76,042 research outputs found

    Seesaw mirroring between light and heavy Majorana neutrinos with the help of the S3S^{}_3 reflection symmetry

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    In the canonical seesaw mechanism we require the relevant neutrino mass terms to be invariant under the S3S^{}_3 charge-conjugation transformations of left- and right-handed neutrino fields. Then both the Dirac mass matrix MDM^{}_{\rm D} and the right-handed neutrino mass matrix MRM^{}_{\rm R} are well constrained, so is the effective light Majorana neutrino mass matrix MνM^{}_\nu via the seesaw formula. We find that these mass matrices can be classified into 22 categories, among which some textures respect the well-known μ\mu-τ\tau permutation or reflection symmetry and flavor democracy. It is also found that there exist remarkable structural equalities or similarities between MνM^{}_\nu and MRM^{}_{\rm R}, reflecting a seesaw mirroring relationship between light and heavy Majorana neutrinos. We calculate the corresponding light neutrino masses and flavor mixing parameters as well as the CP-violating asymmetries in decays of the lightest heavy Majorana neutrino, and show that only the flavored leptogenesis mechanism is possible to work for three categories of MDM^{}_{\rm D} and MRM^{}_{\rm R} in the S3S^{}_3 reflection symmetry limit.Comment: 33 pages, 1 table. v2: matches the version accepted for publication in JHE

    Approximations of Stochastic Partial Differential Equations

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    In this paper we show that solutions of stochastic partial differential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic Burgers equations are discussed

    On q-summation and confluence

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    This paper is divided in two parts. In the first part we consider irregular singular analytic q-difference equations, with q\in ]0,1[, and we show how the Borel sum of a divergent solution of a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of such a q-difference equation. In the second part, we work under the assumption q\in ]1,+\infty[. In this case, at least four different q-Borel sums of a divergent solution of an irregular singular analytic q-difference equations are spread in the literature: under convenient assumptions we clarify the relations among them.Comment: 36 pages. Following the referee's comments, we have clarified the exposition of some proofs and corrected some misprint
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