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

In the canonical seesaw mechanism we require the relevant neutrino mass terms to be invariant under the $S^{}_3$ charge-conjugation transformations of left- and right-handed neutrino fields. Then both the Dirac mass matrix $M^{}_{\rm D}$ and the right-handed neutrino mass matrix $M^{}_{\rm R}$ are well constrained, so is the effective light Majorana neutrino mass matrix $M^{}_\nu$ via the seesaw formula. We find that these mass matrices can be classified into 22 categories, among which some textures respect the well-known $\mu$-$\tau$ permutation or reflection symmetry and flavor democracy. It is also found that there exist remarkable structural equalities or similarities between $M^{}_\nu$ and $M^{}_{\rm R}$, 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 $M^{}_{\rm D}$ and $M^{}_{\rm R}$ in the $S^{}_3$ reflection symmetry limit.Comment: 33 pages, 1 table. v2: matches the version accepted for publication in JHE

Approximations of Stochastic Partial Differential Equations

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

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