Mixing and mq dependence of axial vector mesons in the Coulomb gauge QCD model

Abstract

We discuss pure qq axial-vector mesons in the Tamm-Dancoff approximation of the Coulombgauge QCD model from NCSU. While recent studies have put emphasis in configuration mixing with open meson-meson channels, we here concentrate on the simpler closed-channel problem and follow the 1 + mixing through a wide range of quark masses. We also examine their radial excitations and discuss with them the concept of insensitivity to chiral symmetry breaking.

Bottom-charmed meson spectrum from a QCD approach based on the Tamm-Dancoff approximation

“…For a detailed discussion, we refer the reader to Refs. [36,46]. In this regard, it deserves to be cited that very recent ðn f ¼ 2 þ 1 þ 1Þ-lattice QCD calculations obtained estimations for the charm quark mass by about 980-995 MeV [49,50], which are close to the one that we utilize.…”

“…The vacuum is represented as a coherent BCS ground state with quark and gluon Cooper pairs (condensates), and the hadrons interpreted as quasiparticle excitations. This approach has been successfully applied to the description of properties of some types of light and heavy mesons, glueballs, gluelumps, hybrids, and tetraquarks [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. These reports demonstrate that this model is efficient in retrieving the essential aspects of QCD with a minimal number of free parameters (current quark masses and dynamical constants) and yielding reasonable predictions.…”

“…Let us start by introducing the formalism to be used in the analysis of the B c -meson spectrum. It is a Coulomb gauge QCD-inspired model whose effective Hamiltonian is given by [32][33][34][35][36][37][38]41,42,46,47]…”

“…Concerning the last procedure, we indicate to the reader the Appendix A of Ref. [46], in which the specific case of axial mesons is discussed. Notwithstanding, for completeness we express in detail the wave functions exploited in this work, which can be written as (again omitting the flavor indices)…”

“…That being so, this paper intends to contribute to the discussion and characterization of the B c -meson spectrum by employing a different formalism with respect to the analyses mentioned in the previous paragraph. The framework to be utilized is also known as the Coulomb gauge QCD model [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. This formulation is based on the exact QCD Hamiltonian in the Coulomb gauge, which is replaced by an effective Hamiltonian where the original nonperturbative confining and hyperfine interactions can be rearranged into calculable effective potentials between color densities and currents.…”