Resonance Scattering on the Lattice with Non-Zero Total Momentum

TL;DR

This paper extends Luescher's method to analyze resonance scattering in lattice simulations with non-zero total momentum, enabling more efficient studies of resonances in smaller volumes.

Contribution

It introduces a generalized approach for resonance scattering analysis on the lattice with non-zero total momentum, improving efficiency over previous methods.

Findings

Method successfully applied to a 3+1D spin model

Excellent agreement with zero momentum scattering results

Resonance properties observable in smaller volumes

Abstract

Most hadronic particles are resonances: for example, the rho meson appears as a resonance in the elastic scattering of two pions. A method by Luescher enables one to measure the properties of the resonance particles from finite lattices. We present here a more general method which includes scattering processes where the total momentum of the particles is non-zero. The main advantage is that the resonance scattering can be observed in a considerably smaller spatial volume. We test the method with a simple 3+1 dimensional spin model, and find excellent agreement between the zero momentum and the non-zero momentum scattering sectors.