Resonance form factors from finite-volume correlation functions with the external field method

TL;DR

This paper introduces a new lattice QCD method to extract resonance form factors by analyzing two-particle scattering in an external field, avoiding issues from triangle diagrams.

Contribution

It proposes a generalized Lüscher method for unstable particles in external fields, enabling direct calculation of resonance form factors from pole derivatives.

Findings

Resonance form factors obtained via the new method.

The approach circumvents triangle diagram complications.

Provides a practical framework for lattice calculations of unstable particles.

Abstract

A novel method for the extraction of form factors of unstable particles on the lattice is proposed. The approach is based on the study of two-particle scattering in a static, spatially periodic external field by using a generalization of the L\"uscher method in the presence of such a field. It is shown that the resonance form factor is given by the derivative of the resonance pole position in the complex plane with respect to the coupling constant to the external field. Unlike the standard approach, this proposal does not suffer from problems caused by the presence of the triangle diagram.