Nonlocal Regularization For Non-Abelian Gauge Theories For Arbitrary Gauge Parameter

We study the nonlocal regularization for the non-abelian gauge theories for an arbitrary value of the gauge parameter (\xi). We show that the procedure for the nonlocalization of field theories established earlier by the original authors, when applied in that form to the Faddeev-Popov effective action in a linear gauge cannot lead to a (\xi)-independent result for the observables. We then show that an alternate procedure which is simpler can be used and that it leads to the S-matrix elements (where they exist) independent of (\xi).Comment: 21 pages,postscript fil

Seesaw parametrization for n right-handed neutrinos

Introducing n right-handed neutrinos to the Standard Model yields, in general, massive active neutrinos. We give explicit parametrizations for the involved mixing and coupling matrices in terms of physical parameters for both the top-down and the bottom-up approach for arbitrary n. Bounds on the complex mixing angles in the bottom-up approach from perturbativity of the Yukawa couplings to charged lepton flavor violation are discussed. As a novel illustration of possible effects from n != 3, we extend the neutrino anarchy framework to arbitrary n; we show that while the anarchic mixing angles are insensitive to the number of singlets, the observed ratios of neutrino masses prefer small n for the simplest linear measure.Comment: 12 pages, 4 figures. Added references and details about the sampling algorith

The FeSi phase diagram to 150 GPa

The melting curve of FeSi has been determined to 150 GPa in the laser-heated diamond anvil cell (LH-DAC) on the basis of discontinuities in the power versus temperature function. A multianvil experimental cross-check at 12 GPa using textural criteria as a proxy for melting is in good agreement with our LH-DAC results. The melting point of FeSi reaches ∼4000 K at the core mantle boundary and an extrapolated value of 4900 K at the inner-core boundary (ICB). We also present the melting curve as determined by the Lindemann melting law; this agrees well with our experimental curve to 70 GPa and then diverges to higher temperatures, reaching 6200 K at the ICB. These temperatures are substantially higher than previous LH-DAC determinations. The boundary of the ε-FeSi → CsCl-FeSi subsolidus transition has also been determined by synchrotron-based X-ray diffraction at high pressures, and the results confirm a negative Clapeyron slope for the transition. We conclude that if present, FeSi is likely to be solid within the D″ layer and is unlikely to be present within the inner core for any plausible bulk core silicon content.9 page(s

Reconstructing the two right-handed neutrino model

In this paper we propose a low-energy parametrization of the two right-handed neutrino model, and discuss the prospects to determine experimentally these parameters in supersymmetric scenarios. In addition, we present exact formulas to reconstruct the high-energy leptonic superpotential in terms of the low-energy observables. We also discuss limits of the three right-handed neutrino model where this procedure applies.Comment: 28 pages, 4 figures. Typos corrected, references adde

Ultraviolet Complete Electroweak Model Without a Higgs Particle

An electroweak model with running coupling constants described by an energy dependent entire function is utraviolet complete and avoids unitarity violations for energies above 1 TeV. The action contains no physical scalar fields and no Higgs particle and the physical electroweak model fields are local and satisfy microcausality. The $W$ and $Z$ masses are compatible with a symmetry breaking $SU(2)_L\times U(1)_Y \rightarrow U(1)_{\rm em}$, which retains a massless photon. The vertex couplings possess an energy scale $\Lambda_W > 1$ TeV predicting scattering amplitudes that can be tested at the LHC.Comment: 19 pages, no figures, LaTex file. Equation and text corrected. Reference added. Results remain the same. Final version published in European Physics Journal Plus, 126 (2011

Continuous non-perturbative regularization of QED

We regularize in a continuous manner the path integral of QED by construction of a non-local version of its action by means of a regularized form of Dirac's $\delta$ functions. Since the action and the measure are both invariant under the gauge group, this regularization scheme is intrinsically non-perturbative. Despite the fact that the non-local action converges formally to the local one as the cutoff goes to infinity, the regularized theory keeps trace of the non-locality through the appearance of a quadratic divergence in the transverse part of the polarization operator. This term which is uniquely defined by the choice of the cutoff functions can be removed by a redefinition of the regularized action. We notice that as for chiral fermions on the lattice, there is an obstruction to construct a continuous and non ambiguous regularization in four dimensions. With the help of the regularized equations of motion, we calculate the one particle irreducible functions which are known to be divergent by naive power counting at the one loop order.Comment: 23 pages, LaTeX, 5 Encapsulated Postscript figures. Improved and revised version, to appear in Phys. Rev.

Schur Q-functions and degeneracy locus formulas for morphisms with symmetries

We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our description uses essentially Schur Q-polynomials of a bundle, and is based on a certain push-forward formula for these polynomials in a Grassmann bundle.Comment: 22 pages, AMSTEX, misprints corrected, exposition improved. to appear in the Proceedings of Intersection Theory Conference in Bologna, "Progress in Mathematics", Birkhause