Covariant spectator theory of quark-antiquark bound states: Mass spectra and vertex functions of heavy and heavy-light mesons

Abstract

We use the covariant spectator theory with an effective quark-antiquark interaction, containing Lorentz scalar, pseudoscalar, and vector contributions, to calculate the masses and vertex functions of, simultaneously, heavy and heavy-light mesons. We perform least-square fits of the model parameters, including the quark masses, to the meson spectrum and systematically study the sensitivity of the parameters with respect to different sets of fitted data. We investigate the influence of the vector confining interaction by using a continuous parameter controlling its weight. We find that vector contributions to the confining interaction between 0% and about 30% lead to essentially the same agreement with the data. Similarly, the light quark masses are not very tightly constrained. In all cases, the meson mass spectra calculated with our fitted models agree very well with the experimental data. We also calculate the mesons wave functions in a partial wave representation and show how they are related to the meson vertex functions in covariant form.

arXiv comment23 pages, 10 figures. Minor corrections of previous version. To be published in Phys. Rev. D

References in corpus (52)

• Big-Bang Nucleosynthesis
• Heavy quarkonium: progress, puzzles, and opportunities
• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• Effective field theories for heavy quarkonium
• QCD and strongly coupled gauge theories: challenges and perspectives
• pi- and K-meson Bethe-Salpeter Amplitudes
• Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
• Baryons as relativistic three-quark bound states
• Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD
• The $\pi$, $K^{+}$, and $K^0$ electromagnetic form factors
• The Upsilon spectrum and m_b from full lattice QCD
• Towards the glueball spectrum from unquenched lattice QCD
• Charmonium excited state spectrum in lattice QCD
• Pseudoscalar Meson Radial Excitations
• Covariant spectator theory of np scattering: Phase shifts obtained from precision fits to data below 350 MeV
• Heavy Quarkonium in a Holographic Basis
• Ground-state Spectrum of Light-quark Mesons
• Survey of heavy-meson observables
• The Upsilon spectrum and the determination of the lattice spacing from lattice QCD including charm quarks in the sea
• Vector meson form factors and their quark-mass dependence
• On unifying the description of meson and baryon properties
• Quarkonium as relativistic bound state on the light front
• Electromagnetic properties of ground and excited state pseudoscalar mesons
• Perspective on rainbow-ladder truncation
• QCD modeling of hadron physics
• Relativistic calculation of the triton binding energy and its implications
• Spectra of heavy quarkonia in a Bethe-Salpeter-equation approach
• Quarkonium mass splittings in three-flavor lattice QCD
• Spectra of heavy mesons in the Bethe-Salpeter approach
• Bottomonium spectrum at order v^6 from domain-wall lattice QCD: precise results for hyperfine splittings
• Bottomonium in a Bethe-Salpeter-equation study
• Excited hadrons on the lattice: Mesons
• First Observation of a Upsilon(1D) State
• Properties of light scalar mesons from lattice QCD
• A Relativistic Quark Model for Mesons with an Instanton-Induced Interaction
• Hadron Physics and the Dyson--Schwinger Equations of QCD
• Confinement, quark mass functions, and spontaneous chiral symmetry breaking in Minkowski space
• Covariant spectator theory of np scattering: Effective range expansions and relativistic deuteron wave functions
• A covariant study of tensor mesons
• Observation of the ${\rm Y}(1^3{D}_J)$ Bottomonium State through Decays to ${\pi }^{+}{\pi }^{-}{\rm Y}(1S)$
• Quark-Antiquark Bound States in the Relativistic Spectator Formalism
• The bottomonium spectrum from lattice QCD with 2+1 flavors of domain wall fermions
• The $D_{sJ}^{\ast }(2860)$ Mesons as Excited D-wave $c\bar{s}$ States
• Lattice Study of Low-lying Nonet Scalar Mesons in Quenched Approximation
• Linear confinement in momentum space: singularity-free bound-state equations
• Chiral symmetry and pi-pi scattering in the Covariant Spectator Theory
• Higher angular momentum states of bottomonium in lattice NRQCD
• Applications of Two-Body Dirac Equations to the Meson Spectrum with Three versus Two Covariant Interactions, SU(3) Mixing, and Comparison to a Quasipotential Approach
• On a new approach to meson phenomenology with the Bethe-Salpeter equation
• Covariant Spectator Theory of heavy-light and heavy mesons and the predictive power of covariant interaction kernels
• Unified covariant treatment of hyperfine splitting for heavy and light mesons
• The stability of the spectator, Dirac, and Salpeter equations for mesons

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