particle bound state. We demonstrate that the infinite-volume limit reproduces the expected matrix element and derive the leading finite-volume corrections to this result for a scalar current. Finally, we provide numerical estimates for the expected size of volume effects in future lattice QCD calculations of the deuteron's scalar charge. We find that these effects completely dominate the infinite-volume result for realistic lattice volumes and that applying the present formalism, to analytically remove an infinite-series of leading volume corrections, is crucial to reliably extract the infinite-volume charge of the state.