Baryon and meson masses in the Nambu--Jona-Lasinio model: A Bayesian approach

TL;DR

This paper uses a Bayesian approach to constrain the Nambu--Jona-Lasinio model, successfully reproducing vacuum masses of mesons and baryons and revealing the importance of scalar diquark binding for accurate baryon mass predictions.

Contribution

It introduces a Bayesian framework to calibrate the NJL model parameters, providing new insights into the role of diquark interactions in baryon mass calculations.

Findings

Vacuum meson and baryon masses are well reproduced.

Scalar diquarks must be strongly bound for accurate baryon octet masses.

Scalar diquark coupling exceeds canonical Fierz values.

Abstract

We investigate the capabilities of the Nambu--Jona-Lasinio model to describe and reproduce fundamental vacuum properties of Quantum Chromodynamics, notably the hadronic spectrum. Mesons are described as quark-antiquark bound states at the level of the random phase approximation of the Bethe-Salpeter equation, while baryons are characterized as quark-diquark bound states within the static approximation of the Faddeev equation. Within a Bayesian framework, we constrain the model by phenomenologically known quantities and study the implications on its parameters and predictions in vacuum, as well as the correlations between the two. We find that within our framework, the vacuum masses of mesons and baryons can be reasonably well reproduced. Scalar diquarks need to be significantly bound in order to correctly reproduce the masses of the baryon octet, therefore enforcing values of the scalar diquark coupling larger than what is suggested by the canonical Fierz values. These findings could have important implications on the phenomenology of strongly-interacting matter at high temperature and density as well as of compact star physics.