Chiral symmetry and hyperfine $q\overline{q}$ splittings

Abstract

Abstract. We briefly review theoretical calculations for the pseudoscalar-vector meson hyperfine splitting with no open flavor and also report a many body field theoretical effort to assess the impact of chiral symmetry in the choice of effective potentials for relativistic quark models. Our calculations predict the missing η b meson to have mass near 9400 M eV . The radial excitation ηc(2S) is in agreement with the measurements of the Belle and most recently Babar collaborations. Shortly after the discovery of the J/ψ it was understood that a rich spectroscopy of new mesons awaited classification. In this task the constituent quark model was a useful tool providing a simple periodic table where spectra and various radiative decays could be correlated with the help of a modest number of parameters. In this picture vector mesons are a qq pair, in an S or D wave, with spins parallel giving total angular momentum J = 1. Pseudoscalar mesons correspond to the J = 0 ground state with S-wave qq pairs spins antialigned. Ignoring the Dwave component, the only difference between both systems is the relative spin alignment. Any spectroscopic mass splitting can conveniently be incorporated in the quark model with a term, Aσ 1 · σ 2 that is reminiscent of the electron-nucleus spin-spin coupling, hence the name "hyperfine". This was immediately noted by Appelquist et al. [1] who predicted a charmonium splitting, ∆M (J/ψ − η c ), of about 65 M eV . They extracted the amplitude A by estimating the J/ψ electron-positron width, Γ e − e + , to be 4 keV . Using the currently accepted value of 5.3 keV , the splitting would be about 84 M eV , or about a factor of 2 smaller than the accepted experimental value of 3097 − 2980 ≃ 120 M eV . The need for a confining potential [2] was soon understood and calculations (by Appelquist and Politzer, and independently Schnitzer [3]) including a confining strength yielded a larger splitting (40 − 80 M eV ) than purely Coulombic potentials (15 − 20 M eV ). PACS.In retrospective we see that many of the early models utilized scalar confining potentials, which provided a good a On leave at University of Tuebingen, Inst. fuer Theoretische Physik, auf der Morgenstelle 14, D-72076 Tuebingen, Germany.spin-orbit coupling and radial excitations, but underestimated the hyperfine splittings. In the early eighties, and with the η c experimental state now known, this splitting became a benchmark for new model calculations [4,5,6,7] which now also predicted the corresponding splitting in bottomonium. The variation in these predictions is summarized in Table 1. Subsequently, further progress was achieved through improved, renormalized non-relativistic perturbative QCD calculations (NRPQCD) [8,9] which described bottomonium as a non-relativistic system. However, the calculated radii of most bb states are too large indicating that a Coulombic description, where the relativistic splittings scale linearly with the quark mass, is not reliable and that strong interactions still induce important corrections at this s...

Light exotics: Molecular resonances

“…The purpose of this work is to confirm the latter by a new theoretical analysis which also predicts that the π 1 (1600) is not a color exotic system. Our formalism, referred to as the Coulomb Gauge Model (CGM), has been successfully established in both the quark [18,19,20] and gluon [21] sectors and is based upon the exact QCD Hamiltonian in the Coulomb gauge [22] given by…”

“…with confinement described by a Cornell potential, V (r) = − αs r + σr, where the string tension, σ = 0.135 GeV 2 , and α s = 0.4 have been independently determined from conventional meson studies [18,19,20] within the same field theory approach. We also use the lowest order, unit value, for the Faddeev-Popov determinant in the H g term and treat the H qg interaction using perturbation theory.…”