Scalar and Tensor Charmonium Resonances in Coupled-Channel Scattering from Lattice QCD.

We determine J^{PC}=0^{++} and 2^{++} hadron-hadron scattering amplitudes in the charmonium energy region up to 4100 MeV using lattice QCD, a first-principles approach to QCD. Working at m_{π}≈391 MeV, more than 200 finite-volume energy levels are computed and these are used in extensions of the Lüscher formalism to determine infinite-volume coupled-channel scattering amplitudes. We find that this energy region contains a single χ_{c0} and a single χ_{c2} resonance. Both are found as pole singularities on the closest unphysical Riemann sheet, just below 4000 MeV with widths around 70 MeV. The largest couplings are to kinematically closed D^{*}D[over ¯]^{*} channels in S-wave, and couplings to several decay channels consisting of pairs of open-charm mesons are found to be large and significant in both cases. Above the ground state χ_{c0}, no other scalar bound states or near-DD[over ¯] threshold resonances are found, in contrast to several theoretical and experimental studies.

Quark-Mass Dependence of Elastic πK Scattering from QCD.

We present a determination of the isospin-1/2 elastic πK scattering amplitudes in S and P partial waves using lattice quantum chromodynamics. The amplitudes, constrained for a large number of real-valued energy points, are obtained as a function of light-quark mass, corresponding to four pion masses between 200 and 400 MeV, at a single lattice spacing. Below the first inelastic threshold, the P-wave scattering amplitude is dominated by a single pole singularity that evolves from being a stable bound state at the highest quark mass into a narrow resonance that broadens as the pion and kaon masses are reduced. As in experiment, the S-wave amplitude does not exhibit an obviously resonant behavior, but instead shows a slow rise from threshold, which is not inconsistent with the presence of a κ/K_{0}^{⋆}(700)-like resonance at the considered quark masses. As has been found in analyses of experimental scattering data, simple analytic continuations into the complex energy plane of precisely determined lattice QCD amplitudes on the real energy axis are not sufficient to model-independently determine the existence and properties of this state. The spectra and amplitudes we present will serve as an input for increasingly elaborate amplitude analysis techniques that implement more of the analytic structure expected at complex energies.

Isoscalar ππ Scattering and the σ Meson Resonance from QCD.

We present for the first time a determination of the energy dependence of the isoscalar ππ elastic scattering phase shift within a first-principles numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum, we obtain the S-wave phase shift up to the KK[over ¯] threshold. Calculations are performed at two values of the u, d quark mass corresponding to m_{π}=236,391 MeV, and the resulting amplitudes are described in terms of a σ meson which evolves from a bound state below the ππ threshold at the heavier quark mass to a broad resonance at the lighter quark mass.

Searching for the rules that govern hadron construction.

Just as quantum electrodynamics describes how electrons are bound in atoms by the electromagnetic force, mediated by the exchange of photons, quantum chromodynamics (QCD) describes how quarks are bound inside hadrons by the strong force, mediated by the exchange of gluons. QCD seems to allow hadrons constructed from increasingly many quarks to exist, just as atoms with increasing numbers of electrons exist, yet such complex constructions seemed, until recently, not to be present in nature. Here we describe advances in the spectroscopy of mesons that are refining our understanding of the rules for predicting hadron structure from QCD.

Resonant π

We present the first ab initio calculation of a radiative transition of a hadronic resonance within quantum chromodynamics (QCD). We compute the amplitude for ππ→πγ^{⋆}, as a function of the energy of the ππ pair and the virtuality of the photon, in the kinematic regime where ππ couples strongly to the unstable ρ resonance. This exploratory calculation is performed using a lattice discretization of QCD with quark masses corresponding to m_{π}≈400 MeV. We obtain a description of the energy dependence of the transition amplitude, constrained at 48 kinematic points, that we can analytically continue to the ρ pole and identify from its residue the ρ→πγ^{⋆} form factor.

Resonances in coupled πK-ηK scattering from quantum chromodynamics.

Using a first-principles calculation within quantum chromodynamics, we are able to determine a pattern of strangeness=1 resonances that appear as complex singularities within coupled πK-ηK scattering amplitudes. We make use of numerical computation in the lattice discretized approach to the quantum field theory with light quark masses corresponding to m(π)∼400 MeV and at a single lattice spacing. The energy dependence of scattering amplitudes is extracted through their relationship to the discrete spectrum in a finite volume, which we map out in unprecedented detail.

Highly excited and exotic meson spectrum from dynamical lattice QCD.

Using a new quark-field construction algorithm and a large variational basis of operators, we extract a highly excited isovector meson spectrum on dynamical anisotropic lattices. We show how carefully constructed operators can be used to reliably identify the continuum spin of extracted states, overcoming the reduced cubic symmetry of the lattice. Using this method we extract, with confidence, excited states, states with exotic quantum numbers (0+-, 1-+, and 2+-), and states of high spin, including, for the first time in lattice QCD, spin-four states.

Two-photon decays of charmonia from lattice QCD.

We make the first calculation in lattice QCD of two-photon decays of mesons. Working in the charmonium sector, using the Lehmann-Symanzik-Zimmermann reduction to relate a photon to a sum of hadronic vector eigenstates, we compute form factors in both the spacelike and timelike domains for the transitions eta c --> gamma*gamma* and chi(c0) --> gamma*gamma*. At the on-shell point, we find approximate agreement with experimental world-average values.