Connecting Matrix Elements to Multi-Hadron Form-Factors

TL;DR

This paper reviews recent advances in lattice QCD methods for calculating multi-hadron form-factors and transition processes, emphasizing finite-volume techniques and their applications to resonances.

Contribution

It introduces finite-volume scaling relations for multi-hadron processes and demonstrates their validity through various checks, enabling rigorous definitions of resonance form-factors.

Findings

Finite-volume formalism accurately relates spectra to infinite-volume amplitudes.

Checks confirm the formalism in perturbative and bound state limits.

Framework allows rigorous definition of resonance form-factors.

Abstract

We discuss developments in calculating multi-hadron form-factors and transition processes via lattice QCD. Our primary tools are finite-volume scaling relations, which map spectra and matrix elements to the corresponding multi-hadron infinite-volume amplitudes. We focus on two hadron processes probed by an external current, and provide various checks on the finite-volume formalism in the limiting cases of perturbative interactions and systems forming a bound state. By studying model-independent properties of the infinite-volume amplitudes, we are able to rigorously define form-factors of resonances.