# Scattering phaseshift formulas for mesons and baryons in elongated boxes

## TL;DR

This paper derives Lüscher phaseshift formulas for two-particle states in elongated boxes, enabling more efficient studies of meson and baryon scattering by varying relative momenta and considering boosted states.

## Contribution

It provides new phaseshift formulas for elongated and boosted boxes, expanding the tools for lattice QCD scattering analyses beyond cubic geometries.

## Key findings

- Formulas applicable to meson-meson and meson-baryon scattering.
- Includes scenarios with equal and unequal mass particles.
- Clarifies relations between different moving and zero-momentum states.

## Abstract

We derive L\"{u}scher phaseshift formulas for two-particle states in boxes elongated in one of the dimensions. Such boxes offer a cost-effective way of varying the relative momentum of the particles. Boosted states in the elongated direction, which allow wider access to energies, are also considered. The formulas for the various scenarios (moving and zero-momentum states in cubic and elongated boxes) are compared and relations between them are clarified. The results are applicable to a wide set of meson-meson and meson-baryon elastic scattering processes, with the two-particle system having equal or unequal masses.