Phenomenology of a pseudoscalar glueball and charmed mesons

TL;DR

This paper investigates the properties and decays of pseudoscalar glueballs and charmed mesons using an extended Linear Sigma Model, incorporating charm quarks to predict masses, decay constants, and decay widths relevant to lattice QCD and experimental data.

Contribution

It extends the Linear Sigma Model to include charm quarks and provides detailed predictions for glueball and charmed meson properties and decay processes.

Findings

Predicted pseudoscalar glueball mass at 2.6 GeV.

Calculated decay widths of glueballs and charmed mesons.

Determined masses and decay constants of charmed mesons.

Abstract

We study the vacuum properties of the pseudoscalar glueball and charmed mesons by using the so-called extended Linear Sigma Model (eLSM). This model includes scalar and pseudoscalar mesons, as well as vector and axial-vector mesons. We calculate the mesonic and baryonic decays of the pseudoscalar glueball, where we fixed its mass to $2.6$ GeV, as predicted by lattice-QCD simulations, and take a closer look at the scalar-isoscalar decay channel. As a second step, we enlarge the so-called extended linear Sigma model (eLSM) by including the charm quark to a global $U(4)_r\times U(4)_l$ chiral symmetry. Most of the parameters of the model have been determined in a previous work by fitting hadron properties involving three quark flavours. Only three new parameters, all related to the current charm quark mass, appear when introducing charmed mesons. We compute charmed mesons masses, weak decay constants, and strong decay widths of (open and hidden) charmed mesons. Moreover, we calculate the decay width of a pseudoscalar ground state charmonium $\eta_c$ into a pseudoscalar glueball and the decay widths of a scalar charmonium $\chi_{c0}$ into the scalar glueball.