I=2 $\pi\pi$ scattering using G-parity boundary condition

TL;DR

This paper introduces a method to compute I=2 ππ scattering phase shifts in lattice QCD by applying G-parity boundary conditions, enabling the study of non-zero relative momentum states.

Contribution

The paper presents a novel approach using G-parity boundary conditions to access non-zero momentum ππ states in lattice simulations, improving phase shift calculations.

Findings

Successfully implemented G-parity boundary conditions in lattice QCD.

Calculated I=2 ππ phase shifts using Lüscher's formula.

Demonstrated the feasibility of studying non-zero momentum states.

Abstract

To make the $\pi\pi$ state with non-zero relative momentum as the leading exponential, we impose anti-periodic boundary condition on the pion, which is implemented by imposing G-parity or H-parity on the quark fields at the boundary. With this, we calculate the I=2 $\pi\pi$ phase shift from lattice simulation by using L\"uscher's formula.