Right-handed lepton mixings at the LHC

We study how the elements of the leptonic right-handed mixing matrix can be determined at the LHC in the minimal Left-Right symmetric extension of the standard model. We do it by explicitly relating them with physical quantities of the Keung-Senjanovi\'c process and the lepton number violating decays of the right doubly charged scalar. We also point out that the left and right doubly charged scalars can be distinguished at the LHC, without measuring the polarization of the final state leptons coming from their decays.Comment: 12 pages, 6 figures, discussion in section III expanded and sharpened, one appendix added, updated reference

Spike trains statistics in Integrate and Fire Models: exact results

We briefly review and highlight the consequences of rigorous and exact results obtained in \cite{cessac:10}, characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are subject to noise, without restriction on the synaptic weights connectivity. The main result is that spike trains statistics are characterized by a Gibbs distribution, whose potential is explicitly computable. This establishes, on one hand, a rigorous ground for the current investigations attempting to characterize real spike trains data with Gibbs distributions, such as the Ising-like distribution, using the maximal entropy principle. However, it transpires from the present analysis that the Ising model might be a rather weak approximation. Indeed, the Gibbs potential (the formal "Hamiltonian") is the log of the so-called "conditional intensity" (the probability that a neuron fires given the past of the whole network). But, in the present example, this probability has an infinite memory, and the corresponding process is non-Markovian (resp. the Gibbs potential has infinite range). Moreover, causality implies that the conditional intensity does not depend on the state of the neurons at the \textit{same time}, ruling out the Ising model as a candidate for an exact characterization of spike trains statistics. However, Markovian approximations can be proposed whose degree of approximation can be rigorously controlled. In this setting, Ising model appears as the "next step" after the Bernoulli model (independent neurons) since it introduces spatial pairwise correlations, but not time correlations. The range of validity of this approximation is discussed together with possible approaches allowing to introduce time correlations, with algorithmic extensions.Comment: 6 pages, submitted to conference NeuroComp2010 http://2010.neurocomp.fr/; Bruno Cessac http://www-sop.inria.fr/neuromathcomp

Resummation in QFT with Meijer G-functions

We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion. Using this technique, we consider in detail the $\phi^4$ model where we estimate the non-perturbative $\beta-$function and prove that its asymptotic behavior correctly reproduces instantonic effects calculated using semiclassical methods. After reviewing the emergence of the renormalons in this theory, we also speculate on how one can resum them. Finally, we resum the non-perturbative $\beta-$function of abelian and non-abelian gauge-fermion theories and analyze the behavior of these theories as a function of the number of fermion flavors. While in the former no fixed points are found, in the latter, a richer phase diagram is uncovered and illustrated by the regions of confinement, large-distance conformality, and asymptotic safety.Comment: 22 pages, 10 figures, final version with minor changes, as accepted in NP

Time-reversal symmetry violation in several Lepton-Flavor-Violating processes

We compute a T-odd triple vector correlation for the $\mu\rightarrow e\gamma$ decay and the $\mu\rightarrow e$ conversion process. We find simple results in terms of the CP violating phases of the effective Hamiltonians. Then we focus on the minimal Left-Right symmetric extension of the Standard Model, which can lead to an appreciable correlation. We show that under rather general assumptions, this correlation can be used to discriminate between Parity or Charge-conjugation as the discrete Left-Right symmetry.Comment: 22 pages, 5 figures. Comments added. Sections 5 and 6 expanded. Appendices A and B expanded, accepted for publication in JHE

La réforme des forces de police au Canada : les tensions entre la sécurité des citoyens, les libertés fondamentales et le fédéralisme

Cet article envisage les politiques en matière de sécurité citoyenne et la réforme des forces de police au Canada pendant les 25 dernières années. La Charte canadienne des droits et libertés a établi dans l’article 7 la garantie à la « sécurité de la personne ». La poursuite de cette garantie a supposé, d’une part, une tension entre la décentralisation, le désengagement de l’État et le rôle de la police et, d’autre part, une tension entre son mandat de préserver l’ordre public, entendu comme la sauvegarde de l’État, et la protection des citoyens. Même si ces tensions se révèlent problématiques, elles n’ont pas empêché que le Canada soit un pays sûr dont le taux de criminalité est bas et où règne un important sentiment de sécurité parmi les citoyens.This article looks at policies concerning citizen security and reform among Canada's police forces during the last twenty-five years. Article 7 of the Canadian Charter of Rights and Freedoms established a guarantee of "security of the person". Pursuit of this guarantee has supposed, on one hand, a tension between decentralization, withdrawal of the State, and the role of police, and on the other hand, a tension between the Charter's mandate to preserve public order, understood as the safeguard of the State, and the protection of citizens. Even if revealed as problematic, these tensions did not prevent Canada from being a confident country with low crime rates and a heightened sense of security among its citizens

Phenomenology of the right-handed lepton mixings at the LHC in LR symmetric theory and the Time-Reversal symmetry violation in the \ub5 --> e\u3d2 decay and \ub5 --> e conversion process

We study how the elements of the leptonic right-handed mixing matrix can be determined at the LHC in the minimal Left-Right symmetric extension of the standard model. We do it by explicitly relating them with physical quantities of the Keung-Senjanovi\'c process and the lepton number violating decays of the right doubly charged scalar. We also point out that the left and right doubly charged scalars can be distinguished at the LHC, without measuring the polarization of the final state leptons coming from their decays. Then we study time reversal symmetry violation in the $\mu\rightarrow e\gamma$ decay and the $\mu\rightarrow e$ conversion process and compute a T-odd triple vector correlation for the $\mu\rightarrow e\gamma$ decay and the $\mu\rightarrow e$ conversion process, finding simple results in terms of the CP violating phases of the effective Hamiltonians. Finally we focus on the minimal Left-Right symmetric extension of the Standard Model, which is a complete model of neutrino masses that can lead to an appreciable correlation. We show that under rather general assumptions, this correlation can be used to discriminate between Parity or Charge-conjugation as the discrete Left-Right symmetry

A consistent quantum field theory from dimensional reduction

We incorporate the concept of dimensional reduction at high energies within the perturbative formulation of quantum field theory. In this new framework, space and momentum integrations are modified by a weighting function incorporating an effective mass energy associated with the dimensional reduction scale. We quantize the theory within canonical formalism. We then show that it can be made finite in perturbation theory, free of renormalon ambiguities, and with better analytic behavior for infinitesimal coupling constant compared to standard quantum field theory. The new approach reproduces the known results at low energies. One key feature of this class of models is that the coupling constant always reaches a fixed point in the ultraviolet region, making the models ultra-violet complete.Comment: to appear in J. Phys. A Math. Theo