Charmonium Excited States From Lattice Qcd

We apply the variational method with a large basis of interpolating operators to demonstrate the feasibility of extracting multiple excited states in charmonium from lattice QCD. The calculation is performed in the quenched approximation to QCD, using the clover fermion action on an anisotropic lattice. A crucial element of our approach is a knowledge of the continuum limit of the interpolating operators, providing important additional information on the spin assignment of the states, even at a single value of the lattice spacing. Though we find excited-state masses that are systematically high with respect to the quark potential model, and the experimental masses where known, we attribute this as most likely an artifact of the quenched approximation.

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.

Properties of excited mesons are studied using a lattice QCD simulation of a system comparable to charmonium. We extract a spectrum of states, including those with manifestly exotic quantum numbers. Radiative transition form-factors are also computed, in particular the transition from exotic ·c1 to J /È 3 which is found to be large on the usual scale of magnetic dipole transitions.

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.

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).

Radiative transitions between charmonium states offer an insight into the internal structure of heavy-quark bound states within QCD. We compute, for the first time within lattice QCD, the transition form-factors of various multipolarities between the lightest few charmonium states. In addition, we compute the experimentally unobservable, but physically interesting vector form-factors of the [eta]{sub c}, J/[psi] and [chi]{sub c0}. To this end we apply an ambitious combination of lattice techniques, computing three-point functions with heavy domain wall fermions on an anisotropic lattice within the quenched approximation. With an anisotropy [xi] = 3 at a{sub s} ≈ 0.1 fm we find a reasonable gross spectrum and a hyperfine splitting ≈90 MeV, which compares favorably with other improved actions. In general, after extrapolation of lattice data at non-zero Q2 to the photopoint, our results agree within errors with all well measured experimental values. Furthermore, results are compared with the expectations of simple quark models where we find that many features are in agreement; beyond this we propose the possibility of constraining such models using our extracted values of physically unobservable quantities such as the J/[psi] quadrupole moment. We conclude that our methods are successful and propose to apply them to the problem of radiative transitions involving hybrid mesons, with the eventual goal of predicting hybrid meson photoproduction rates at the GlueX experiment.

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 author develops a novel analysis method for QCD sum rules (QCDSR) by applying the maximum entropy method (MEM) to arrive at an analysis with less artificial assumptions than previously held. This is a first-time accomplishment in the field. In this thesis, a reformed MEM for QCDSR is formalized and is applied to the sum rules of several channels: the light-quark meson in the vector channel, the light-quark baryon channel with spin and isospin 1/2, and several quarkonium channels at both zero and finite temperatures. This novel technique of combining QCDSR with MEM is applied to the study of quarkonium in hot matter, which is an important probe of the quark-gluon plasma currently being created in heavy-ion collision experiments at RHIC and LHC.