A framework for the calculation of the $\Delta N\gamma^*$ transition form factors on the lattice

TL;DR

This paper develops a lattice QCD framework using non-relativistic effective field theory to extract $elta Neta transition form factors, including a L"uscher approach for unstable states and detailed analysis of kinematic and symmetry considerations.

Contribution

It introduces a novel lattice methodology for calculating $elta Neta transition form factors, incorporating complex plane analytic continuation and group-theoretical analysis.

Findings

Formulation of a L"uscher-like approach for unstable states.

Detailed treatment of kinematic settings and partial-wave mixing.

Analytic continuation techniques for complex plane analysis.

Abstract

Using the non-relativistic effective field theory framework in a finite volume, we discuss the extraction of the $\Delta N\gamma^*$ transition form factors from lattice data. A counterpart of the L\"uscher approach for the matrix elements of unstable states is formulated. In particular, we thoroughly discuss various kinematic settings, which are used in the calculation of the above matrix element on the lattice. The emerging L\"uscher-Lellouch factor and the analytic continuation of the matrix elements into the complex plane are also considered in detail. A full group-theoretical analysis of the problem is made, including the partial-wave mixing and projecting out the invariant form factors from data.