Rummukainen-Gottlieb's formula on two-particle system with different mass

Abstract

Lüscher established a non-perturbative formula to extract the elastic scattering phases from two-particle energy spectrum in a torus using lattice simulations. Rummukainen and Gottlieb further extend it to the moving frame, which is devoted to the system of two identical particles. In this work, we generalize Rummukainen-Gottlieb's formula to the generic two-particle system where two particles are explicitly distinguishable, namely, the masses of the two particles are different. The finite size formula are achieved for both $C_{4v}$ and $C_{2v}$ symmetries. Our analytical results will be very helpful for the study of some resonances, such as kappa, vector kaon, and so on.

matching its published paper and make it concise, and to remove text overlap with arXiv:hep-lat/9503028, arXiv:hep-lat/0404001 by other authors

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