Erratum: Hyperfine splittings in bottomonium and theBq(q=n,s,c)mesons [Phys. Rev. D81, 071502 (2010)]

Abstract

A universal description of the hyperfine splittings (HFS) in bottomonium and the Bq (q = n, s, c) mesons is obtained with a universal strong coupling constant αs(µ) = 0.305(2) in a spin-spin potential. Other characteristics are calculated within the Field Correlator Method, taking the freezing value of the strong coupling independent of n f

Higher excitations of theDandDsmesons

“…The latter HF splitting was predicted in Ref. [27], if a ''universal'' coupling HF ¼ 0:31 is used in the HF potential.…”

Hyperfine splittings in the system

“…A comparison of the data with various model results is presented in the concluding section of this paper. This large hyperfine splitting has recently been investigated as a possible indicator of new physics [8], as a means of adjusting the value of the strong coupling parameter [9], and to fix the value of α S in an investigation other quarkonium states [10]. While further data should clarify these points, in this paper we investigate whether the model we employed in our 2007 paper [11], is robust enough to accommodate this new data.…”

“…Given the numerous approaches to the calculation of the bb hyperfine splittings, including the delta function approach of Ref. [10], our perturbative treatment is relevant to the overall discussion of the Υ (nS) − η b (nS) mass difference.…”

Hyperfine splitting and the experimental candidates forηb(2S)

“…Lattice QCD Gray et al [9] 61 ± 14 30 ± 19 Meinel [10] 60.3 ± 7.7 † 23.5 ± 4.7 † Meinel [10] 28.0 ± 4.2 ‡ Dowdall et al [11] 70 ± 9 35 ± 3 ‡ Lewis and Woloshyn [12,13] 56 ± 1 24 ± 3 Burch and Ehmann [14] 37 ± 11 13 ± 26 Burch and Ehmann [14] 71 ± 8⋄ 27 ± 17⋄ Potential models and related Badalian et al [15] 64.2 ± 0.4 36 ± 2 Badalian et al [15] 70.0 ± 0.4 36 ± 2 Badalian et al [16] 63.4 36 ± 2 Badalian et al [16] 71 1S splitting. As discussed previously, recent experiments [1,2,6] all measure a smaller value for the 1S splitting, which would imply that these lattice predictions are overestimates.…”

“…All of the models which postdate the discovery of the η b (1S) [15,16,28,37,46,48] are fit to the earlier 1S splittings measured at BaBar [3,5] and CLEO [4], or to the PDG averages at the time, and do not take account of the more recent, smaller values of Belle [2,6] and Dobbs et al [1] shown in Table I. Each of these models also predicts a 2S splitting somewhat larger than that observed at Belle.…”