Partial Wave Mixing in Hamiltonian Effective Field Theory

TL;DR

This paper introduces a new method to simplify the finite-volume Hamiltonian in Hamiltonian effective field theory by analyzing partial-wave mixing, validated through an isospin-2 ππ scattering example.

Contribution

It proposes a novel approach to reduce Hamiltonian dimensionality in partial-wave mixing scenarios, offering a new perspective and matrices to quantify mixing effects.

Findings

Method effectively reduces Hamiltonian size.

Consistent results with Lüscher's method in ππ scattering.

Provides matrices reflecting partial-wave mixing degree.

Abstract

Within general partial-wave mixing, a method for reducing the high dimension of the finite-volume Hamiltonian from Hamiltonian effective field theory is proposed. This method provides a new viewpoint on partial-wave mixing, and a set of matrices that can reflect the degree of partial-wave mixing. An example of isospin-2 $\pi\pi$ scattering is used to examine the consistency between this method and L\"{u}scher's method.