We present a detailed description of the extraction of the highly excited isovector meson spectrum on dynamical anisotropic lattices using a new quark-field construction algorithm and a large variational basis of operators. With careful operator construction, the combination of these techniques is used to identify the continuum spin of extracted states reliably, overcoming the reduced rotational symmetry of the cubic lattice. Excited states, states with exotic quantum numbers (0 +− , 1 −+ and 2 +− ) and states of high spin are resolved, including, for the first time in a lattice QCD calculation, spin-four states. The determinations of the spectrum of isovector mesons and kaons are performed on dynamical lattices with two volumes and with pion masses down to ∼ 400 MeV, with statistical precision typically at or below 1% even for highly excited states.

We present a calculation of the Nucleon and Delta excited state spectrum on dynamical anisotropic clover lattices. A method for operator construction is introduced that allows for the reliable identification of the continuum spins of baryon states, overcoming the reduced symmetry of the cubic lattice. Using this method, we are able to determine a spectrum of single-particle states for spins up to and including J = 7 2 , of both parities, the first time this has been achieved in a lattice calculation. We find a spectrum of states identifiable as admixtures of SU (6) ⊗ O(3) representations and a counting of levels that is consistent with the non-relativistic qqq constituent quark model. This dense spectrum is incompatible with quark-diquark model solutions to the "missing resonance problem" and shows no signs of parity doubling of states.

A new quark-field smearing algorithm is defined which enables efficient calculations of a broad range of hadron correlation functions. The technique applies a low-rank operator to define smooth fields that are to be used in hadron creation operators. The resulting space of smooth fields is small enough that all elements of the reduced quark propagator can be computed exactly at reasonable computational cost. Correlations between arbitrary sources, including multihadron operators can be computed a posteriori without requiring new lattice Dirac operator inversions. The method is tested on realistic lattice sizes with light dynamical quarks.

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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 ηc, J/ψ and χc0.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 ξ = 3 at as ∼ 0.1 fm we find a reasonable gross spectrum and a hyperfine splitting ∼ 90MeV, which compares favourably with other improved actions.In general, after extrapolation of lattice data at non-zero Q 2 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/ψ 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 calculate the light hadron spectrum in full QCD using two plus one flavor Asqtad sea quarks and domain wall valence quarks. Meson and baryon masses are calculated on a lattice of spatial size L ≈ 2.5 fm, and a lattice spacing of a ≈ 0.124 fm, for pion masses as light as mπ ≈ 300 MeV, and compared with the results by the MILC collaboration with Asqtad valence quarks at the same lattice spacing. Two-and three-flavor chiral extrapolations of the baryon masses are performed using both continuum and mixed-action heavy baryon chiral perturbation theory. Both the threeflavor and two-flavor functional forms describe our lattice results, although the low-energy constants from the next-to-leading order SU (3) fits are inconsistent with their phenomenological values. Nextto-next-to-leading order SU (2) continuum formulae provide a good fit to the data and yield and extrapolated nucleon mass consistent with experiment, but the convergence pattern indicates that even our lightest pion mass may be at the upper end of the chiral regime. Surprisingly, our nucleon masses are essentially lineaer in mπ over our full range of pion masses, and we show this feature is common to all recent dynamical calculations of the nucleon mass. The origin of this linearity is not presently understood, and lighter pion masses and increased control of systematic errors will be needed to resolve this puzzling behavior.

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.Comment: Fixed typos: normalisation of chi-squared, some operator projections in appendix, missing lattice irrep tabl

Future high-precision neutrino interaction experiments are needed to extend the current program of GeV-scale neutrino interactions and should include:1. A feasibility study of a high-statistics hydrogen or deuterium scattering experiment to supplement the currently poorly known (anti)neutrino-nucleon cross sections.2. The need for (anti)neutrino Ar scattering data in the energy range relevant for the DUNE experiment.3. The possibility of muon-based neutrino beams providing extremely accurate knowledge of the neutrino flux and an intense electron neutrino beam.• Current and future long-and short-baseline neutrino oscillation programs should evaluate and articulate what additional neutrino-nucleus interaction data is required to meet their ambitious goals and support experiments that provide this data.In addition to these general challenges facing the community, there are more specific concerns for particular topics and interaction channels. These are summarized below in the form of observations, problem description or recommendations. For a deeper insight, the reader is encouraged to consult the subsequent sections of this paper.