Brian Russell Hill

An Effective Field Theory for the Calculation of Matrix Elements Involving Heavy Quarks

Abstract To measure matrix elements involving heavy quarks on the lattice, including fB and the B meson decay constant, the dependence on the heavy quark mass must first be extracted analytically. We present the resulting continuum effective field theory action and illustrate its utility by calculating the one-loop renormalization of an arbitrary heavy-light bilinear. We also discuss the limits of the approximation.

No more corrections to the topological mass term in QED3

We consider the theory of a photon interacting with scalar, spinor, and/or vector fields with arbitrary gauge-invariant interactions, in three spacetime dimensions. We show that to all orders in perturbation theory, all corrections to the topological mass term (beyond the known one-loop correction) vanish identically.

Static effective field theory: 1m corrections

Abstract The static approximation, which is the zeroth order approximation in an expansion in the inverse of the mass of a heavy quark, has previously been formulated in terms of an effective field theory action. In this formulation, corrections to the approximation can be systematically included by the addition of higher dimensional operators to the action. We determine the coefficients to one loop of the dimension-five operators incorporating the 1 m corrections to the theory.

Renormalization of heavy-light bilinears and fB for Wilson fermions

Abstract The B meson decay constant can be measured on the lattice using the static effective field theory. We present the order α s comparison of the matrix elements of heavy-light bilinears measured on the lattice using Wilson fermions to their counterparts in the continuum. The time component of the axial current determines f B . A subtlety associated with a linear divergence in the heavy quark self-energy is discussed.

Properties of B-Mesons in Lattice QCD

The results of an extensive study of {ital B}-meson properties in quenched lattice QCD are presented. The studies are carried out in the static quark limit where the {ital b} quark is taken to be infinitely massive. Our computations rely on a multistate smearing method introduced previously, with smearing functions generated from a relativistic lattice quark model. Systematic errors arising from excited state contamination, finite volume effects, and the chiral extrapolation for the light quarks are estimated. We obtain continuum results for the mass splitting {ital M}{sub {ital B}{ital s}}{minus}{ital M}{sub {ital B}{ital u}}=86{plus_minus}12(stat){sub {minus}9}{sup +7}(syst) MeV, the ratio of decay constants {ital f}{sub {ital B}{ital s}}/{ital f}{sub {ital B}{ital u}}=1.22{plus_minus}0.04(stat){plus_minus}0.02(syst). For the {ital B}-meson decay constant we separately exhibit the sizable uncertainties in the extrapolation to the continuum limit ({ital a}{r_arrow}0) and higher-order perturbative matching. We obtain {ital f}{sub {ital B}}=188{plus_minus}23(stat){plus_minus}15(syst){sub {minus}0}{sup +26}(extrap){plus_minus}14(pert) MeV.

Properties of {ital B} mesons in lattice QCD

The results of an extensive study of {ital B}-meson properties in quenched lattice QCD are presented. The studies are carried out in the static quark limit where the {ital b} quark is taken to be infinitely massive. Our computations rely on a multistate smearing method introduced previously, with smearing functions generated from a relativistic lattice quark model. Systematic errors arising from excited state contamination, finite volume effects, and the chiral extrapolation for the light quarks are estimated. We obtain continuum results for the mass splitting {ital M}{sub {ital B}{ital s}}{minus}{ital M}{sub {ital B}{ital u}}=86{plus_minus}12(stat){sub {minus}9}{sup +7}(syst) MeV, the ratio of decay constants {ital f}{sub {ital B}{ital s}}/{ital f}{sub {ital B}{ital u}}=1.22{plus_minus}0.04(stat){plus_minus}0.02(syst). For the {ital B}-meson decay constant we separately exhibit the sizable uncertainties in the extrapolation to the continuum limit ({ital a}{r_arrow}0) and higher-order perturbative matching. We obtain {ital f}{sub {ital B}}=188{plus_minus}23(stat){plus_minus}15(syst){sub {minus}0}{sup +26}(extrap){plus_minus}14(pert) MeV.

Tadpole-improved perturbation theory for heavy-light lattice operators.

Lattice calculations of matrix elements involving heavy-light quark bilinears are of interest in calculating a variety of properties of [ital B] and [ital D] mesons, including decay constants and mixing parameters. A large source of uncertainty in the determination of these properties has been uncertainty in the normalization of the lattice-regularized operators that appear in the matrix elements. Tadpole-improved perturbation theory, as formulated by Lepage and Mackenzie, promises to reduce these uncertainties below the ten percent level at one loop. In this paper we study this proposal as it applies to lattice-regularized heavy-light operators. We consider both the commonly used zero-distance bilinear and the distance-one point-split operator. A self-contained selection on the application of these results is included. The calculation reduces the value of [ital f][sub [ital B]] obtained from lattice calculations using the heavy quark effective theory.

B - B* splitting: A Test of heavy quark methods

Abstract We determine the one-loop QCD matching between lattice and continuum theories of the chromomagnetic moment operator. The operator is responsible for breaking the degeneracy of B and B ∗ mesons at order 1/ m in the static approximation.

Properties of low-lying heavy-light mesons

Abstract We present preliminary results for fB and masses of low-lying heavy-light mesons in the static limit. Calculations were performed in the quenched approximation using multistate smearing functions generated from a Hamiltonian for a spinless relativistic quark. The 2S-1S and 1P-1S mass splitting are measured. Using the 1P-1S charmonium splitting to set the overall scale, the ground state decay constant fB, is 319 ± 11 (stat) MeV.

The static approximation, staggered fermions and fB

Abstract Matrix elements of heavy-light bilinears measured on the lattice are compared to their continuum counterparts. The heavy quark is treated using the static effective field theory, and the light quark is treated as a staggered fermion. The time component of the axial current is the bilinear used to determine f B . We derive identities which simplify the calculations involving staggered fermions by reducing them to calculations involving naive fermions.