Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion

TL;DR

This paper develops a formalism to extract scattering phase shifts, mixing parameters, and transition amplitudes for multi-channel two-hadron systems in finite volume, enabling direct lattice QCD calculations of processes like proton-proton fusion.

Contribution

It extends finite volume formalism to multiple coupled channels and provides a method to determine transition amplitudes for processes such as proton-proton fusion from lattice QCD data.

Findings

Derived energy quantization conditions for multi-channel systems.

Extended formalism to three channels.

Demonstrated extraction of proton-proton fusion amplitude.

Abstract

The spectrum of a system with multiple channels composed of two hadrons with nonzero total momentum is determined in a finite cubic volume with periodic boundary conditions using effective field theory methods. The results presented are accurate up to exponentially suppressed corrections in the volume due to the finite range of hadronic interactions. The formalism allows one to determine the phase shifts and mixing parameters of pipi-KK isosinglet coupled channels directly from Lattice Quantum Chromodynamics. We show that the extension to more than two channels is straightforward and present the result for three channels. From the energy quantization condition, the volume dependence of electroweak matrix elements of two-hadron processes is extracted. In the non-relativistic case, we pay close attention to processes that mix the 1S0-3S1 two-nucleon states, e.g. proton-proton fusion (pp -> d+ e^+ + nu_e), and show how to determine the transition amplitude of such processes directly from lattice QCD.