The matching problem between functional shapes via a BV-penalty term: a Γ\Gamma-convergence result

In this paper we study a variant of the matching model between functional shapes introduced in \cite{ABN}. Such a model allows to compare surfaces equipped with a signal and the matching energy is defined by the $L^2$-norm of the signal on the surface and a varifold-type attachment term. In this work we study the problem with fixed geometry which means that we optimize the initial signal (supported on the initial surface) with respect to a target signal supported on a different surface. In particular, we consider a $BV$ or $H^1$-penalty for the signal instead of its $L^2$-norm. Several numerical examples are shown in order to prove that the $BV$-penalty improves the quality of the matching. Moreover, we prove a $\Gamma$-convergence result for the discrete matching energy towards the continuous-one

Minimal Asymmetric Dark Matter

In the early Universe, any particle carrying a conserved quantum number and in chemical equilibrium with the thermal bath will unavoidably inherit a particle-antiparticle asymmetry. A new particle of this type, if stable, would represent a candidate for asymmetric dark matter (DM) with an asymmetry directly related to the baryon asymmetry. We study this possibility for a minimal DM sector constituted by just one (generic) $SU(2)_L$ multiplet $\chi$ carrying hypercharge, assuming that at temperatures above the electroweak phase transition an effective operator enforces chemical equilibrium between $\chi$ and the Higgs boson. We argue that limits from DM direct detection searches severely constrain this scenario, leaving as the only possibilities scalar or fermion multiplets with hypercharge $y = 1$, preferentially quintuplets or larger $SU(2)$ representations, and with a mass in the few TeV range.Comment: 9 pages, 2 figures, included t-channel scattering, added details on charged-neutral mass splitting and indirect detection, accepted in PL

Z', new fermions and flavor changing processes, constraints on E6_6 models from μ\mu --> eee

We study a new class of flavor changing interactions, which can arise in models based on extended gauge groups (rank $>$4) when new charged fermions are present together with a new neutral gauge boson. We discuss the cases in which the flavor changing couplings in the new neutral current coupled to the $Z^\prime$ are theoretically expected to be large, implying that the observed suppression of neutral flavor changing transitions must be provided by heavy $Z^\prime$ masses together with small $Z$-$Z^\prime$ mixing angles. Concentrating on E$_6$ models, we show how the tight experimental limit on $\mu \rightarrow eee$ implies serious constraints on the $Z^\prime$ mass and mixing angle. We conclude that if the value of the flavor changing parameters is assumed to lie in a theoretically natural range, in most cases the presence of a $Z^\prime$ much lighter than 1 TeV is unlikely.Comment: plain tex, 22 pages + 2 pages figures in PostScript (appended after `\bye'), UM-TH 92-1

Competitive nucleation in reversible Probabilistic Cellular Automata

The problem of competitive nucleation in the framework of Probabilistic Cellular Automata is studied from the dynamical point of view. The dependence of the metastability scenario on the self--interaction is discussed. An intermediate metastable phase, made of two flip--flopping chessboard configurations, shows up depending on the ratio between the magnetic field and the self--interaction. A behavior similar to the one of the stochastic Blume--Capel model with Glauber dynamics is found

Squeezing out predictions with leptogenesis from SO(10)

We consider the see-saw mechanism within a non-supersymmetric SO(10) model. By assuming the SO(10) quark-lepton symmetry, and after imposing suitable conditions that ensure that the right-handed (RH) neutrino masses are at most mildly hierarchical (compact RH spectrum) we obtain a surprisingly predictive scenario. The absolute neutrino mass scale, the Dirac and the two Majorana phases of the neutrino mixing matrix remain determined in terms of the set of already measured low energy observables, modulo a discrete ambiguity in the signs of two neutrino mixing angles and of the Dirac phase. The RH neutrinos mass spectrum is also predicted, as well as the size and sign of the leptogenesis CP asymmetries. We compute the cosmological baryon asymmetry generated through leptogenesis and obtain the correct sign and a size compatible with observations.Comment: 18 pages, 2 figures; minor changes, version accepted for publication in PR

