Progress on the three-particle quantization condition

TL;DR

This paper advances the relativistic three-particle quantization condition to broader theories, including transition processes and bound state energy shifts, aligning with non-relativistic results and enhancing theoretical tools for particle physics.

Contribution

It extends the relativistic three-particle quantization formalism to include 2->3 and 3->2 transitions and computes the finite-volume energy shift of Efimov-like states.

Findings

Inclusion of 2->3 and 3->2 transitions in the formalism

Agreement of finite-volume energy shift with non-relativistic results

Progress in extending the quantization condition to more theories

Abstract

We report progress on extending the relativistic model-independent quantization condition for three particles, derived previously by two of us, to a broader class of theories, as well as progress on checking the formalism. In particular, we discuss the extension to include the possibility of 2->3 and 3->2 transitions and the calculation of the finite-volume energy shift of an Efimov-like three-particle bound state. The latter agrees with the results obtained previously using non-relativistic quantum mechanics.