Path Integral Quantization of Landau-Ginzburg Theory

Hamilton-Jacobi approach for a constrained system is discussed. The equation of motion for a singular systems are obtained as total differential equations in many variables. The integrability conditions are investigated without using any gauge fixing condition. The path integral quantization for systems with finite degrees of freedom is applied to the field theories with constraints. The Landau-Ginzburg theory is investigated in details.Comment: 8 page

Decay of the pseudoscalar glueball into vector, axial-vector, scalar and pseudoscalar mesons

We resume the investigation of the ground-state pseudoscalar glueball, $J^{PC}=0^{-+}$, by computing its two- and three-body decays into vector and axial-vector quark-antiquark meson fields additional to scalar and pseudoscalar mesons through the construction of an interaction chiral Lagrangian that produces these decays. We evaluate the branching ratio, via a parameter-free calculation, by setting the mass of the pseudoscalar glueball to $2.6$ GeV as predicted by lattice QCD simulations. We duplicate the computation for the branching ratios for a pseudoscalar glueball mass $2.37$ GeV which matches to the resonance $X(2370)$ mass in the BESIII experiment suppress measuring. We observe that the $\rho\pi$ decay mode is the largest, followed by the $K^*(892)K$ one. Both of them are sizable and could explain the $\rho\pi$ puzzle of the charmonium state $\psi(2S)$. The present channels and states are potentially reached and are interesting for the running BESIII and Belle-II experiments and the planned PANDA experiment at FAIR/GSI which will be able to detect the pseudoscalar glueball within the accessible energy range.Comment: 11 pages, 2 tables, 1 figur

Decays of open charmed mesons in the extended Linear Sigma Model

We enlarge the so-called extended linear Sigma model (eLSM) by including the charm quark according to the global $U(4)_r\times U(4)_l$ chiral symmetry. In the eLSM, besides scalar and pseudoscalar mesons, also vector and axial-vector mesons are present. Almost all the parameters of the model were fixed in a previous study of mesons below 2 GeV. In the extension to the four-flavor case, only three additional parameters (all of them related to the bare mass of the charm quark) appear. We compute the (OZI-dominant) strong decays of open charmed mesons. The results are compatible with the experimental data, although the theoretical uncertainties are still large.Comment: 3 pages, 1 table, prepared for proceedings of the 13th International Workshop on Meson Production, Properties and Interaction, 29th May - 3rd June 2014, Cracow, POLAN

Hadronic decays of the (pseudo-)scalar charmonium states ηc\eta_c and χc0\chi_{c0} in the extended Linear Sigma Model

We study the phenomenology of the ground-state (pseudo-)scalar charmonia $\eta_c$ and $\chi_{c0}$ in the framework of a $U(4)_r \times U(4)_l$ symmetric linear sigma model with (pseudo-)scalar and (axial-) vector mesons. Based on previous results for the spectrum of charmonia and the spectrum and (OZI-dominant) strong decays of open charmed mesons, we extend the study of this model to OZI-suppressed charmonia decays. This includes decays into 'ordinary' mesons but also particularly interesting channels with scalar-isoscalar resonances $f_0(1370),\, f_0(1500),\, f_0(1710)$ that may include sizeable contributions from a scalar glueball. We study the variation of the corresponding decay widths assuming different mixings between glueball and quark-antiquark states. We also compute the decay width of the pseudoscalar $\eta_c$ into a pseudoscalar glueball. In general, our results for decay widths are in reasonable agreement with experimental data where available. Order of magnitude predictions for as yet unmeasured states and channels are potentially interesting for BESIII, Belle II, LHCb as well as the future PANDA experiment at the FAIR facility.Comment: 20 pages, 3 figures, 6 tabe

Phenomenology of charmed mesons in the extended Linear Sigma Model

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.Comment: 19 pages, 1 figure, 3 table