R. Horsley

NON-PERTURBATIVE RENORMALISATION OF COMPOSITE OPERATORS IN LATTICE QCD

Abstract We investigate the non-perturbative renormalisation of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields. These include operators which are relevant to the calculation of moments of hadronic structure functions. The computations are based on Monte Carlo simulations using quenched Wilson fermions.

Polarized and unpolarized nucleon structure functions from lattice QCD

We report on a high statistics quenched lattice QCD calculation of the deep-inelastic structure functions {ital F}{sub 1}, {ital F}{sub 2}, {ital g}{sub 1}, and {ital g}{sub 2} of the proton and neutron. The theoretical basis for the calculation is the operator product expansion. We consider the moments of the leading twist operators up to spin four. Using Wilson fermions the calculation is done for three values of {kappa}, and we perform the extrapolation to the chiral limit. The renormalization constants, which lead us from lattice to continuum operators, are calculated in perturbation theory to one loop order. {copyright} {ital 1996 The American Physical Society.}

Pion and Rho Structure Functions from Lattice QCD

We calculate the lower moments of the deep-inelastic structure functions of the {pi} and the {rho} meson on the lattice. Of particular interest to us are the spin-dependent structure functions of the {rho}. The calculations are done with Wilson fermions and for three values of the quark mass, so that we can perform an extrapolation to the chiral limit. {copyright} {ital 1997} {ital The American Physical Society}

Transverse spin structure of the nucleon from lattice QCD simulations

We present the first calculation in lattice QCD of the lowest two moments of transverse spin densities of quarks in the nucleon. They encode correlations between quark spin and orbital angular momentum. Our dynamical simulations are based on two flavors of clover-improved Wilson fermions and Wilson gluons. We find significant contributions from certain quark helicity flip generalized parton distributions, leading to strongly distorted densities of transversely polarized quarks in the nucleon. In particular, based on our results and recent arguments by Burkardt [Phys. Rev. D 72, 094020 (2005)], we predict that the Boer-Mulders function h(1/1), describing correlations of transverse quark spin and intrinsic transverse momentum of quarks, is large and negative for both up and down quarks.

Scaling laws, renormalization group flow and the continuum limit in non-compact lattice QED

Abstract We investigate the ultra-violet behavior of non-compact lattice QED with ligth staggered fermions. The main question is whether QED is a non-trivial theory in the continuum limit, and if not, what is its range of validity as a low-energy theory. Perhaps the limited range of validity could offer an explanation of why the fine-structure constant is so small. Non-compact QED undergoes a second-order chiral phase transition at strong coupling, at which the continuum limit can be taken. We examine the phase diagram and the critical behavior of the theory in detail. Moreover, we address the question as to whether QED confines in the chirally broken phase. This is done by investigating the potential between static external charges. We then compute the renormalized charge and derive the Callan-Symanzik β-function in the critical region. No ultra-violet stable zero is found. Instead, we find that the evolution of charge is well described by renormalized perturbation theory, and that the renormalized charge vanishes at the critical point. The consequence is that QED can only be regarded as a cut-off theory. We evaluate the maximum value of the cut-off as a function of the renormalized charge. Next, we compute the masses of fermion-antifermion composite states. The scaling behavior of these masses is well described by an effective action with mean-field critical exponents plus logarithmic corrections. This indicates that also the matter sector of the theory is non-interacting. Finally, we investigate and compare the renormalization group flow of different quantities. Altogether, we find that QED is a valid theory only for small renormalized charges.

Electric Dipole Moment of the Neutron from 2+1 Flavor Lattice QCD.

We compute the electric dipole moment d(n) of the neutron from a fully dynamical simulation of lattice QCD with 2+1 flavors of clover fermions and nonvanishing θ term. The latter is rotated into a pseudoscalar density in the fermionic action using the axial anomaly. To make the action real, the vacuum angle θ is taken to be purely imaginary. The physical value of dd(n) is obtained by analytic continuation. We find d(n)=-3.9(2)(9)×10(-16) θ  e cm, which, when combined with the experimental limit on d(n), leads to the upper bound |θ|≲7.4×10(-11).

A Lattice calculation of the nucleon's spin dependent structure function g(2) revisited

Our previous calculation of the spin-dependent structure function g_2 is revisited. The interest in this structure function is to a great extent motivated by the fact that it receives contributions from twist-two as well as from twist-three operators already in leading order of 1/Q^2 thus offering the unique possibility of directly assessing higher-twist effects. In our former calculation the lattice operators were renormalized perturbatively and mixing with lower-dimensional operators was ignored. However, the twist-three operator which gives rise to the matrix element d_2 mixes non-perturbatively with an operator of lower dimension. Taking this effect into account leads to a considerably smaller value of d_2, which is consistent with the experimental data.

Separating perturbative and non-perturbative contributions to the plaquette

Abstract We try to separate the perturbative and non-perturbative contributions to the plaquette of pure SU (3) gauge theory. To do this we look at the large- n asymptotic behaviour of the perturbation series in order to estimate the contribution of the as-yet uncalculated terms in the series. We find no evidence for the previously reported Λ 2 contribution to the gluon condensate. Attempting to determine the conventional Λ 4 condensate gives a value ∼ 0.03(2) GeV 4 , in reasonable agreement with sum rule estimates, though with very large uncertainties.

Probing nucleon structure on the lattice

Abstract.The QCDSF/UKQCD Collaboration has an ongoing program to calculate nucleon matrix elements with two flavours of dynamical O(a) improved Wilson fermions. Here we present recent results on the electromagnetic form factors, the quark momentum fraction 〈x〉 and the first three moments of the nucleons spin-averaged and spin-dependent generalised parton distributions, including preliminary results with pion masses as low as 320MeV.

First moments of the nucleon generalized parton distributions from lattice QCD

A. Sternbeck∗1† , M. Gockeler1, Ph. Hagler2, R. Horsley3, Y. Nakamura4, A. Nobile5, D. Pleiter1,5, P.E.L. Rakow6, A. Schafer1, G. Schierholz7, J. Zanotti8 1 Institut fur Theoretische Physik, Universitat Regensburg, 93040 Regensburg, Germany 2 Institut fur Kernphysik, Johannes Gutenberg-Universitat Mainz, 55128 Mainz, Germany 3 School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, UK 4 RIKEN Advanced Institute for Computational Science, Kobe, Hyogo 650-0047, Japan 5 JSC, Julich Research Centre, 52425 Julich, Germany 6 Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK 7 Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg, Germany 8 School of Chemistry and Physics, University of Adelaide, SA 5005, Australia E-mail: andre.sternbeck@ur.de