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 (Mπ ≈ 156(7) MeV) with a lattice cutoff of a −1 ≈ 2.2 GeV and a spatial volume of (3 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 (ηc and J/ψ mesons), while the charmed-strange potential are calculated from the Ds and D * s 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 DD and DK thresholds excellently agree with well-established experimental data.

Properties of Charmonium States in a Phenomenological Approach

“…The spin triplet states χ cJ are in good agreement with both experiment and other phenomenological models. The lattice QCD obtains the masses 20 − 25 MeV smaller than the experimental val-ues for these states [61]. We have also predicted masses of low lying D wave states which is reasonably in good agreement with available experimental data [56]and with other theoretical models [58], [59], [60] The spin-orbit and tensor potentials in eqn(6) are responsible for the splitting of the charmonium levels.…”

“…The mass of spin-singlet P-wave charmonium h c (1P ) is in good agreement with experiment and other theoretical models. However the lattice QCD predicts a mass of 3506 ± 6 MeV for h c (1P ) state which is slightly below the experimental value [61]. The spin triplet states χ cJ are in good agreement with both experiment and other phenomenological models.…”

“…The masses of radially excited Charmonium state η c (2S) and its triplet partner ψ(2S) calculated in our model are in good agreement with both experimental value and with other theoretical models. The lattice QCD calculations predict a slightly less mass value for η c (2S), (M (η c (2S)) = 3612 ± 9 MeV) and for ψ(2S)(M ψ(2S) = 3653 ± 12 MeV) [61]. It is clear from the table, that the mass of η c (3S) and its triplet partner calculated in our model is reasonably in good agreement with the experimental and with other model values.…”

Bethe-Salpeter wave functions of ηc(2S) and ψ(2S) states from

“…Although we only focused on the BS wave function of the ground state in the previous works [13][14][15][16], we here intend to obtain the BS wave function of the radially excited states. For this purpose, we adopt the variational method [17,18] to find an optimal meson operator O opt n , which solely couples to a specific (nth) state in Eq.…”

“…In the past several years, we have demonstrated that 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 successfully determined from the BS wave functions of the ground state of S-wave charmonium and charm-strange mesons [14][15][16]. A natural question arises: if we simply apply our proposed method on not only the ground state, but also its excited states, what result comes out, especially from the BS wave function of radially excited states?…”