Staggered Heavy Baryon Chiral Perturbation Theory

Although taste violations significantly affect the results of staggered calculations of pseudoscalar and heavy-light mesonic quantities, those entering staggered calculations of baryonic quantities have not been quantified. Here I develop staggered chiral perturbation theory in the light-quark baryon sector by mapping the Symanzik action into heavy baryon chiral perturbation theory. For 2+1 dynamical quark flavors, the masses of flavor-symmetric nucleons are calculated to third order in partially quenched and fully dynamical staggered chiral perturbation theory. To this order the expansion includes the leading chiral logarithms, which come from loops with virtual decuplet-like states, as well as terms the order of the cubed pion mass, which come from loops with virtual octet-like states. Taste violations enter through the meson propagators in loops and tree-level terms the order of the squared lattice spacing. The pattern of taste symmetry breaking and the resulting degeneracies and mixings are discussed in detail. The resulting chiral forms are appropriate to lattice results obtained with operators already in use and could be used to study the restoration of taste symmetry in the continuum limit. I assume that the fourth root of the fermion determinant can be incorporated in staggered chiral perturbation theory using the replica method.Comment: 54 pages; v2: corrected discussion in Sec. III.C, conclusions unchange

Standard-model particles and interactions from field equations on spin 9+1 dimensional space

We consider a Dirac equation set on an extended spin space that contains fermion and boson solutions. At given dimension, it determines the scalar symmetries. The standard field equations can be equivalently written in terms of such degrees of freedom, and are similarly constrained. At 9+1 dimensions, the SU(3) X SU(2)_L X U(1) gauge groups emerge, as well as solution representations with quantum numbers of related gauge bosons, leptons, quarks, Higgs-like particles and others as lepto-quarks. Information on the coupling constants is also provided; e. g., for the hypercharge g'=(1/2) sqrt(3/5) ~ >.387, at tree level.Comment: 13 pages, Fig. 1(a)-(d

Goldstone boson counting in linear sigma models with chemical potential

We analyze the effects of finite chemical potential on spontaneous breaking of internal symmetries within the class of relativistic field theories described by the linear sigma model. Special attention is paid to the emergence of ``abnormal'' Goldstone bosons with quadratic dispersion relation. We show that their presence is tightly connected to nonzero density of the Noether charges, and formulate a general counting rule. The general results are demonstrated on an SU(3)xU(1) invariant model with an SU(3)-sextet scalar field, which describes one of the color-superconducting phases of QCD.Comment: 10 pages, REVTeX4, 4 eps figures, v2: general discussion in Sec. IV expanded and improved, references added, other minor corrections throughout the tex

Comment on "The Phenomenology of a Nonstandard Higgs Boson in W_L W_L Scattering"

We show that in Composite Higgs models, the coupling of the Higgs resonance to a pair of $W$ bosons is weaker than the corresponding Standard Model coupling, provided the Higgs arises from electroweak doublets only. This is partly due to the effects of the nonlinear realization of the chiral symmetries at the compositeness scale.Comment: 6 pages, BU-HEP 94-2

Power law in a gauge-invariant cut-off regularisation

We study one-loop quantum corrections of a compactified Abelian 5d gauge field theory. We use a cut-off regularisation procedure which respects the symmetries of the model, i.e. gauge invariance, exhibits the expected power-like divergences and therefore allows the derivation of power-law behavior of the effective 4d gauge coupling in a coherent manner.Comment: 5 pages, 1 figure, 5 graphs, few references added, to appear in Phys.Rev. Rapid Communication

Comparison of 1/mQ^2 Corrections in Mesons and Baryons

We extend our relativistic quark model to the study of the decay Lambda_b -> Lambda_c ell nu and verify that the model satisfies the heavy-quark symmetry constraints at order 1/mQ^2. We isolate a strong dependence on a parameter which measures the relative distortion in the light-quark wave functions of the Lambda_b and Lambda_c. This parameter and the 1/mQ^2 corrections turn out to be small. The dependence on a corresponding parameter in the meson case leads to large 1/mQ^2 corrections.Comment: 9 pages, LaTeX, 3 self-contained LaTeX figures in separate fil

Chaos at the border of criticality

The present paper points out to a novel scenario for formation of chaotic attractors in a class of models of excitable cell membranes near an Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics admits a simple and visual description in terms of the families of one-dimensional first-return maps, which are constructed using the combination of asymptotic and numerical techniques. The bifurcation structure of the continuous system (specifically, the proximity to a degenerate AHB) endows the Poincare map with distinct qualitative features such as unimodality and the presence of the boundary layer, where the map is strongly expanding. This structure of the map in turn explains the bifurcation scenarios in the continuous system including chaotic mixed-mode oscillations near the border between the regions of sub- and supercritical AHB. The proposed mechanism yields the statistical properties of the mixed-mode oscillations in this regime. The statistics predicted by the analysis of the Poincare map and those observed in the numerical experiments of the continuous system show a very good agreement.Comment: Chaos: An Interdisciplinary Journal of Nonlinear Science (tentatively, Sept 2008