Phenomenology of a pseudoscalar glueball and charmed mesons

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.