Chiral nonet mixing inπKscattering

Abstract

The underlying mixing of quark components of scalar mesons is probed in πK scattering within a generalized linear sigma model that contains two scalar meson nonets and two pseudoscalar meson nonets (a quark-antiquark and a four-quark). In the leading order of this model, all free parameters have been previously fixed using the mass spectra and several low-energy parameters known from experiment and consistent predictions have been made. As other predictions of the model, in the present work the isospins I= 1/2, 3/2 and J=0 projection of πK scattering amplitude (as well as phase shifts) are computed and compared with experiment. In the I=1/2 channel, it is shown that within the uncertainties of the model parameters a good agreement with experimental data up to an energy of about 1 GeV is obtained, whereas in the I=3/2 channel there is a better agreement with experiment which extends to about 1.4 GeV. The effect of final state interactions of πK in the I=1/2 channel is approximated by the K-matrix method and the poles of the unitarized scattering amplitude are found. It is shown that the model predicts a light and broad kappa resonance with a mass and decay width of 670-770 MeV and 640-750 MeV consistent with other prior works. Moreover, the scattering lengths in the I=1/2, 3/2 are also computed and shown to qualitatively agree with experiment. The overall predictions presented here further support previous findings that the scalar mesons below and above 1 GeV have substantial underlying mixings and that those below 1 GeV have dominant four-quark substructures while those above 1 GeV are closer to conventional P -wave quark-antiquark states.

Mixing among lowest-lying scalar mesons and scalar glueball

“…This model can greatly improve the results of SNLSM for decay widths, masses and quark components of mesons below 1 GeV and also in some cases above 1 GeV. Moreover, in GLSM, the obtained scattering amplitudes for ππ [53] and πK [54] are in good agreement with the experimental data up to 1 GeV. However, the predictions of the model for the mentioned scattering amplitudes for the energy region above 1 GeV is far from experiment.…”

“…At present there is no agreement in literature that among the two strongest candidates, i.e., f 0 (1500) and f 0 (1710), which one is the lightest scalar glueball. While in [23,[57][58][59][60][61], f 0 (1500) is believed to be mostly gluonic, in [62,63] f 0 (1710) was argued to be an unmixed scalar glueball. Moreover the mass obtained from Lattice calculations for the 0 ++ glueball candidate is around 1600 − 1700 MeV with the uncertainty of 100 MeV.…”

Contributions of $$ {K}_0^{\ast } $$(1430) and $$ {K}_0^{\ast } $$(1950) in the three-body decays B → Kπh

“…The kaon-pion scattering has been extensively studied in refs. [74][75][76][77][78][79][80] in recent years. While the primary source of the information on I = 1/2 S-wave Kπ system comes from the LASS experiment for the reaction K − p → K − π + n [81].…”

Abelian decomposition and glueball-quarkonium mixing in QCD

“…In the literature there have been diverse interpretations of the scalar mesons. One of the popular views is that f 0 (500) and f 0 (980) are the tetra-quark states [52][53][54][55][56][57][58][59][60][61][62][63], f 0 (1370) and f 0 (1500) are the mixed state [64][65][66][67][68][69][70], and f 0 (1710) is a scalar glueball [71][72][73]. Another view is that f 0 (1370), f 0 (1710), a 0 (1450), and K * 0 (1430) are the members of the flavor nonet, f 0 (1710) being mainly the ss state [74,75].…”