Charmonium-nucleon interaction from lattice QCD with a relativistic heavy quark action

Detailed information of the low-energy interaction between the charmonia ({\eta}c and J/{\psi}) and the nucleon is indispensable for exploring the formation of charmonium bound to nuclei. In order to investigate the charmonium-nucleon interactions at low energies, we adopt two essentially different approaches in lattice QCD simulations. The charmonium-nucleon potential can be calculated from the equal-time Bethe-Salpeter amplitude through the effective Schr\"odinger equation. This novel method is based on the same idea originally applied for the nucleon force by Aoki- Hatsuda-Ishii. Another approach is to utilize extended L\"uscher's formula with partially twisted boundary conditions, which allows us to calculate the s-wave phase shift at any small value of the relative momentum even in a finite box. We then extract model independent information of the scattering length and the effective range from the phase shift through the effective-range expansion. Our simulations are carried out at a lattice cutoff of $1/a \approx$ 2 GeV in a spatial volume of (3 fm)^3 with the non-perturbatively O(a)-improved Wilson fermions for the light quarks and a relativistic heavy quark action for the charm quark. Although our main results are calculated in quenched lattice calculations, we also present a preliminary full QCD result by using the 2+1 flavor gauge configurations generated by PACS-CS Collaboration. We have found that the charmonium-nucleon potential is weakly attractive at short distances and exponentially screened at large distances. We have also successfully evaluated both the scattering length and effective range from the charmonium-nucleon scattering phase shift.Comment: 13 pages, 9 figures; To appear in proceedings of 28th International Symposium on Lattice Field Theory, Lattice2010, June 14-19, 2010, Villasimius, Ital

Potential description of the charmonium from lattice QCD

We present spin-independent and spin-spin interquark potentials for charmonium states, that are calculated using a relativistic heavy quark action for charm quarks on the PACS-CS gauge configurations generated with the Iwasaki gauge action and 2+1 flavors of Wilson clover quark. The interquark potential with finite quark masses is defined through the equal-time Bethe-Salpeter amplitude. The light and strange quark masses are close to the physical point where the pion mass corresponds to $M_\pi \approx 156(7)$ MeV, and charm quark mass is tuned to reproduce the experimental values of $\eta_c$ and $J/\psi$ states. Our simulations are performed with a lattice cutoff of $a^{-1}\approx 2.2$ GeV and a spatial volume of $(3 {\rm fm})^3$. We solve the nonrelativistic Schr\"odinger equation with resulting charmonium potentials as theoretical inputs. The resultant charmonium spectrum below the open charm threshold shows a fairly good agreement with experimental data of well-established charmonium states.Comment: 12 pages, 4 figures, the Proceedings of the Conference "XIth Quark Confinement and the Hadron Spectrum", September 8 to 12, Saint-Petersburg State University, Russi

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

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 $(3~{\rm fm})^3$. 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 Schr\"odinger 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.Comment: 23 pages, 13 figure

Interquark potential for the charmonium system with almost physical quark masses

We study an interquark QQ^bar potential for the charmonium system, that is determined from the the equal-time and Coulomb gauge QQ^bar Bethe-Salpeter (BS) wavefunction through the effective Schr\"odinger equation. This novel approach enables us to evaluate a kinetic heavy quark mass m_Q and a proper interquark potential at finite quark mass m_Q, which receives all orders of 1/m_Q corrections on the static QQ^bar potential from Wilson loops, simultaneously. Precise information of the interquark potential for both charmonium and bottomonium states directly from lattice QCD provides us a chance to improve quark potential models, where the spin-independent interquark potential is phenomenologically described by the Cornell potential and the spin-dependent parts are deduced within the framework of perturbative QCD, from first-principles calculations. In this study, calculations are carried out in both quenched and dynamical fermion simulations. We first demonstrate that the interquark potential at finite quark mass calculated by the BS amplitude method smoothly approaches the conventional static heavy quark potential from Wilson loops in the infinitely heavy quark limit within quenched lattice QCD simulations. Secondly, we determine both spin-independent and -dependent parts of the interquark potential for the charmonium system in 2+1 flavor dynamical lattice QCD using the PACS-CS gauge configurations at the lightest pion mass, M_\pi=156 MeV.Comment: 7 pages, 5 figures; To appear in proceedings of 29th International Symposium on Lattice Field Theory, Lattice2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, California, US

Hadronic form factors for rare semileptonic BB decays

We discuss first results for the computation of short distance contributions to semileptonic form factors for the rare $B$ decays $B \to K^{*} \ell^+\ell^-$ and $B_s \to \phi \ell^+ \ell^-$. Our simulations are based on RBC/UKQCD's $N_f=2+1$ ensembles with domain wall light quarks and the Iwasaki gauge action. For the valence $b$-quark we chose the relativistic heavy quark action.Comment: 7 pages, 1 table, 3 figures, presented at the 33rd International Symposium on Lattice Field Theory (Lattice2015), July 14-18, 2015, Kobe, Japa