Finite volume corrections to the two-particle decay of states with nonzero momentum

We study the effects of finite volume on the two-particle decay rate of an unstable state with nonzero momentum. First, L\"uscher'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 nonzero total momentum, confirming earlier results of Rummukainen and Gottlieb. We then use this result and the method of Lellouch and L\"uscher to determine the corrections needed for a finite-volume calculation of a two-particle decay amplitude when the decaying particle has nonvanishing center-of-mass momentum.