Charge dependence of mesons with flavored contact-interaction couplings

TL;DR

The paper addresses how to incorporate flavor symmetry breaking into a covariant, confining contact-interaction model for QCD by deriving flavor-dependent couplings from one-loop background-field polarization and expressing them in terms of a single gluon-mass scale and common regulators. This framework is used to solve the gap equation and the Bethe-Salpeter equation for pseudoscalar mesons, enabling a unified description of $\pi$, $K$, $D$, $D_s$, and $\eta_c$ states with reduced free parameters. The results show good agreement with PDG values for masses and decay constants, predict realistic isospin splittings such as $m_{\pi^+}-m_{\pi^0} \approx 0.3$ MeV and $m_{K^0}-m_{K^\pm} \approx 2.3$ MeV, but reveal limitations for heavier quarkonia (e.g., $\eta_c$ and $D$-meson splittings) that may require additional scales or extensions to SU(5). Overall, the work demonstrates that a flavor-symmetry-informed CI model can serve as a computationally efficient, benchmarking tool for exploring hadron structure across light and heavy sectors. $m_g$ acts as the central scale relating all flavored couplings, providing a physically transparent link between constituent masses and bound-state observables.

Abstract

Effective interaction models of quantum chromodynamics, based on quark degrees of freedom, have been successfully employed to compute the properties of a large array of ground and excited meson and baryon states, along with their electromagnetic form factors, distribution functions and thermal behavior. Amongst them, the contact-interaction model, while non-renormalizable, implements confinement, satisfies Lorentz covariance and correctly describes chiral symmetry and its dynamical breaking pattern. Original studies focused on the light hadron sector in the isospin limit and were thereafter extended to heavy mesons and baryons. The strong effective couplings, as well as infrared and ultraviolet regulators, are flavor-dependent model parameters adjusted to reproduce hadronic observables. In contrast, in this study we combine SU(4) flavor-symmetry breaking couplings, obtained from one-loop vacuum polarization amplitudes in the presence of background constituent quark currents, with the contact-interaction model. This allows us to reduce the number of mass-dimensioned parameters and to consistently relate all flavored couplings to a single mass scale, while the masses and weak decay constants of the pions, kaons, $D$ and $D_s$ mesons are in good agreement with average reference values. Allowing for realistic isospin breaking, $m_d/m_u = 1.7$, in conjunction with the effect of the flavored couplings, leads to a mass splitting, $m_{π^+}- m_{π^0} \approx 0.3$ MeV, that agrees with lattice QCD values. For the kaons, the mass difference is $m_{K^0}- m_{K^\pm} \approx 2.3$ MeV, whereas $m_{D^\pm} - m_{D^0} \approx 0.5$ MeV and the $η_c$ is 6\% lighter than the experimental mass.