Higher η c(nS) and η b(nS) mesons

Abstract

The hyperfine splittings in heavy quarkonia are studied using new experimental data on the di-electron widths. The smearing of the spinspin interaction is taken into account, while the radius of smearing is fixed by the known J/ψ − η c (1S) and ψ(2S) − η ′ c (2S) splittings and appears to be small, r ss ≈ 0.06 fm. Nevertheless, even with such a small radius an essential suppression of the hyperfine splittings (∼ 50%) is observed in bottomonium. For the nS bb states (n = 1, 2, ...6) the values we predict (in MeV) are 28, 12, 10, 6, 6, and 3, respectively. In single-channel approximation for the 3S and 4S charmonium states the splittings 16(2) MeV and 12(4) MeV are obtained.

Channel coupling in heavy quarkonia: Energy levels, mixing, widths, and new states

“…QQ , E n1 refer to the eigenfunctions and eigenvalues of the relativistic string Hamiltonian H 0 [9], for charmonium those were calculated in [12] and for bottomonium in [25]. In sector II the counterpart of (1) consists of Green's function of the pair (Qq), (qQ).…”

“…motion of these mesons). The numbers of ω Q , ω q are computed from the relativistic string Hamiltonian in [12,25]. In practical calculations it is more useful to exploit the (2 × 2) reduction of the bispinor wave functions in (4), as…”

“…Let us now turn to the relativistic string Hamiltonian (RSH) H 0 , derived from the gauge-invariant meson Green's function in QCD in the one-channel case in [9]. This Hamiltonian has been successfully applied to light mesons [26], heavy-light mesons [23,27], and heavy quarkonia [12,25] and has a simple form:…”

“…The potential V B (r) in (22) is derived in the framework of the Field Correlator Method [10][11][12] and is the sum of a pure scalar confining term and a gluon-exchange part,…”

“…First of all, it is the one-channel description of charmonia and bottomonia as cc, bb states in relativistic Hamiltonian formalism [9], developed in the framework of the Field Correlator method (FCM) [10] (see [11] for a review) and wave functions of stable states in x or p space cast in the numerical form. The latter have been accurately computed using this method with only universal input: the string tension σ, the current (pole) quark masses m i , and the strong coupling α s (q) [12].…”