PAMELA's cosmic positron from decaying LSP in SO(10) SUSY GUT

We propose two viable scenarios explaining the recent observations on cosmic positron excess. In both scenarios, the present relic density in the Universe is assumed to be still supported by thermally produced WIMP or LSP (\chi). One of the scenarios is based on two dark matter (DM) components (\chi,X) scenario, and the other is on SO(10) SUSY GUT. In the two DM components scenario, extremely small amount of non-thermally produced meta-stable DM component [O(10^{-10}) < n_X /n_\chi] explains the cosmic positron excess. In the SO(10) model, extremely small R-parity violation for LSP decay to e^\pm is naturally achieved with a non-zero VEV of the superpartner of one right-handed neutrino (\tilde{\nu}^c) and a global symmetry.Comment: 6 pages, Talks presented in PASCOS, SUSY, and COSMO/CosPA in 201

Kaon and Φ\Phi production vs Participants in Nuclear Collisions

Data on kaon and $\Phi$ production in nuclear collisions as a function of centrality are analysed both at AGS and SPS energy range. We compare the results of several experiments, looking for common trend in `participant scaling' of production yields. We find a smooth description of scaled kaon and $\Phi$ yields as a function of participant density. We also show a participant density dependence of kaons and $\Phi$ produced in the forward hemisphere for proton-nucleus collisions.Comment: Proceedings of the International Conference on Strangeness in Quark Matter, 20-25 July 2000, Berkeley, CA. To appear in Journal of Physics G: Nuclear and Particle Physic

R_b and New Physics: A Comprehensive Analysis

We survey the implications for new physics of the discrepancy between the LEP measurement of $R_b$ and its Standard Model prediction. Two broad classes of models are considered: ($i$) those in which new Z\bbar b couplings arise at tree level, through $Z$ or $b$-quark mixing with new particles, and ($ii$) those in which new scalars and fermions alter the Z \bbar b vertex at one loop. We keep our analysis as general as possible in order to systematically determine what kinds of features can produce corrections to $R_b$ of the right sign and magnitude. We are able to identify several successful mechanisms, which include most of those which have been recently been proposed in the literature, as well as some earlier proposals (\eg\ supersymmetric models). By seeing how such models appear as special cases of our general treatment we are able to shed light on the reason for, and the robustness of, their ability to explain $R_b$.Comment: 60 pages, 8 figures, plain tex, uses epsf. Final version to appear in Phys. Rev. D; propgating sign error corrected in eqs. 78, 87, 88, 89, 98, and 107; results unchange

Signals of Unconventional E6_6 Models at e+e−e^+e^- Colliders

Generation dependent discrete symmetries often appear in models derived from superstring theories. In particular, in the framework of E$_6$ models the presence of such symmetries is required in order to allow for the radiative generation of naturally small neutrino masses. Recently it was shown that by imposing suitable generation dependent discrete symmetries, a class of models can be consistently constructed in which the three sets of known fermions in each generation do not have the same assignments with respect to the {\bf 27} representation of E$_6$. In this scenario, the different embedding in the gauge group of the three generations implies in particular that the known charged leptons couple in a non--universal way to the new neutral gauge bosons $(Z_\beta)$ present in these models. We exploit this fact to study the signature of this class of models at present and future $e^+e^-$ colliders. We show that some signals of deviation from lepton universality as well as some other discrepancies with the standard model predictions which have been observed at the TRISTAN collider in the production rate of $\mu$ and $\tau$, can be accounted for if the $Z_\beta$ mass is not much heavier than 300 GeV. We also study the discovery limits for lepton universality violation of this type at LEP-2 and at the 500 GeV $e^+e^-$ Next Linear Collider (NLC). We show that models predicting unconventional assignments for the leptons will give an unmistakable signature, when the $Z_\beta$ mass is as heavy as $\sim 800$ GeV (LEP-2) and $\sim 2$ TeV (NLC).Comment: Plain Tex, 20 pages. 4 PostScript figures (uses `epsf.tex'). Modified file-format. No changes in the tex