P.E.L. Rakow

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.

The nucleon mass in Nf=2 lattice QCD: Finite size effects from chiral perturbation theory

Abstract In the framework of relativistic SU(2) f baryon chiral perturbation theory we calculate the volume dependence of the nucleon mass up to and including O ( p 4 ). Since the parameters in the resulting finite size formulae are fixed from the pion mass dependence of the large volume nucleon masses and from phenomenology, we obtain a parameter-free prediction of the finite size effects. We present mass data from the recent N f =2 simulations of the UKQCD and QCDSF Collaborations and compare these data as well as published mass values from the dynamical simulations of the CP-PACS and JLQCD Collaborations with the theoretical expectations. Remarkable agreement between the lattice data and the predictions of chiral perturbation theory in a finite volume is found.

Generalized parton distributions from lattice QCD

We perform a quenched lattice calculation of the first moment of twist-two generalized parton distribution functions of the proton, and assess the total quark (spin and orbital angular momentum) contribution to the spin of the proton.

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).

Quenched spectroscopy with fixed-point and chirally improved fermions

Abstract We present results from quenched spectroscopy calculations with the parametrized fixed-point and the chirally improved Dirac operators. Both these operators are approximate solutions of the Ginsparg–Wilson equation and have good chiral properties. This allows us to work at small quark masses and we explore pseudoscalar-mass to vector-mass ratios down to 0.28. We discuss meson and baryon masses, their scaling properties, finite volume effects and compare our results with recent large scale simulations. We find that the size of quenching artifacts of the masses is strongly correlated with their experimentally observed widths and that the gauge and hadronic scales are consistent.

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}

A determination of the Lambda parameter from full lattice QCD

We present a determination of the QCD parameter Lambda in the quenched approximation (n_f=0) and for two flavours (n_f=2) of light dynamical quarks. The calculations are performed on the lattice using O(a) improved Wilson fermions and include taking the continuum limit. We find Lambda_{n_f=0} = 259(1)(20) MeV and Lambda_{n_f=2} = 261(17)(26) MeV}, using r_0 = 0.467 fm to set the scale. Extrapolating our results to five flavours, we obtain for the running coupling constant at the mass of the Z boson alpha_s(m_Z) = 0.112(1)(2). All numbers refer to the MSbar scheme.

Nucleon mass and sigma term from lattice QCD with two light fermion flavors

Abstract We analyze N f = 2 nucleon mass data with respect to their dependence on the pion mass down to m π = 157 MeV and compare it with predictions from covariant baryon chiral perturbation theory (BChPT). A novel feature of our approach is that we fit the nucleon mass data simultaneously with the directly obtained pion–nucleon σ-term. Our lattice data below m π = 435 MeV is well described by O ( p 4 ) BChPT and we find σ = 37 ( 8 ) ( 6 ) MeV for the σ-term at the physical point. Using the nucleon mass to set the scale we obtain a Sommer parameter of r 0 = 0.501 ( 10 ) ( 11 ) fm .