Interquark potential for the charmonium system with almost physical quark masses
Taichi Kawanai, Shoichi Sasaki
备注：
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, USA
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 Schrödinger 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_π=156 MeV.
The interquark potential in charmonium states is calculated for the first time in both the zero and non-zero temperature phases from a first-principles lattice QCD calculation. Simulations with two dynamical quark flavours were used with temperatures T in the range 0.4 T_c \lesssim T \lesssim 1.7 T_c, where T_c is the deconfining temperature. The correlators of point-split operators were analysed to gain spatial information about the charmonium states. A method, introduced by the HAL QCD collaboration and based on the Schroedinger equation, was applied to obtain the interquark potential. We fi…
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 $M_π\approx 156(7)$ MeV, and charm quark mass is tuned to reproduce the experimental values of $η_c$ and $J/…
We present spin-independent and spin-spin interquark potentials for the charmonium and charmed-strange mesons, which are calculated in 2+1 flavor lattice QCD simulations using the PACS-CS gauge configurations generated at the lightest pion mass ($M_π\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…
We present both spin-independent and -dependent parts of a central interquark potential for charmonium states, which is calculated in 2+1 flavor dynamical lattice QCD using the PACS-CS gauge configurations with a lattice cutoff of a^{-1}~2.2 GeV. Our simulations are performed with a relativistic heavy quark action for the charm quark at the lightest pion mass, M_π=156(7) MeV, in a spatial volume of 3fm^3. We observe that the spin-independent charmonium potential obtained from lattice QCD with almost physical quark masses is quite similar to the Conrnell potential used in non-relativistic poten…
The charmonium states at non-zero temperature are studied on anisotropic lattices with 2 dynamical quark flavours. Non-local operators are used to determine the Nambu-Bethe-Salpeter (NBS) wavefunctions via both conventional fitting methods and the Maximum Entropy Method. The interquark potential is determined from the solution of the Schrodinger equation, given the NBS wavefunction as input following the HAL QCD method. We observe a temperature dependent potential which becomes steeper as the temperature decreases.
We consider the potential-model approach for obtaining the spectrum of charmonium and bottomonium, replacing the usual gluon propagator by one obtained from lattice simulations. The resulting spectra are compared to the corresponding ones in the Cornell-potential case. We also estimate the interquark distance in both cases.
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We discuss the internal structure of radially excited charmonium mesons based on the equal-time and Coulomb gauge Bethe-Salpeter (BS) amplitudes, which are obtained in lattice QCD. Our simulations are performed with a relativistic heavy-quark action for the charm quark on the 2+1 flavor PACS-CS gauge configurations at the lightest pion mass, $M_π=156(7)$ MeV. The variational method is applied to the study of optimal charmonium operator for ground and first excited states of $S$-wave charmonia. We successfully calculate the BS wave functions of $η_c(2S)$ and $ψ(2S)$ states, as well as $η_c(1S)$…
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We propose a novel method for the determination of the interquark potential together with quark "kinetic mass'' $m_Q$ from the equal-time $Q\bar{Q}$ Bethe-Salpeter (BS) amplitude in lattice QCD. Our approach allows us to calculate spin-dependent $Q\bar{Q}$ potentials, e.g. the spin-spin potential, as well. In order to investigate several systematic uncertainties on such $Q\bar{Q}$ potentials, we carry out lattice QCD simulations using quenched gauge configurations generated with the single plaquette gauge action with three different lattice spacings, $a \approx$ 0.093, 0.068 and 0.047 fm, and …
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We extract (for the first time) the ratio of the gluon condensate < g^3f_{abc}G^3 >/< alpha_s G^2 > expressed in terms of the liquid instanton radius rho_c from charmonium moments sum rules by examining the effects of < alpha_s G^2 > in the determinations of both rho_c and the running MS mass m_c(m_c). Using a global analysis of selected ratios of moments at different Q^2=0, 4m_c^2 and 8m_c^2 and taking < alpha_s G^2 > from 0.06 GeV^4, where the estimate of rho_c is almost independent of < alpha_s G^2 >, we deduce: rho_c=0.98(21) GeV^{-1} which corresponds to < g^3f_{abc}G^3 > = (31+- 13) GeV^…
