The design and implementation of large sets of spatially extended, gauge-invariant operators for use in determining the spectrum of baryons in lattice QCD computations are described. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used in all isospin channels. The operators are constructed to maximize overlaps with the low-lying states of interest, while minimizing the number of sources needed in computing the required quark propagators. Issues related to the identification of the spin quantum numbers of the states in the continuum limit are addressed.

Large sets of baryon interpolating field operators are developed for use in lattice QCD studies of baryons with zero momentum. Operators are classified according to the double-valued irreducible representations of the octahedral group. At first, three-quark smeared, local operators are constructed for each isospin and strangeness and they are classified according to their symmetry with respect to exchange of Dirac indices. Nonlocal baryon operators are formulated in a second step as direct products of the spinor structures of smeared, local operators together with gauge-covariant lattice displacements of one or more of the smeared quark fields. Linear combinations of direct products of spinorial and spatial irreducible representations are then formed with appropriate Clebsch-Gordan coefficients of the octahedral group. The construction attempts to maintain maximal overlap with the continuum SU2 group in order to provide a physically interpretable basis. Nonlocal operators provide direct couplings to states that have nonzero orbital angular momentum.

Energies for excited isospin I 1 2 and I 3 2 states that include the nucleon and families of baryons are computed using quenched, anisotropic lattices. Baryon interpolating field operators that are used include nonlocal operators that provide G 2 irreducible representations of the octahedral group. The decomposition of spin 5 2 or higher spin states is realized for the first time in a lattice QCD calculation. We observe patterns of degenerate energies in the irreducible representations of the octahedral group that correspond to the subduction of the continuum spin 5 2 or higher. The overall pattern of low-lying excited states corresponds well to the pattern of physical states subduced to the irreducible representations of the octahedral group.

We present a lattice calculation of the electromagnetic (EM) effects on the masses of light pseudoscalar mesons. The simulations employ 2+1 dynamical flavors of asqtad QCD quarks, and quenched photons. Lattice spacings vary from ≈ 0.12 fm to ≈ 0.045 fm. We compute the quantity , which parameterizes the corrections to Dashen's theorem for the K + -K 0 EM mass splitting, as well as K 0 , which parameterizes the EM contribution to the mass of the K 0 itself. An extension of the nonperturbative EM renormalization scheme introduced by the BMW group is used in separating EM effects from isospin-violating quark mass effects. We correct for leading finite-volume effects in our realization of lattice electrodynamics in chiral perturbation theory, and remaining finitevolume errors are relatively small. While electroquenched effects are under control for , they are estimated only qualitatively for K 0 , and constitute one of the largest sources of uncertainty for that quantity. We find = 0.78(1) stat ( + 8 −11 ) syst and K 0 = 0.035(3) stat (20) syst . We then use these results on 2+1+1 flavor pure QCD highly improved staggered quark (HISQ) ensembles and find m u /m d = 0.4529(48) stat ( +150 − 67 )

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