Abstract
Mass spectra of bottomonium states are computed using the Instanton Induced potential obtained from Instanton Liquid Model for QCD vacuum and incorporating a stronger confinement term. Spin dependent interactions through confined one gluon exchange potential are incorporated to remove the mass degeneracy. The mass spectra of the bbar{b} states up to 4S states are found to be in good agreement with the values reported by PDG(2020). Mixing of nearby isoparity states are also studied. We found the state varUpsilon (10{,}860) as an admixture of 5^3S_1 and 6^3D_1 Upsilon states with mixing angle theta = 39.98^{circ } and the mixed state di-leptonic decay width is found to be 0.25 keV as against the width of 0.31 pm 0.07 keV reported by PDG. Further the state varUpsilon (11{,}020) is also found to be the admixture of 6^3S_1 and 5^3D_1 Upsilon states with the mixing angle theta = 51.69^{circ } and the di-leptonic decay width of the mixed state is obtained as 0.14 keV which is very close to the width of 0.13 pm 0.03 keV reported by PDG. Present results indicates that addition of confinement to the instanton potential is crucial for the determination of the mass spectroscopy of heavy hadrons.
Highlights
Quarkonia are regarded as the simple and appropriate hadronic systems to explore the QCD aspects at the low energy regimes through its spectroscopy [1,2,3,4]
We have compared our data set with the theoretical model predictions such as relativistic Dirac Model [93], QCD Relativistic functional approach [107] where authors have used two different methods rainbow-ladder truncation of Dyson– Schwinger and Bethe–Salpeter in search of the effects of the varying shapes of the effective running coupling on ground as well as excited states in the channels having quantum numbers J less than or equal to 3, Constituent quark model [41], Relativistic quark model [42,108], Relativistic potential model [100] and with the recent experimental data listed by PDG [43]
It is evident from the fact that the leptonic decay width (0.31 ± 0.07 keV) of Υ (10,860) is higher than that of Υ (4S) (0.272±0.029 keV) state [43]
Summary
Looking to the advances in the experimental side, it is necessary to review earlier theoretical attempts to understand the quarkonia systems. Such non-perturbative effects will increase at the larger distances [2,55] Such attempts are key to the lattice QCD calculations. As the form of the instanton potential contains the term which gives the non-perturbative effect at the larger distance as well as coloumbian type behaviour of the shorter distance together make it suitable for the study of the spectroscopy of bottomonium. The detailed description of the form of instanton potential for heavy quark can be found in [57] where authors have added the spin dependent attributes into it. The computed results are tabulated and compared with other available theoretical and experimental data and we draw important conclusions
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