Finite Volume Corrections to the Two-Particle Decay of States with Non-Zero Momentum

TL;DR

This paper extends finite volume correction methods for two-particle decay rates to cases with non-zero momentum, providing formulas to accurately compute decay amplitudes in finite lattice simulations.

Contribution

It generalizes Luscher's relation and Lellouch-Luscher method to non-zero momentum cases, enabling precise finite-volume decay calculations.

Findings

Derived generalized Luscher relation for non-zero momentum.

Compared new formulas with previous results of Rummukainen and Gottlieb.

Provided correction factors for finite-volume decay amplitude calculations.

Abstract

We study the effects of finite volume on the two-particle decay rate of an unstable state with non-zero momentum. First Luscher's field-theoretic relation between the infinite volume scattering phase shifts and the quantized energy levels of a finite volume, two-particle system is generalized to the case of non-zero total momentum and compared with the earlier results of Rummukainen and Gottlieb. We then use this result and the method of Lellouch and Luscher to determine the corrections needed for a finite-volume calculation of a two-particle decay amplitude when the decaying particle has non-vanishing center-of-mass momentum.