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

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

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

Quantization of Non-Abelian Yang-Mills Theories

A non-Abelian theory of fermions interacting with gauge bosons, the constrained system, is studied. The equations of motion for a singular system are obtained as total differential equations in many variables. The integrability conditions are investigated and the set of equations of motion is integrable. The Senjanovic and the canonical methods are used to quantize the system, and the integration is taken over the canonical phase space coordinates.Comment: 9 pages. arXiv admin note: substantial text overlap with arXiv:2003.06238; text overlap with arXiv:hep-th/0404036 by other author