Three-body interactions from the finite-volume QCD spectrum

TL;DR

This study analyzes the finite-volume QCD spectrum of three pions to extract three-body interactions, revealing mass-dependent behaviors and potential for constraining two-body amplitudes with sufficient data.

Contribution

It applies a relativistic three-particle quantization condition to lattice QCD data, providing new insights into three-body forces at different pion masses.

Findings

Data at 315 MeV pion mass shows near-zero contact term.

Data at 220 MeV pion mass exhibits significant energy dependence.

Results indicate potential to constrain two-body amplitudes with more energy levels.

Abstract

We perform a fit of the finite-volume QCD spectrum of three pions at maximal isospin to constrain the three-body force. We use the unitarity-based relativistic three-particle quantization condition, with the GWUQCD spectrum obtained at 315 MeV and 220 MeV pion mass in two-flavor QCD. For the heavier pion mass we find that the data is consistent with a constant contact term close to zero, whereas for the lighter mass we see a statistically significant energy dependence in tension with the prediction of leading order ChPT. Our results also suggest that with enough three-body energy levels, the two-body amplitude could be constrained.