Mixing among lowest-lying scalar mesons and scalar glueball

Abstract

Scalar glueball is implemented in single nonet linear sigma model (SNLSM) which basically includes lowest lying scalar and pseudoscalar mesons. Our new version of SNLSM involves mixing among scalar matter fields and glueball field which is enforced by scale symmetry considerations and the associated anomaly. Performing iterative Monte Carlo simulations, it is found that among the three candidates of scalar glueball, i.e., f0(1370), f0(1500) and f0 (1710), only f0 (1500) is predominately a glueball state with the mass prediction of 1.566 ± 0.046 GeV and the other two are predominately quarkonium. The ππ, πK and πη scatterings are reinvestigated in the presence of scalar glueball and it is found that the overall behavior of the real part of the K-matrix unitarized ππ scattering amplitude is more compatible with observed data compared with the case of SNLSM without glueball. We have also presented the predictions of the model for the masses and decay widths of the scalars obtained from the poles of the K-matrix unitarized ππ, πK and πη scattering amplitudes. Moreover the ππ scattering phase shift predicted by our model is compared with the prediction of generalized linear sigma model (GLSM) which contains two nonets of scalar mesons and two nonets of pseudoscalar mesons (a quark-antiquark nonet and a four-quark nonet). Despite the fact that at this stage our model lacks the second meson nonet above 1 GeV, its prediction for the ππ scattering phase shift is close to the prediction of GLSM for √ s < 1.1 GeV and in better agreement with experimental data for √ s > 1.1 GeV in comparison with GLSM.

Dispersive analysis of glueball masses

“…Another located at 1.50 GeV with a broader width about 200 MeV arises from the combined contribution of the f 0 (1370), f 0 (1500) and f 0 (1700) mesons, since f 0 (1500) with a narrow width cannot accommodate the broad peak alone. Our solution indicates that f 0 (500) and f 0 (980) contain some amount of gluonia, and the f 0 (1370), f 0 (1500) and f 0 (1700) mesons are the glue-rich states, in agreement with the multiple-resonance mixing picture for scalar mesons widely discussed in the literature [29][30][31][32][33][34][35]. The prediction for the scalar glueball mass around 1.50 GeV is close to those from sum rules [13,18,36] (but a bit lower than in [37]) and lattice QCD [38][39][40][41], and smaller than from holographic QCD [42].…”

Scalar-involved three-point Green functions and their phenomenology

“…Similar studies have been carried out in the last years, see for instance [45][46][47][48][49][50][51][52] and references therein.…”

Singlet-octet-glueball mixing of scalar mesons

“…The discovery of two scalar mesons, f 0 (1370) and f 0 (1500) (see [20] and references therein) stimulated Amsler and Close to propose a mixing scheme where two scalar q q mesons and the scalar glueball mix to create the three observed states f 0 (1370), f 0 (1500), f 0 (1710) [21,22]. This paper led to a large number of follow-up studies with different mixing schemes [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. These all have one property in common: they impose that the sum of the fractional glueball contributions from these three resonances adds up to one.…”