The meson spectrum in a covariant quark model

Abstract

Within the framework of the instantaneous Bethe-Salpeter equation, we present a detailed analysis of light meson spectra with respect to various parameterizations of confinement in Dirac space. Assuming a linearly rising quark-antiquark potential, we investigate two different spinorial forms (Dirac structures), namely 1 2 (1 I⊗1 I−γ 0 ⊗γ 0 ) as well as the UA(1)-invariant combination 1 2 (1 I⊗1 I−γ 5 ⊗ γ 5 − γ µ ⊗ γµ), both providing a good description of the ground state Regge trajectories up to highest observed angular momenta. Whereas the first structure is slightly prefered concerning numerous meson decay properties (see [41]), we find the UA(1)-invariant force to be much more appropriate for the description of a multitude of higher mass resonances discovered in the data of the Crystal Barrel collaboration during the last few years. Furthermore, this confinement structure has the remarkable feature to yield a linear dependence of masses on their radial excitation number. For many experimental resonances such a trajectory-like behaviour was observed by Anisovich et al. We can confirm that almost the same slope occurs for all trajectories. Adding the UA(1)-breaking instanton induced 't Hooft interaction we can compute the pseudoscalar mass splittings with both Dirac structures and for the scalar mesons a natural mechanism of flavour mixing is achieved. In the scalar sector, the two models provide completely different ground state and excitation masses, thus leading to different assignments of possibleqq states in this region. The scalar meson masses calculated with the structure 1 2 (1 I ⊗ 1 I − γ 5 ⊗ γ 5 − γ µ ⊗ γµ) are in excellent agreement with the K-matrix poles deduced from experiment by Anisovich and coworkers. *

Systematics of quark–antiquark states and scalar exotic mesons

“…We reject this Solution, for it contradicts both the linearity of f → ππ, KK, ηη, ηη ′ [8,11,57]. Moreover, model calculations of masses of the qq-mesons also point to a possible location of the 1 3 P 0 qq-nonet in the range 900-1300 MeV [86]. Still, by considering the nonet classification, the question arises about large ss-component in the lightest qq state: 67% in f bare 0 (700 ± 100) and (45 − 75)% in f 0 (980).…”

Baryons as relativistic three-quark bound states

“…Relativistic corrections to interquark potentials have been provided in Refs. [18,128,129], whilst attempts at formulating a covariant picture have been made for mesons [130,131] and baryons [132][133][134].…”

Splitting of theπ−ρspectrum in a renormalized light-cone QCD-inspired model

“…Another approach to the meson spectrum within a covariant quark model [13], using the framework of instantaneous Bethe-Salpeter equation, also pointed out the importance of the short-range attraction in the meson spectrum, due to the large mass splittings in the pseudo scalar (J = 0) sector, which in that work was attributed to the two-body point-like part of 't Hooft's instant induced U A (1) symmetry breaking interaction [14].…”