Perturbed Yukawa Textures in the Minimal Seesaw Model

\noindent We revisit the \textit{minimal seesaw model}, i.e., the type-I seesaw mechanism involving only two right-handed neutrinos. % This model represents an important minimal benchmark scenario for future experimental updates on neutrino oscillations. % It features four real parameters that cannot be fixed by the current data: two $CP$-violating phases, $\delta$ and $\sigma$, as well as one complex parameter, $z$, that is experimentally inaccessible at low energies. % The parameter $z$ controls the structure of the neutrino Yukawa matrix at high energies, which is why it may be regarded as a label or index for all UV completions of the minimal seesaw model. % The fact that $z$ encompasses only two real degrees of freedom allows us to systematically scan the minimal seesaw model over all of its possible UV completions. % In doing so, we address the following question: Suppose $\delta$ and $\sigma$ should be measured at particular values in the future---to what extent is one then still able to realize approximate textures in the neutrino Yukawa matrix? % Our analysis, thus, generalizes previous studies of the minimal seesaw model based on the assumption of exact texture zeros. % In particular, our study allows us to assess the theoretical uncertainty inherent to the common texture ansatz. % One of our main results is that a normal light-neutrino mass hierarchy is, in fact, still consistent with a two-zero Yukawa texture, provided that the two texture zeros receive corrections at the level of $\mathcal{O}\left(\textrm{10}\,\%\right)$. % While our numerical results pertain to the minimal seesaw model only, our general procedure appears to be applicable to other neutrino mass models as well.Comment: 30 pages, 7 figures, 2 tables; v2: updated references, extended discussion in the introduction and conclusions, new title, results unchanged, content matches version published in JHE

Surrogate data for non-stationary signals

Standard tests for nonlinearity reject the null hypothesis of a Gaussian linear process whenever the data is non-stationary. Thus, they are not appropriate to distinguish nonlinearity from non-stationarity. We address the problem of generating proper surrogate data corresponding to the null hypothesis of an ARMA process with slowly varying coefficients.Comment: 4 pages, 4 figures. proceeding for a poste

Surrogate time series

Before we apply nonlinear techniques, for example those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified "by the data". While many processes in nature seem very unlikely a priori to be linear, the possible nonlinear nature might not be evident in specific aspects of their dynamics. The method of surrogate data has become a very popular tool to address such a question. However, while it was meant to provide a statistically rigorous, foolproof framework, some limitations and caveats have shown up in its practical use. In this paper, recent efforts to understand the caveats, avoid the pitfalls, and to overcome some of the limitations, are reviewed and augmented by new material. In particular, we will discuss specific as well as more general approaches to constrained randomisation, providing a full range of examples. New algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains. The main limitation, which lies in the interpretability of the test results, will be illustrated through instructive case studies. We will also discuss some implementational aspects of the realisation of these methods in the TISEAN (http://www.mpipks-dresden.mpg.de/~tisean) software package.Comment: 28 pages, 23 figures, software at http://www.mpipks-dresden.mpg.de/~tisea

Garbled Elections

Majority rules are frequently used to decide whether or not a public good should be provided, but will typically fail to achieve an efficient provision. We provide a worst-case analysis of the majority rule with an optimally chosen majority threshold, assuming that voters have independent private valuations and are exante symmetric (provision cost shares are included in the valuations). We show that if the population is large it can happen that the optimal majority rule is essentially no better than a random provision of the public good. But the optimal majority rule is worst-case asymptotically efficient in the large-population limit if (i) the voters’ expected valuation is bounded away from 0, and (ii) an absolute bound for valuations is known

Low-Scale Leptogenesis in the Scotogenic Neutrino Mass Model

The scotogenic model proposed by Ernest Ma represents an attractive and minimal example for the generation of small Standard Model neutrino masses via radiative corrections in the dark matter sector. In this paper, we demonstrate that, in addition to neutrino masses and dark matter, the scotogenic model also allows to explain the baryon asymmetry of the Universe via low-scale leptogenesis. First, we consider the case of two right-handed neutrinos (RHNs) N_{1,2}, for which we provide an analytical argument why it is impossible to push the RHN mass scale below M_1^min ~ 10^10 GeV, which is identical to the value in standard thermal leptogenesis in the type-I seesaw scenario with the same washout strength. Then, we present a detailed study of the three-RHN case based on both an analytical and a numerical analysis. In the case of three RHNs, we obtain a lower bound on the N_1 mass of around 10 TeV. Remarkably enough, successful low-scale leptogenesis can be achieved without any degeneracy in the RHN mass spectrum. The only necessary condition is a suppression in the N_1 Yukawa couplings, which results in suppressed washout and a small active neutrino mass of around 10^-12 eV. This leads to the fascinating realization that low-scale leptogenesis in the scotogenic model can be tested in experiments that aim at measuring the absolute neutrino mass scale.Comment: 13 pages, 2 figures; v2: minor changes to the text, updated discussion on direct detection bounds; content matches published versio

Garbled Elections

Majority rules are frequently used to decide whether or not a public good should be provided, but will typically fail to achieve an efficient provision. We provide a worst-case analysis of the majority rule with an optimally chosen majority threshold, assuming that voters have independent private valuations and are exante symmetric (provision cost shares are included in the valuations). We show that if the population is large it can happen that the optimal majority rule is essentially no better than a random provision of the public good. But the optimal majority rule is worst-case asymptotically efficient in the large-population limit if (i) the voters’ expected valuation is bounded away from 0, and (ii) an absolute bound for valuations is known.