Partial Flavor Symmetry Restoration for Chiral Staggered Fermions

We study the leading discretization errors for staggered fermions by first constructing the continuum effective Lagrangian including terms of O(a^2), and then constructing the corresponding effective chiral Lagrangian. The terms of O(a^2) in the continuum effective Lagrangian completely break the SU(4) flavor symmetry down to the discrete subgroup respected by the lattice theory. We find, however, that the O(a^2) terms in the potential of the chiral Lagrangian maintain an SO(4) subgroup of SU(4). It follows that the leading discretization errors in the pion masses are SO(4) symmetric, implying three degeneracies within the seven lattice irreducible representations. These predictions hold also for perturbatively improved versions of the action. These degeneracies are observed, to a surprising degree of accuracy, in existing data. We argue that the SO(4) symmetry does not extend to the masses and interactions of other hadrons (vector mesons, baryons, etc), nor to higher order in a^2. We show how it is possible that, for physical quark masses of O(a^2), the new SO(4) symmetry can be spontaneously broken, leading to a staggered analogue of the Aoki-phase of Wilson fermions. This does not, however, appear to happen for presently studied versions of the staggered action.Comment: 26 pages, 2 figures (using psfig). Version to appear in PRD (clarifications added to introduction and section 6; typos corrected; references updated

Applications of Partially Quenched Chiral Perturbation Theory

Partially quenched theories are theories in which the valence- and sea-quark masses are different. In this paper we calculate the nonanalytic one-loop corrections of some physical quantities: the chiral condensate, weak decay constants, Goldstone boson masses, B_K and the K+ to pi+ pi0 decay amplitude, using partially quenched chiral perturbation theory. Our results for weak decay constants and masses agree with, and generalize, results of previous work by Sharpe. We compare B_K and the K+ decay amplitude with their real-world values in some examples. For the latter quantity, two other systematic effects that plague lattice computations, namely, finite-volume effects and unphysical values of the quark masses and pion external momenta are also considered. We find that typical one-loop corrections can be substantial.Comment: 22 pages, TeX, refs. added, minor other changes, version to appear in Phys. Rev.

Constraints on the Existence of Chiral Fermions in Interacting Lattice Theories

It is shown that an interacting theory, defined on a regular lattice, must have a vector-like spectrum if the following conditions are satisfied: (a)~locality, (b)~relativistic continuum limit without massless bosons, and (c)~pole-free effective vertex functions for conserved currents. The proof exploits the zero frequency inverse retarded propagator of an appropriate set of interpolating fields as an effective quadratic hamiltonian, to which the Nielsen-Ninomiya theorem is applied.Comment: LaTeX, 9 pages, WIS--93/56--JUNE--P

Negative-Energy Spinors and the Fock Space of Lattice Fermions at Finite Chemical Potential

Recently it was suggested that the problem of species doubling with Kogut-Susskind lattice fermions entails, at finite chemical potential, a confusion of particles with antiparticles. What happens instead is that the familiar correspondence of positive-energy spinors to particles, and of negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind time derivative. To show this we highlight the role of the spinorial ``energy'' in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting lattice fermions at zero temperature and nonzero chemical potential. We consider Kogut-Susskind fermions and, for comparison, fermions with an asymmetric one-step time derivative.Comment: 14p

Interpolating between low and high energy QCD via a 5D Yang-Mills model

We describe the Goldstone bosons of massless QCD together with an infinite number of spin-1 mesons. The field content of the model is SU(Nf)xSU(Nf) Yang-Mills in a compact extra-dimension. Electroweak interactions reside on one brane. Breaking of chiral symmetry occurs due to the boundary conditions on the other brane, away from our world, and is therefore spontaneous. Our implementation of the holographic recipe maintains chiral symmetry explicit throughout. For intermediate energies, we extract resonance couplings. These satisfy sum rules due to the 5D nature of the model. These sum rules imply, when taking the high energy limit, that perturbative QCD constraints are satisfied. We also illustrate how the 5D model implies a definite prescription for handling infinite sums over 4D resonances. Taking the low energy limit, we recover the chiral expansion and the corresponding non-local order parameters. All local order parameters are introduced separately.Comment: Corresponds to published version, with some typos correcte

