Walaa I. Eshraim In collaboration with Stanislaus Janowski, Francesco Giacosa and Dirk H. Rischke Xth Quark Confinement and the Hadron Spectrum, München, Germany, Oct Institut Für Theoretische PhysikGoethe Universität Frankfurt am Main

Quantum chromodynamic (QCD) is the theory of the strong interactions. QCD predicts colorless gluonic bound states. (the glueballs). Experimental candidate for glueballs exist, but no conclusive proof of their existence yet. Phenomenological importance. Lattice QCD prediction.

Lattice QCD calculations [C. Morningstar and M. J. Peardon, AIP Conf. Proc. 688, 220 (2004) [arXiv:nucl-th/ ]] [Y. Chen et al., Phys. Rev. D 73, (2006)] We study the extended linear sigma model with a pseudoscalar glueball,, which has a mass of about 2.6 GeV as predicted by lattice QCD calculation.

Two experiments related to our work : 1. PANDA experiment at the FAIR facility. It will be capable to scan the mass region above 2.5 GeV. 1. BESIII experiment. A pseudoscalar glueball with mass 2.37 GeV could be the resonance X(2370 )

An effective interacting Lagrangian with the glueball chiral symmetry where is a dimensionless coupling constant, Ğ is pseduoscalar glueball and is a multiplet of the scalar and pseudoscalar quark-antiquark states and are the generators of the group. The multiplet transforms as and it is invariant under but not under.

Consider the case of and the explicit representation of the scalar and pseudoscalar mesons. C. Amsler and F. E. Close, Phys. Rev. D 53 (1996) 295 [arXiv:hep-ph/ ]. W. J. Lee and D. Weingarten, Phys. Rev. D 61, (2000). [arXiv:hep- lat/ ]; F. E. Close and A. Kirk, Eur. Phys. J. C 21, 531 (2001). [arXiv:hep- ph/ ]. F. Giacosa, T. Gutsche, V. E. Lyubovitskij and A. Faessler, Phys. Rev. D 72, (2005). [arXiv:hep- ph/ ]. F. Giacosa, T. Gutsche, V. E. Lyubovitskij and A. Faessler, Phys. Lett. B 622, 277 (2005) [arXiv:hep- ph/ ]. F. Giacosa, T. Gutsche and A. Faessler, Phys. Rev. C 71, (2005) [arXiv:hep-ph/ ]. H. Y. Cheng, C. K. Chua and K. F. Liu, Phys. Rev. D 74 (2006) [arXiv:hep-ph/ ]. V. Mathieu, N. Kochelev and V. Vento, Int. J. Mod. Phys. E 18 (2009) 1 [arXiv: [hep-ph]].

The assignment of the quark-antiquark fields is as follows: (i) In the pseudoscalar fields (pion) and K(kaons). The bare fields are the non- strange and strange mixing contributions of the physical state and [W. I. Eshraim, S. Janowski, F. Giacosa and D. H. Rischke (2012) [arXiv: [hep-ph]].

(ii) In the scalar sector we assign the field to the physical isotriplete state (1450) and the kaons fields to the physical isodoublt state (1430). Finally, the non-strange and strange bare fields are assigned to the physical isoscalar resonances (1370) and (1710). The mixing of the bare fields is neglected.

Shifting the fields with *The value of mixing between unphysical is large. * The mixing of with Ğ is small so neglected it. [D. Parganlija, F. Giacosa and D. H. Rischke, Phys. Rev. D 82, (2010) [arXiv: [hep-ph]]. [ D. Parganlija, P. Kovacs, G. Wolf, F. Giacosa and D. H. Rischke, arXiv: [hep-ph].

A. Scenario with as a prediction for the PANDA experiment In this scenario we set the bare mass of the pseudoscalar glueball, according to the lightest pseudoscalar-isoscalar glueball obtained from lattice QCD simulations. B. Scenario with with respect to the BESIII experiment The calculations in second scenario are implemented with respect to the results of the experiment BESIII, where the resonance X(2370) was observed and therefore we used as the physical mass of the pseudoscalar glueball.

Branching ratios for the decay of the pseudoscalar glueball Ğ into three pseudoscalar mesons

The branching ratios of Ğ for the decays into a scalar and a pseudoscalar meson. where the total decays width

FIG. 1: Solid (blue) line: Total decay width of the pseudoscalar glueball with the bare mass as function of the coupling Dashed (red) line: Same curve for

In the case of in which the identification Ğ ≡ X(2370) has been made, we can indeed use the experimental knowledge on the full decay width to determine the coupling constant to be [M. Ablikim et al. (BES Collaboration), Phys. Rev. Lett. 95, (2005); N. Kochelev and D. P. Min, Phys. Lett. B 633, 283 (2006); M. Ablikim et al. (BES III Collaboration), Phys. Rev. Lett (2011).]

* Presentation of a globally chirally invariant effective lagrangian with scalar and pseudoscalar quark- antiquark states and a pseudoscalar glueball state. * Study of Decay : The decays of the pseudoscalar glueball with a mass above 2 GeV. * Two scenarios regarding the mass of the pseudoscalar glueball were investigated. * We have prediction which can be tested by experiment.