C.T. Sachrajda

A GENERAL METHOD FOR NON-PERTURBATIVE RENORMALIZATION OF LATTICE OPERATORS

We propose a non-perturbative method for computing the renormalization constants of generic composite operators. This method is intended to reduce some systematic errors, which are present when one tries to obtain physical predictions from the matrix elements of lattice operators. We also present the results of a calculation of the renormalization constants of several two-fermion operators, obtained, with our method, by numerical simulation of QCD, on a 16 3 × 32 lattice, at � = 6.0. The results of this simulation are encouraging, and further applications to four-fermion operators and to the heavy quark effective theory are proposed.

Physical results from 2+1 flavor domain wall QCD and SU(2) chiral perturbation theory

We have simulated QCD using 2+1 flavors of domain wall quarks on a (2.74fm)3 volume with an inverse lattice scale of a?1=1.729(28) GeV. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617 and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter BK and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulae from both approaches fit our data for light quarks, we find the higher order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory for accurate results. We use the masses of the ? baryon, and the ? and K mesons to set the lattice scale and determine the quark masses. We then find f?=124.1(3.6)stat(6.9)systMeV, fK=149.6(3.6)stat(6.3)systMeV and fK/f?=1.205(0.018)stat(0.062)syst. Using non-perturbative renormalization to relate lattice regularized quark masses to RI-MOM masses, and perturbation theory to relate these to MS¯ we find mMS¯ud(2GeV)=3.72(0.16)stat(0.33)ren(0.18)systMeV and mMS¯s(2GeV)=107.3(4.4)stat(9.7)ren(4.9)systMeV.

Twisted boundary conditions in lattice simulations

Abstract By imposing twisted boundary conditions on quark fields it is possible to access components of momenta other than integer multiples of 2 π / L on a lattice with spatial volume L 3 . We use chiral perturbation theory to study finite-volume effects with twisted boundary conditions for quantities without final-state interactions, such as meson masses, decay constants and semileptonic form factors, and confirm that they remain exponentially small with the volume. We show that this is also the case for partially twisted boundary conditions, in which (some of) the valence quarks satisfy twisted boundary conditions but the sea quarks satisfy periodic boundary conditions. This observation implies that it is not necessary to generate new gluon configurations for every choice of the twist angle, making the method much more practicable. For K → π π decays we show that the breaking of isospin symmetry by the twisted boundary conditions implies that the amplitudes cannot be determined in general (on this point we disagree with a recent claim).

The improvement of hadronic matrix elements in lattice QCD

Abstract We present a practical method to eliminate all terms of order a ( a being the lattice spacing) in the calculations of hadronic matrix elements with Wilson fermions. The method is based on an “improved” Wilson action combined with a suitable modification of the fermion operators. With this technique one expects to reduce significantly the systematic errors which arise due to the finiteness of the lattice spacing. We estimate that these errors will be reduced from about 20–30% (as found in recent numerical simulations) to just a few percent.

A lattice computation of the decay constant of the B-meson

Abstract We compute the decay constant of the B-meson, ƒB, on a 102 × 20 × 40 lattice at β = 6.0, with Wilson fermions, using 30 gauge field configurations, generated in the quenched approximation. For the propagator of the b-quark we keep only the leading term in the 1/mb expansion. To improve our results we use, as the interpolating fields for the B-meson, lattice operators which are “smeared” over several lattice sites. We observe a clear signal for the lightest B-meson state, and obtain the value ƒ B = 310 ± 25 ± 50 MeV , where the first error is statistical and the second represents our uncertainty in the value of the lattice spacing. This result, combined with earlier lattice measurements of ƒ D (ƒ D ⋍ 180 MeV , demonstrates that the asymptotic scaling law for the decay constants of heavy pseudoscalar mesons P, (i.e. ƒ P √M P ∼ constant ), has large corrections for charmed mesons. We estimate that the non-scaling corrections will reduce the above value of ƒB by about 25%.

Finite-volume effects for two-hadron states in moving frames

We determine the finite-volume corrections to the spectrum and matrix elements of two-hadron states in a moving frame, i.e., one in which the total momentum of the two hadrons is non-zero. The analysis is performed entirely within field theory and the results are accurate up to exponential corrections in the volume. Our results for the spectrum are equivalent to those of Rummukainen and Gottlieb which had been obtained using a relativistic quantum mechanical approach. A technical step in our analysis is a simple derivation of the summation formulae relating the loop summations over the momenta of the two hadrons in finite volume to the corresponding integrals in infinite volume.

The Kaon B-parameter and K-π and K-ππ transition amplitudes on the lattice

We present the results of a computation of the K0−K0 and ΔI = 32 K−π and K−ππ amplitudes in lattice QCD. The numerical simulation has been done using the standard one-plaquette action and Wilson fermions, in the quenched approximation. Combining the tesults obtained at β = 6 on a 102 × 20 × 40 lattice with 30 configurations with those at β = 6.2 on a 163 × 48 lattice with 15 configurations, we have obtained for the kaon B-parameterBK0 − K0 = 0.65 ± 0.15 at μ = 3 GeV. We have also evaluated the ΔI = 32K−π and K−π weak hamiltonian matrix elements. The relevant renormalized operator O4 has been found to satisfy soft-pion theorems and chiral lagrangian relations at the 30% level, and this makes us confident about our results. We find (〈K+|HW|π+π0〉/mK) = (7 ± 2) × 10−8 to be compared with the experimental value of 3.7 × 10−8.

Gauge-invariant smearing and matrix correlators using Wilson fermions at beta =6.2.

We present an investigation of gauge-invariant smearing for Wilson fermions in quenched lattice QCD on a

Meson spectroscopy and decay constants with Wilson fermions at β = 6.4

24^3 \times 48

Renormalization of lattice two-fermion operators with improved nearest-neighbour action

lattice at