Mesons and Baryons: Parity Partners

TL;DR

This paper calculates the masses of negative parity mesons and baryons with various quark flavors using a symmetry-preserving quark-diquark model based on Schwinger-Dyson equations, extending previous positive parity studies.

Contribution

It introduces a novel application of a Schwinger-Dyson equations framework to compute negative parity baryon and meson spectra with heavy quarks, including diquark correlations.

Findings

Good agreement with experimental data for known states.

Predictions for unobserved heavier states.

Validated the model's consistency with QCD features.

Abstract

We calculate masses of light and heavy mesons as well as baryons of negative parity containing $u,d,s,c$ and $b$ quarks. It is an extension of our previous work where we had studied the positive parity baryons. We adopt a quark-diquark picture of baryons where the diquarks are non-pointlike with a finite spatial extension. The mathematical foundation for this analysis is implemented through a symmetry-preserving Schwinger-Dyson equations treatment of a vector-vector contact interaction, which preserves key features of quantum chromodynamics, such as confinement, chiral symmetry breaking, axial vector Ward-Takahashi identity and low-energy Goldberger-Treiman relations. This treatment simultaneously describes mesons and provides attractive correlations for diquarks in the $\overline{3}$ representation. Employing this model, we compute the spectrum and masses of all spin-1/2 and spin-3/2 baryons of negative parity, supplementing our earlier evaluation of positive parity baryons, containing 1, 2 or 3 heavy quarks. In the process, we calculate masses of a multitude of mesons and corresponding diquarks. Wherever possible, we make comparisons of our results with known experimental observations as well as theoretical predictions of several models and approaches including lattice quantum chromodynamics, finding satisfactory agreement. We also make predictions for heavier states not yet observed in the experiment.