Quarkonium spectra and quantum chromodynamics

Abstract

cFand bbspectra, including fine and hyperfine structures, are investigated with the use of a recently derived quantum-chromodynamic potential supplemented by a phenomenological longrange confining potential. Our theoretical results for all energy levels below the charm and bottom thresholds as well as their leptonic widths are in excellent agreement with experiments. We also give unambiguous theoretical predictions for unobserved bbenergy levels, and present reasonable estimates for energy levels of Our values of the strong coupling constant a, and the QCD scale parameter A are consistent with those extracted from high-energy positronelectron annihilation. (i) Introduction.Recently the quark-antiquark potential to the fourth order in perturbative quantum chromodynamics was obtained' with special emphasis on a precise determination of the spin-dependent interaction terms. We shall now investigate the cF, b& and gspectra, including their fine and hyperfine structures, with the use of this quantum-chromodynamic potential supplemented by a phenomenological long-range confining potentiaL2The confining potential was originally taken to be a spin-independent linear potential.3 But it was subsequently pointed out4" that relativistic corrections to the linear potential will give rise to spin-dependent terms, whose nature depends on whether we regard the confining potential as a vector or a scalar exchange. Our approach is based on the belief that the quark-antiquark potential at short distances can be determined fairly accurately by perturbative quantum chromodynamics, and therefore the confining terms should not unduly affect the potential at short distances, which requires the confining potential to be a scalar exchange.It is well known that results of physical interest obtained from perturbative quantum chromodynamics

Heavy quarkonium and nonrelativistic effective field theories

“…The above representation of the potential can be related with others found in the literature [12] by the use of the equations of motion.…”

Improved perturbative QCD approach to the bottomonium spectrum

“…The spin-dependent operators δU LS and δU S were derived in [15,16]. (Earlier incomplete results can be found in [17,11].) We derived δW N A from the result of [18] in the following way: We discard the logarithm originating from the IR divergence associated with the energy scale.…”

Variational estimation of the wave function at the origin for heavy quarkonium

“…It is noteworthy that in Gupta's papers [6,7] , the non-relativistic reduction was performed with respect to the power of p 2 /E 2 so that the singular r −3 potential term can be avoided. Our recent study indicates that the variational method can give some interesting sight to the singular 1 r 3 problem.…”