Heavy-meson chiral Lagrangians, effective flavored couplings, SU(4) flavor breaking and their consequences

TL;DR

This paper reviews heavy meson effective theories, explores flavor symmetry breaking in couplings, and demonstrates how nonperturbative QCD approaches can improve understanding of meson decays and interactions.

Contribution

It provides a detailed analysis of flavor symmetry breaking in heavy meson couplings using Dyson-Schwinger and Bethe-Salpeter equations, with new results for $J/c$ couplings.

Findings

SU(4) flavor symmetry relations are invalidated by off-shell effects.

Flavor symmetry breaking significantly affects meson coupling dependencies.

New calculations for $J/c DD$ and $J/c D^*D$ couplings are presented.

Abstract

We review heavy quark flavor and spin symmetries, their exploitation in heavy meson effective theories and the flavored couplings of charmed and light mesons in the definition of their effective Lagrangians. We point out how nonperturbative continuum QCD approaches based on Dyson-Schwinger and Bethe-Salpeter equations can be used to calculate strong and leptonic decays of open-charm mesons and heavy quarkonia. The strong decay $D^*\to D\pi$ serves as a benchmark, as it is the only physical open-charm observable that can be related to the effective Lagrangian's couplings. Nonetheless, a quantitative comparison of $D^*D\pi$, $\rho DD$, $\rho D^*D$ and $\rho D^* D^*$ couplings for a range of off-shell momenta of the $\rho$-meson invalidates SU(4)$_F$ symmetry relations between these couplings. Thus, besides the breaking of flavor symmetry by mass terms in the Lagrangians, the flavor-symmetry breaching in couplings and their dependence on the $\rho$-meson virtuality cannot be ignored. We also take the opportunity to present new results for the effective $J/\psi DD$ and $J/\psi D^*D$ couplings. We conclude this contribution with a discussion on how the description of pseudoscalar and vector $D$, $D_s$, $B$ and $B_s$ meson properties can be drastically improved with a modest modification of the flavor-dependence in the Bethe-Salpeter equation.