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

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

2011-10-03

arxiv.org/abs/1110.0319v3

Phys. Rev. D 85, 014506 (2012)

Physics

High Energy Physics

High Energy Physics - Lattice

Add strict provement of d-periodic and some numerical results

Scientific paper

10.1103/PhysRevD.85.014506

A proposal by L\"uscher enables us to extract elastic scattering phases from two-particle energy spectrum in a cubic box 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 states where two particles are explicitly distinguishable, namely, the masses of the two particles are different. Their relations with the elastic scattering phases of two-particle energy spectrum in the continuum are obtained 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.

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