Quenched Approximation Artifacts: A study in 2-dimensional QED

The spectral properties of the Wilson-Dirac operator in 2-dimensional QED responsible for the appearance of exceptional configurations in quenched simulations are studied in detail. The mass singularity structure of the quenched functional integral is shown to be extremely compicated, with multiple branch points and cuts. The connection of lattice topological charge and exactly real eigenmodes is explored using cooling techniques. The lattice volume and spacing dependence of these modes is studied, as is the effect of clover improvement of the action. A recently proposed modified quenched approximation is applied to the study of meson correlators, and the results compared with both naive quenched and full dynamical calculations of the same quantity.Comment: 34 pages (Latex) plus 9 embedded figures; title change

A Lattice QCD Analysis of the Strangeness Magnetic Moment of the Nucleon

The outcome of the SAMPLE Experiment suggests that the strange-quark contribution to the nucleon magnetic moment, G_M^s(0), may be greater than zero. This result is very difficult to reconcile with expectations based on the successful baryon magnetic-moment phenomenology of the constituent quark model. We show that careful consideration of chiral symmetry reveals some rather unexpected properties of QCD. In particular, it is found that the valence u-quark contribution to the magnetic moment of the neutron can differ by more than 50% from its contribution to the Xi^0 magnetic moment. This hitherto unforeseen result leads to the value G_M^s(0) = -0.16 +/- 0.18 with a systematic error, arising from the relatively large strange quark mass used in existing lattice calculations, that would tend to shift G_M^s(0) towards small positive values.Comment: RevTeX, 20 pages, 12 figure

Heavy-Meson Observables at One-Loop in Partially Quenched Chiral Perturbation Theory

I present one-loop level calculations of the Isgur-Wise functions for B -> D^{(*)} + e + nu, of the matrix elements of isovector twist-2 operators in B and D mesons, and the matrix elements for the radiative decays D^* -> D + gamma in partially quenched heavy quark chiral perturbation theory. Such expressions are required in order to extrapolate from the light quark masses used in lattice simulations of the foreseeable future to those of nature.Comment: 13 pages, 3 fig

Effective Lagrangian for strongly coupled domain wall fermions

We derive the effective Lagrangian for mesons in lattice gauge theory with domain-wall fermions in the strong-coupling and large-N_c limits. We use the formalism of supergroups to deal with the Pauli-Villars fields, needed to regulate the contributions of the heavy fermions. We calculate the spectrum of pseudo-Goldstone bosons and show that domain wall fermions are doubled and massive in this regime. Since we take the extent and lattice spacing of the fifth dimension to infinity and zero respectively, our conclusions apply also to overlap fermions.Comment: 26 pp. RevTeX and 3 figures; corrected error in symmetry breaking scheme and added comments to discussio

The Standard Model from a New Phase Transition on the Lattice

Several years ago it was conjectured in the so-called Roma Approach, that gauge fixing is an essential ingredient in the lattice formulation of chiral gauge theories. In this paper we discuss in detail how the gauge-fixing approach may be realized. As in the usual (gauge invariant) lattice formulation, the continuum limit corresponds to a gaussian fixed point, that now controls both the transversal and the longitudinal modes of the gauge field. A key role is played by a new phase transition separating a conventional Higgs or Higgs-confinement phase, from a phase with broken rotational invariance. In the continuum limit we expect to find a scaling region, where the lattice correlators reproduce the euclidean correlation functions of the target (chiral) gauge theory, in the corresponding continuum gauge.Comment: 16 pages, revtex, one figure. Clarifications made, mainly in sections 3 and 6 that deal with the fermion action, to appear in Phys Rev