Bottomonium spectroscopy motivated by general features of pNRQCD

Abstract

The bottomonium mass spectra are computed in the framework of potential non-relativistic quantum chromodynamics. The potential consists of a static term incorporating the Coulomb plus confinement part along with a correction term added non-perturbatively from pNRQCD, which is classified in powers of the inverse of the heavy quark mass O(1/m). The masses of excited bottomonia are calculated by perturbatively adding spin–hyperfine, spin–orbit and tensor components of one-gluon exchange interactions in powers of O(1/m 2). Calculated masses are found to be consistent with other theoretical studies and experimental data. The Regge trajectories of the calculated mass spectra are also constructed. The values of the wave functions are extracted and employed to calculate the electromagnetic transition widths and γγ, e + e −, light hadron and γγγ decay widths of several states at various leading orders, within the non-relativistic QCD formalism. Some of the experimentally reported states of bottomonium family like ϒ(10 860), ϒ(11 020) and X(10 610) are identified as mixed S–D wave and P wave states.

Bottomonium spectroscopy using Coulomb plus linear (Cornell) potential

“…we observe that our calculated di-photon decay width results for n 3 P 0 states are lower when compared to the decay widths predicted by other theoretical models, whereas decay widths for n 3 P 2 states are lower in comparison to decay widths predicted by Ref. [79,75,25,91,72,81,94,92].…”

Opportunities for studying C+ resonances at 3--12 GeV photon collider

“…Two-photon widths are successfully predicted with nonrelativistic quark models [21,22]. In the nonrelativistic limit two-photon widths of the meson are proportional to the square of the wave function or its derivative at the origin.…”

“…In Table 1 and Fig. 1 we list known cc and b b resonances with positive C-parity with experimental data from PDG [16] and summary of theoretical predictions on their masses and two-photon widths [18][19][20][21][22].…”

“…Values of the masses and two-photon width for various charmonium and bottomonium states from PDG and various theoretical predictions[18][19][20][21][22] …”

Mass Spectrum and Decay Constants of Heavy Quarkonia

“…The thresholds for the charmonium and bottomunium systems are approximately 3.71 and 10.50 GeV, respectively [2]. Many charmonium and bottomonium states below thresholds have been experimentally observed and theoretically studied through various relativistic and non-relativistic potential models [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and approaches like chiral perturbation theory [20], heavy quark effective field theory, lattice QCD [21][22][23][24][25][26][27][28][29][30][31], QCD sum rules [32][33][34][35][36][37][38], NRQCD [39][40][41], and dynamical equations based approaches like Bethe Salpeter and Dyson-Schwinger equations [41][42][43][44]. The heavy quarkonia were observed so far, still have many puzzles [17].…”