Phenomenology of charmed mesons in the extended Linear Sigma Model

TL;DR

This paper extends the linear sigma model to include four quark flavors, successfully predicting open charmed meson masses and mass splittings, highlighting the residual influence of chiral symmetry despite explicit breaking by the charm quark mass.

Contribution

The paper introduces a four-flavor extended linear sigma model incorporating charm quarks, providing quantitative predictions for charmed meson masses and splittings consistent with experimental data.

Findings

Open charmed meson masses agree with experimental data

Charmonia masses are underpredicted by about 10%

Correct prediction of spin-0 and spin-1 negative-parity open charm mass splitting

Abstract

We study the so-called extended linear sigma model for the case of four quark flavors. This model is based on global chiral symmetry and dilatation invariance and includes, besides scalar and pseudoscalar mesons, vector and axial-vector mesons. Most of the parameters of the model have been determined in previous work by fitting properties of mesons with three quark flavors. Only three new parameters, all related to the current charm quark mass, appear when introducing charmed mesons. Surprisingly, within the accuracy expected from our approach, the masses of open charmed mesons turn out to be in quantitative agreement with experimental data. On the other hand, with the exception of $J/\psi$, the masses of charmonia are underpredicted by about 10\%. It is remarkable that our approach correctly predicts (within errors) the mass splitting between spin-0 and spin-1 negative-parity open charm states. This indicates that, although the charm quark mass breaks chiral symmetry quite strongly explicitly, this symmetry still seems to have some influence on the properties of charmed mesons.