Two-current transition amplitudes with two-body final states

TL;DR

This paper develops a model-independent framework for two-current transition amplitudes involving hadrons, enabling precise extraction of form factors and resonance properties from lattice QCD data, with broad applicability in QCD and Standard Model tests.

Contribution

It introduces a general formalism for on-shell two-current amplitudes with two-hadron final states, valid for arbitrary Lorentz structures and multiple channels, facilitating lattice QCD analysis.

Findings

Derived analytic form of transition amplitudes summing all strong interactions

Extracted resonance form factors consistent with previous results

Established constraints from Ward-Takahashi identity for conserved currents

Abstract

We derive the on-shell form of amplitudes containing two external currents with a single hadron in the initial state and two hadrons in the final state, denoted as $1+\mathcal{J}\to 2+\mathcal{J}$. This class of amplitude is relevant in precision tests of the Standard Model as well as for exploring the structure of excited states in the QCD spectrum. We present a model-independent description of the amplitudes where we sum to all orders in the strong interaction. From this analytic form we are able to extract transition and elastic resonance form factors consistent with previous work as well as a novel Compton-like amplitude coupling a single particle state to a resonance. The results also hold for reactions where the one-particle state is replaced with the vacuum, namely $\mathcal{J}\to 2+\mathcal{J}$ amplitudes. We also investigate constraints placed upon the formalism for the case of a conserved vector current in the form of the Ward-Takahashi identity. The formalism presented here is valid for currents of arbitrary Lorentz structure and quantum numbers with spinless hadrons where any number of two-particle intermediate channels may be open. When combined with the appropriate finite-volume framework, this work facilitates the extraction of physical observables from this class of amplitudes via lattice QCD calculations.