Potential description of charmonium and charmed-strange mesons from lattice QCD

Abstract

We present spin-independent and spin-spin interquark potentials for the charmonium and charmed-strange mesons, which are calculated in 2+1 flavor lattice QCD simulations using the PACS-CS gauge configurations generated at the lightest pion mass ($M_{\pi }\approx 156(7)$~MeV) with a lattice cutoff of $a^{-1}\approx 2.2$ GeV and a spatial volume of $(3\mathrm{fm}{)}^3$. For the charm quark, we use a relativistic heavy quark (RHQ) action with fine tuned RHQ parameters, which closely reproduce both the experimental spin-averaged mass and hyper-fine splitting of the $1S$ charmonium. The interquark potential and the quark kinetic mass, both of which are key ingredients within the potential description of heavy-heavy and heavy-light mesons, are determined from the equal-time Bethe-Salpeter (BS) amplitude. The charmonium potentials are obtained from the BS wave function of $1S$ charmonia (${\eta }_c$ and $J/\psi$ mesons), while the charmed-strange potential are calculated from the $D_s$ and $D_s^{\ast }$ heavy-light mesons. We then use resulting potentials and quark masses as purely theoretical inputs so as to solve the nonrelativistic Schrödinger equation for calculating accessible energy levels of charmonium and charmed-strange mesons without unknown parameters. The resultant spectra below the $D\bar{D}$ and $DK$ thresholds excellently agree with well-established experimental data.

23 pages, 13 figures

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Cited by in corpus (14)

• A review of the open charm and open bottom systems
• Heavy meson spectroscopy under strong magnetic field
• Non-linear Regge trajectories with AdS/QCD
• Cigar-shaped quarkonia under strong magnetic field
• Bethe-Salpeter wave functions of ${\eta }_c(2S)$ and $\psi (2S)$ states from full lattice QCD
• Models of $J/\Psi$ photo-production reactions on the nucleon
• Instanton effects on the heavy-quark static potential
• Dynamics of the quark-antiquark interaction and the universality of Regge trajectories
• Quark-diquark potential and diquark mass from Lattice QCD
• Survival probabilities of charmonia as a clue to measure transient magnetic fields
• Structure of heavy quarkonia in a strong magnetic field
• The charmed mesons in the region above 3.0 GeV
• Building diquark model from Lattice QCD
• Quarkonium spectra with magnetically induced anisotropic confinement