Locally smeared operator product expansions in scalar field theory

We propose a new locally smeared operator product expansion to decompose nonlocal operators in terms of a basis of smeared operators. The smeared operator product expansion formally connects nonperturbative matrix elements determined numerically using lattice field theory to matrix elements of nonlocal operators in the continuum. These nonperturbative matrix elements do not suffer from power-divergent mixing on the lattice, which significantly complicates calculations of quantities such as the moments of parton distribution functions, provided the smearing scale is kept fixed in the continuum limit. The presence of this smearing scale complicates the connection to the Wilson coefficients of the standard operator product expansion and requires the construction of a suitable formalism. We demonstrate the feasibility of our approach with examples in real scalar field theory

Finite volume renormalization scheme for fermionic operators

We propose a new finite volume renormalization scheme. Our scheme is based on the Gradient Flow applied to both fermion and gauge fields and, much like the Schr\"odinger functional method, allows for a nonperturbative determination of the scale dependence of operators using a step-scaling approach. We give some preliminary results for the pseudo-scalar density in the quenched approximation.Comment: Proceedings of the 31st International Symposium on Lattice Field Theory, July 29 - August 3, 2013, Mainz, Germany; LaTeX source, 7 pages, 5 figure

Finite continuum quasi distributions from lattice QCD

We present a new approach to extracting continuum quasi distributions from lattice QCD. Quasi distributions are defined by matrix elements of a Wilson-line operator extended in a spatial direction, evaluated between nucleon states at finite momentum. We propose smearing this extended operator with the gradient flow to render the corresponding matrix elements finite in the continuum limit. This procedure provides a nonperturbative method to remove the power-divergence associated with the Wilson line and the resulting matrix elements can be directly matched to light-front distributions via perturbation theory.Comment: Eight pages, two figures. Proceedings of the 35th International Symposium on Lattice Field Theor

Unitary Limit of Two-Nucleon Interactions in Strong Magnetic Fields

Two-nucleon systems are shown to exhibit large scattering lengths in strong magnetic fields at unphysical quark masses, and the trends toward the physical values indicate that such features may exist in nature. Lattice QCD calculations of the energies of one and two nucleons systems are performed at pion masses of m(pi) similar to 450 and 806 MeV in uniform, time-independent magnetic fields of strength vertical bar B vertical bar similar to 10(19)-10(20) G to determine the response of these hadronic systems to large magnetic fields. Fields of this strength may exist inside magnetars and in peripheral relativistic heavy ion collisions, and the unitary behavior at large scattering lengths may have important consequences for these systems

Lattice Gauge Theory for Nuclear Physics

Quantum Chromodynamcs (QCD) is now established as the theory of strong interactions. A plethora of hadronic physics phenomena can be explained and described by QCD. From the early days of QCD, it was clear that low energy phenomena require a non-perturbative approach. Lattice QCD is a non-perturbative formulation of QCD that is particularly suited for numerical calculations. Today, supercomputers have achieved performance capable of performing calculations that allow us to understand complex phenomena that arise from QCD. In this talk I will review the most recent results, relevant to nuclear physics. In particular, I will focus on results relevant to the structure and interactions of hadrons. Finally, I will comment on the opportunities opening up as we approach the era of exaflop computing

Nucleon structure functions with domain wall fermions

We present a quenched lattice QCD calculation of the first few moments of the polarized and un-polarized structure functions of the nucleon. Our calculations are done using domain wall fermions and the DBW2 gauge action with inverse lattice spacing ~1.3GeV, physical volume approximatelly (2.4 fm)^3, and light quark masses down to about 1/4 the strange quark mass. Values of the individual moments are found to be significantly larger than experiment, as in past lattice calculations, but interestingly the chiral symmetry of domain wall fermions allows for a precise determination of the ratio of the flavor non-singlet momentum fraction to the helicity distribution, which is in very good agreement with experiment. We discuss the implications of this result. Next, we show that the chiral symmetry of domain wall fermions is useful in eliminating mixing of power divergent lower dimensional operators with twist-3 operators. Finally, we find the isovector tensor charge at renormalization scale 2 GeV in the MS bar scheme to be 1.192(30), where the error is the statistical error only.Comment: 41 pages, 17 figure