Finite-Volume Effects for Two-Hadron States in Moving Frames

TL;DR

This paper derives finite-volume corrections for two-hadron states in moving frames within field theory, providing results consistent with previous relativistic quantum mechanical approaches, and simplifies the derivation of key summation formulas.

Contribution

It offers a field-theoretic derivation of finite-volume effects for moving two-hadron states, aligning with prior results and simplifying the mathematical framework.

Findings

Finite-volume spectrum corrections match previous relativistic quantum mechanical results.

Derived summation formulas relate finite-volume sums to infinite-volume integrals.

Results are accurate up to exponential volume corrections.

Abstract

We determine the finite-volume corrections to the spectrum and matrix elements of two-hadron states in a moving frame, i.e. one in which the total momentum of the two-hadrons is non-zero. The analysis is performed entirely within field theory and the results are accurate up to exponential corrections in the volume. Our results for the spectrum are equivalent to those of Rummukainen and Gottlieb which had been obtained using a relativistic quantum mechanical approach. A technical step in our analysis is a simple derivation of the summation formulae relating the loop summations over the momenta of the two hadrons in finite volume to the corresponding integrals in infinite volume.