Three-body interactions from the finite-volume QCD spectrum

Ruairí Brett,Andrei Alexandru,Frank X Lee,Chris Culver,Michael Döring,Maxim Mai

doi:10.1103/physrevd.104.014501

Ruairí Brett, Andrei Alexandru + Show 4 more

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https://doi.org/10.1103/physrevd.104.014501

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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.

Highlights

It is a long-term quest of nuclear physics to understand hadron interactions as they emerge from quark and gluon dynamics
Formalisms that connect the finite-volume QCD spectrum and infinite-volume three-body scattering amplitude, called quantization conditions, are reaching maturity. Such progress has allowed the possibility of extracting quantitative information on the three-body force from first principles
We find that the heavy quark mass results are compatible with expectations from leading order chiral perturbation theory (ChPT), but our lower mass results are in tension with the predictions

Summary

Introduction

It is a long-term quest of nuclear physics to understand hadron interactions as they emerge from quark and gluon dynamics. The main challenge lies in the fact that perturbation theory fails at low energies, because the interactions are strong. Lattice QCD (LQCD) offers a nonperturbative method which has quarks and gluons as fundamental degrees of freedom while keeping all systematics under control. LQCD calculations are performed in a finite volume and in Euclidean time, leaving only indirect methods to study real-time infinite-volume scattering. The relation between finite-volume spectrum and infinite-volume scattering amplitudes is called quantization condition, which has been known for two-hadron systems since the pioneering work of Lüscher [1]. The last decade has witnessed significant progress using this approach for a variety of interacting two-particle systems. Recently has the quantization condition been extended to the threehadron sector

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