Decay of charmonium states into a scalar and a pseudoscalar glueball

Walaa I Eshraim,L Bravina,Y Foka,S Kabana

doi:10.1051/epjconf/201612604017

Walaa I Eshraim, L Bravina + Show 2 more

Open Access

https://doi.org/10.1051/epjconf/201612604017

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Abstract

In the framework of a chiral symmetric model, we expand a U (4)R × U (4)L symmetric linear sigma model with (axial-)vector mesons by including a dilaton field, a scalar glueball, and the pseudoscalar glueball. We compute the decay width of the scalar charmonium state χ C 0 (IP ) into a predominantly scalar glueball f 0 (1710). We calculate the decay width of the pseudoscalar charmonium states ηC (IS ) into a predominantly scalar glueball f 0 (1710) as well as into a pseudoscalar glueball with a mass of 2.6 GeV (as predicted by Lattice-QCD simulations) and with a mass of 2.37 GeV (corresponding to the mass of the resonance X (2370)). This study is interesting for the upcoming PANDA experiment at the FAIR facility and BESIII experiment. Moreover, we obtain the mixing angle between a pseudoscalar glueball, with a mass of 2.6 GeV, and the charmonium state ηC .

Highlights

Charmonium is a bound state of a charm and an anti-charm quark
The study of the charmonium spectroscopy is very neccessary for understanding hadronic dynamics as the hydrogen atom [6] and the strong interaction physics
The dilaton field, a scalar glueball G, and a pseudoscalar glueball Gare included in the extended Linear Sigma model withscalar andvector mesons as seen in Refs. [17,18,19]

Summary

Introduction

Charmonium is a bound state of a charm and an anti-charm quark. It is one of the simplest bound states of Quantum Chromodynamic (QCD), the strong interaction theory of quarks and gluons, like positronium in Quantum Electrodynamic (QED). The pseudoscalar glueball has first been included into the eLSM via the interaction of the pseudoscalar glueball and (pseudo)scalar mesons in the case of N f = 3 as seen in Ref.[17]. The dilaton field, a scalar glueball G, and a pseudoscalar glueball Gare included in the extended Linear Sigma model (eLSM) with (pseudo)scalar and (axial-)vector mesons as seen in Refs. The last field included in the eLSM is the pseudoscalar glueball G ≡ |gg , with quantum numbers J pc = 0−+, via icGΦG(detΦ − detΦ†) This term couples the pseudoscalar glueball with (pseudo)scalar mesons. Where cGφ is a dimensionless coupling constant This term has been successfully studied in the decay of a pseudoscalar glueball into scalar and pseudoscalar mesons in the case of N f = 3 as seen in Ref.[17]. Where G0 is the gluon condensate equal to Λ ≈ 3.3 GeV [13]. φN, φS , and φC represent the chiralnonstrange, strange, and charm quark-antiquark condensates [14, 15], respectively

Results

Mixing of a pseudoscalar glueball G and a charmonium state ηC

Conclusion