A Lattice Qcd Calculation Of The Charmonium Spectrum

We compare the results of a numerical lattice QCD calculation of the charmonium spectrum with the structure of a general non-relativistic potential model. To achieve this we form the non-relativistic reduction of derivative-based fermion bilinear interpolating fields used in lattice QCD calculations and compute their overlap with $c\bar{c}$ meson states at rest constructed in the non-relativistic quark model, providing a bound-state model interpretation for the lattice data. Essential gluonic components in the bound-states, usually called hybrids, are identified by considering interpolating fields that involve the gluonic field-strength tensor and which have zero overlap onto simple $c\bar{c}$ model states.

The calculation of the spectrum of QCD is key to an understanding of the strong interactions, and vital if we are to capitalize on the experimental study of the spectrum. In this paper, we describe progress towards understanding the spectrum of resonances of both mesons and baryons from lattice QCD, focusing in particular on the resonances of the $I=1/2$ nucleon states, and of charmonium mesons composed of the heavy charmed quarks.

It is emphasized in the 2015 NSAC Long Range Plan [1] that "understanding the structure of hadrons in terms of QCD's quarks and gluons is one of the central goals of modern nuclear physics." Over the last three decades, lattice QCD has developed into a powerful tool for ab initio calculations of strong-interaction physics. Up until now, it is the only theoretical approach to solving QCD with controlled statistical and systematic errors. Since 1985, we have proposed and carried out first-principles calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and large scale computer simulation. We started out by calculating the nucleon form factors − electromagnetic [2], axial-vector [3], ? NN [4], and scalar [5] form factors, the quark spin contribution [6] to the proton spin, the strangeness magnetic moment [7], the quark orbital angular momentum [8], the quark momentum fraction [9], and the quark and glue decomposition of the proton momentum and angular momentum [10]. These first round of calculations were done with Wilson fermions in the q̀uenched' approximation where the dynamical effects of the quarks in the sea are not taken into account in the Monte Carlo simulation to generate the background gauge configurations. Beginning in 2000, we have started implementing the overlap fermion formulation into the spectroscopy and structure calculations [11, 12]. This is mainly because the overlap fermion honors chiral symmetry as in the continuum. It is going to be more and more important to take the symmetry into account as the simulations move closer to the physical point where the u and d quark masses are as light as a few MeV only. We began with lattices which have quark masses in the sea corresponding to a pion mass at ̃300 MeV and obtained the strange form factors [13], charm and strange quark masses, the charmonium spectrum and the Ds meson decay constant fDs [14], the strangeness and charmness [15], the meson mass decomposition [16] and the strange quark spin from the anomalous Ward identity [17]. Recently, we have started to include multiple lattices with different lattice spacings and different volumes including large lattices at the physical pion mass point. We are getting quite close to being able to calculate the hadron structure at the physical point and to do the continuum and large volume extrapolations which is our ultimate aim. We have now finished several projects which have included these systematic corrections. They include the leptonic decay width of the [18], the N sigma and strange sigma terms [19], and the strange quark magnetic moment [20]. Over the years, we have also studied hadron spectroscopy with lattice calculations and in phenomenology. These include Roper resonance [21, 22], pentaquark state [23], charmonium spectrum [24, 14], glueballs [25, 26, 27, 28], scalar mesons a0(1450) and (600) [29] and other scalar mesons [30], and the 1−+ meson [31]. In addition, we have employed the canonical approach to explore the first order phase transition and the critical point at finite density and finite temperature [32, 33]. We have also discovered a new parton degree of freedom − the connected sea partons, from the path-integral formulation of the hadronic tensor [34, 35] which explains the experimentally observed Gottfried sum rule violation [34]. Combining experimental result on the strange parton distribution, the CT10 global fitting results of the total u and d anti-partons and the lattice result of the ratio of the momentum fraction of the strange vs that of u or d in the disconnected insertion, we have shown that the connected sea partons can be isolated [36]. In this final technical report, we shall present a few representative highlights that have been achieved in the project.

Working with a large basis of covariant derivative-based meson interpolating fields we demonstrate the feasibility of reliably extracting multiple excited states using a variational method. The study is performed on quenched anisotropic lattices with clover quarks at the charm mass. We demonstrate how a knowledge of the continuum limit of a lattice interpolating field can give additional spin-assignment information, even at a single lattice spacing, via the overlap factors of interpolating field and state. Excited state masses are systematically high with respect to quark potential model predictions and, where they exist, experimental states. We conclude that this is most likely a result of the quenched approximation.

Charmonium states provide a relevant source of knowledge for determining fundamental parameters of the Standard Model. An important aspect of understanding Quantum ChromoDynamics (QCD) is to make precise predictions of the hadron spectrum and to test them against high-quality experimental data. Our theoretical framework is Lattice QCD, which is considered to be the only known way to treat the full QCD Lagrangian non perturbatively from first principles, in a manner well suited to numerical computation. By using the Wilson-Clover action with N_f = 2 dynamical flavors, we will study the two charmonium mesons eta_c and J/ psi. We will also investigate some properties of their first radial excitations eta_c(2S) and psi(2S).

We use the dynamical gluon configurations provided by the MILC collaboration in a study of the charmonium spectrum and [psi] leptonic width. We examine sea quark effects on mass splitting and on the leptonic decay matrix element for light masses as low as m{sub s}/5, while keeping the strange quark mass fixed and the lattice spacing nearly constant.

Charmonium is an attractive system for the application of lattice QCD methods. While the sub-threshold spectrum has been considered in some detail in previous works, it is only very recently that excited and higher-spin states and further properties such as radiative transitions and two-photon decays have come to be calculated. I report on this recent progress with reference to work done at Jefferson Lab.

This book provides an update on our understanding of strong interaction, with theoretical and experimental highlights included. It is divided into five sections. The first section is devoted to the investigations into and the latest results on the mechanism of quark confinement. The second and third sections focus respectively on light and heavy quarks (effective field theories, Schwinger-Dyson approach and lattice QCD results). The fourth section deals with the deconfinement mechanism and quark-gluon plasma formation signals. The last section presents highlights of experiments, new physics beyond QCD, and nonperturbative approaches in other theories (strings and SUSY) that may be useful in QCD.