H. Perlt

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.}

Moments of pseudoscalar meson distribution amplitudes from the lattice

Based on lattice simulations with two flavours of dynamical, O(a)-improved Wilson fermions we present results for the first two moments of the distribution amplitudes of pseudoscalar mesons at several values of the valence quark masses. By extrapolating our results to the physical masses of up/down and strange quarks, we find the first two moments of the K^+ distribution amplitude and the second moment of the pi^+ distribution amplitude. We use nonperturbatively determined renormalisation coefficients to obtain results in the MSbar scheme. At a scale of 4 GeV^2 we find a_2^pi=0.201(114) for the second Gegenbauer moment of the pions distribution amplitude, while for the kaon, a_1^K=0.0453(9)(29) and a_2^K=0.175(18)(47).

Flavour blindness and patterns of flavour symmetry breaking in lattice simulations of up, down and strange quarks

QCD lattice simulations with 2+1 flavours (when two quark flavours are mass degenerate) typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass and then the up-down quark mass to its respective physical value. Here we discuss an alternative method of tuning the quark masses, in which the singlet quark mass is kept fixed. Using group theory the possible quark mass polynomials for a Taylor expansion about the flavour symmetric line are found, first for the general 1+1+1 flavour case and then for the 2+1 flavour case. This ensures that the kaon always has mass less than the physical kaon mass. This method of tuning quark masses then enables highly constrained polynomial fits to be used in the extrapolation of hadron masses to their physical values. Numerical results for the 2+1 flavour case confirm the usefulness of this expansion and an extrapolation to the physical pion mass gives hadron mass values to within a few percent of their experimental values. Singlet quantities remain constant which allows the lattice spacing to be determined from hadron masses (without necessarily being at the physical point). Furthermore an extension of this programme to include partially quenched results is given.

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}

Renormalisation and off-shell improvement in lattice perturbation theory

Abstract We discuss the improvement of flavour non-singlet point and one-link lattice quark operators, which describe the quark currents and the first moment of the DIS structure functions respectively. Suitable bases of improved operators are given, and the corresponding renormalisation factors and improvement coefficients are calculated in one-loop lattice perturbation theory, using the Sheikholeslami–Wohlert (clover) action. To this order we achieve off-shell improvement by eliminating the effect of contact terms. We use massive fermions, and our calculations are done keeping all terms up to first order in the lattice spacing, for arbitrary m 2 /p 2 , in a general covariant gauge. We also compare clover fermions with fermions satisfying the Ginsparg–Wilson relation, and show how to remove O(a) effects off-shell in this case too, and how this is in many aspects simpler than for clover fermions. Finally, tadpole improvement is also considered.

Scaling of nonperturbatively O ( a ) -improved Wilson fermions: Hadron spectrum, quark masses, and decay constants

We compute the hadron mass spectrum, the quark masses, and the meson decay constants in quenched lattice QCD with nonperturbatively

Lattice operators for moments of the structure functions and their transformation under the hypercubic group

O(a)

Hyperon sigma terms for 2+1 quark flavours

-improved Wilson fermions. The calculations are done for two values of the coupling constant

Tuning the strange quark mass in lattice simulations

\ensuremath{\beta}=6.0