The hyperfine splittings in heavy-light mesons and quarkonia

Abstract

Hyperfine splittings (HFS) are calculated within the Field Correlator Method, taking into account relativistic corrections. The HFS in bottomonium and the Bq (q=n,s) mesons are shown to be in full agreement with experiment if a universal coupling αHF = 0.310 is taken in perturbative spin-spin potential. It gives M (B * ) − M (B) = 45.7(3) MeV, M (B * s ) − M (Bs) = 46.7(3) MeV (n f = 4), while in bottomonium ∆HF (bb) = M (Υ(9460)) − M (η b (1S)) = 63.4 MeV for n f = 4 and 71.1 MeV for n f = 5 are obtained; just latter agrees with recent BaBar data. For unobserved excited states we predict M (Υ(2S)) − M (η b (2S)) = 36(2) MeV, M (Υ(3S)) − M (η(3S)) = 28(2) MeV, and also M (B * c ) = 6334(4) MeV, M (Bc(2S)) = 6868(4) MeV, M (B * c (2S)) = 6905 (4) MeV. The mass splittings between D(2 3 S1) − D(2 1 S0), Ds(2 3 S1) − Ds(2 1 S0) are predicted to be ∼ 70 MeV, which are significantly smaller than in several other studies. * Electronic address: badalian@itep.ru † Electronic address: blg.bakker@few.vu.nl ‡ Electronic address: danilkin@itep.ru

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.…”

Variational analysis of mass spectra and decay constants for ground state pseudoscalar and vector mesons in the light-front quark model

“…While we use the common potential parameters (a, b, α s ) for all the mesons, it was shown in [32,41] …”

Two body relativistic wave equations

“…At a smaller extent the same can be said for ρ(770). See [109][110][111][112] for results using different methods.…”

“…Few years later, exploiting the QFT advances [22,23], these shifts were calculated up to the fifth order in the fine structure constant α [24,25]. However, in those calculations and in many of the others that followed, the final results were obtained in the semiclassical approximation: a crucial role was played by the value at the origin of the non relativistic Coulomb wave function, raising a long lasting question on the opportunity of adopting some kind of smearing of the corresponding δ-function [26,27]. In parallel with the investigations of the relativistic few body systems, the interest increased also for the analysis of their non-quantum counterpart, mainly based on the group symmetries and on the constraint theory [28][29][30]: the hope was to be able to catch the essence of the relationship between canonicity and relativistic covariance, in order to have sound guidelines to the quantization procedure.…”