A. Duncan

ELECTROMAGNETIC SPLITTINGS AND LIGHT QUARK MASSES IN LATTICE QCD

A method for computing electromagnetic properties of hadrons in lattice QCD is described and preliminary numerical results are presented. The electromagnetic field is introduced dynamically, using a noncompact formulation. Employing enhanced electric charges, the dependence of the pseudoscalar meson mass on the (anti)quark charges and masses can be accurately calculated. At {beta}=5.7 with Wilson action, the {pi}{sup +}-{pi}{sup 0} splitting is found to be 4.9(3) MeV. Using the measured {ital K}{sup 0}-{ital K}{sup +} splitting, we also find {ital m}{sub {ital u}}/{ital m}{sub {ital d}}=0.512(6). Systematic errors are discussed. {copyright} {ital 1996 The American Physical Society.}

Nonperturbative physics from interpolating actions

Abstract We study the expansion in an artificial parameter δ which interpolates between a solvable theory at δ = 0 and the desired theory at δ = 1. The interpolating actions are form δS + (1− δ ) S 0 ; and augmented by an optimization procedure which introduces nonperturbative features into our results. This procedure relies on the freedom in choosing the best S 0 without affecting the convergent results at δ =1. Our linear interpolation is similar in spirit but differs in detail from the novel δ expansion that was recently formulated for scalar theories where the parameter 2(1+δ) was the power of the field in the interaction lagrangian. Here we use interpolating actions for the first time in fermionic and gauge theories.

Systematic ionic screening theory of macroions

Techniques of lattice field theory are utilized to compute the free energy of a system of fixed charged macroions surrounded by small (atomic size) mobile ions. The grand partition function for the simple ions is written down as a functional integral over a three‐dimensional auxiliary field. This functional integral is discretized on a lattice, and then subjected to saddle point analysis. The lowest order or ‘‘mean field’’ result of the analysis isolates a field which satisfies the Poisson–Boltzmann equation, and from which the Helmholtz free energy can be extracted. The formalism also provides a minimum principle for the Poisson–Boltzmann field that can be realized numerically by elementary annealing techniques. Most importantly, the mean field approximation can be systematically corrected by evaluating fluctuations around the saddle point to successive orders in an appropriate interaction strength. It is shown by numerical tests on a two‐macroion system that the hierarchy of corrections converges rapidl...

Asymptotic Behavior of Exclusive and Almost Exclusive Processes

Abstract The elastic nucleon form factor, the pion longitudinal structure function at x near 1, and wide angle elastic π-π scattering are discussed in the context of the renormalization group.

Light quarks, zero modes, and exceptional configurations

In continuum QCD, nontrivial gauge topologies give rise to zero eigenvalues of the massless Dirac operator. In lattice QCD with Wilson fermions, analogs of these zero modes appear as exactly real eigenvalues of the Wilson-Dirac operator, leading to poles in the quark propagator in the vicinity of the critical hopping parameter. It is shown that {open_quotes}exceptional configurations,{close_quotes} which arise in the quenched approximation at small quark mass, are the result of the fluctuation of the position of zero mode poles to subcritical values of hopping parameter on particular gauge configurations. We describe a procedure for correcting these lattice artifacts by first isolating the contribution of zero mode poles to the quark propagator and then shifting the subcritical poles to the critical point. This procedure defines a modified quenched approximation in which accurate calculations can be carried out for arbitrarily small quark masses. {copyright} {ital 1998} {ital The American Physical Society}

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.

Statistical mechanics of a Coulomb gas with finite size particles: A lattice field theory approach

A recently proposed lattice field theory approach to the statistical mechanics of a classical Coulomb gas [J. Chem. Phys. 97, 5653 (1992)] is generalized to treat gas particles of finite size. To do this, a repulsive Yukawa interaction between all pairs of gas particles is added to the usual pairwise Coulombic interactions of the gas particles with each other and also with an arbitrary collection of immobile charges. Such a model is directly relevant for understanding the energetics of systems composed of macroions in electrolytic solutions when the simple ions that comprise the electrolyte are sufficiently large. A field theoretic representation of the grand partition function for the modified Coulomb gas is derived. Two coupled three‐dimensional scalar fields are involved. Physically, one is related to the electrostatic potential and the other to the Yukawa potential. The field theory expression, once discretized onto an appropriate lattice, can be evaluated via saddle point expansion. The zeroth order ...

Convergence of the optimized delta expansion for the connected vacuum amplitude: Zero dimensions.

Recent proofs of the convergence of the linear delta expansion in zero and in one dimensions have been limited to the analogue of the vacuum generating functional in field theory. In zero dimensions it was shown that with an appropriate,

Monte Carlo calculations with fermions: The Schwinger model

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Heavy quarkonium decays and the renormalization group

-dependent, choice of an optimizing parameter