Calculating error bars for neutrino mixing parameters

One goal of contemporary particle physics is to determine the mixing angles and mass-squared differences that constitute the phenomenological constants that describe neutrino oscillations. Of great interest are not only the best fit values of these constants but also their errors. Some of the neutrino oscillation data is statistically poor and cannot be treated by normal (Gaussian) statistics. To extract confidence intervals when the statistics are not normal, one should not utilize the value for chisquare versus confidence level taken from normal statistics. Instead, we propose that one should use the normalized likelihood function as a probability distribution; the relationship between the correct chisquare and a given confidence level can be computed by integrating over the likelihood function. This allows for a definition of confidence level independent of the functional form of the !2 function; it is particularly useful for cases in which the minimum of the !2 function is near a boundary. We present two pedagogic examples and find that the proposed method yields confidence intervals that can differ significantly from those obtained by using the value of chisquare from normal statistics. For example, we find that for the first data release of the T2K experiment the probability that chisquare is not zero, as defined by the maximum confidence level at which the value of zero is not allowed, is 92%. Using the value of chisquare at zero and assigning a confidence level from normal statistics, a common practice, gives the over estimation of 99.5%.Comment: 9 pages, 6 figure

Neutrino Oscillations: Hierarchy Question

The only experimentally observed phenomenon that lies outside the standard model of the electroweak interaction is neutrino oscillations. A way to try to unify the extensive neutrino oscillation data is to add a phenomenological mass term to the Lagrangian that is not diagonal in the flavor basis. The goal is then to understand the world's data in terms of the parameters of the mixing matrix and the differences between the squares of the masses of the neutrinos. An outstanding question is what is the correct ordering of the masses, the hierarchy question. We point out a broken symmetry relevant to this question, the symmetry of the simultaneous interchange of hierarchy and the sign of $\theta_{13}$. We first present the results of an analysis of data that well determine the phenomenological parameters but are not sensitive to the hierarchy. We find $\theta_{13} = 0.152\pm 0.014$, $\theta_{23} = 0.25^{+0.03}_{-0.05} \pi$ and $\Delta_{32} = 2.45\pm 0.14 \times 10^{-3}$ eV$^2$, results consistent with others. We then include data that are sensitive to the hierarchy and the sign of $\theta_{13}$. We find, unlike others, four isolated minimum in the $\chi^2$-space as predicted by the symmetry. Now that Daya Bay and RENO have determined $\theta_{13}$ to be surprisingly large, the Super-K atmospheric data produce meaningful symmetry breaking such that the inverse hierarchy is preferred at the 97.2 % level.Comment: to appear in Proceedings of the 5th International Conference on Fission and Neutron Rich Nuclei (ICFN5), (Sanibel Island, Florina, Nov. 4-10, 2012).10 pages, 8 figure

DFT study of electronic and redox properties of TiO2 supported on olivine for modelling regolith on Moon and Mars conditions

Titanium dioxide (TiO) is one of the most studied oxides in photocatalysis, due to its electronic structure and its wide variety of applications, such as gas sensors and biomaterials, and especially in methane-reforming catalysis. Titanium dioxide and olivine have been detected both on Mars and our Moon. It has been postulated that on Mars photocatalytic processes may be relevant for atmospheric methane fluctuation, radicals and perchlorate productions etc. However, to date no investigation has been devoted to modelling the properties of TiO adsorbed on olivine surface. The goal of this study is to investigate at atomic level with electronic structure calculations based on the Density Functional Theory (DFT), the atomic interactions that take place during the adsorption processes for formation of a TiO regolith. These models are formed with different titanium oxide films adsorbed on olivine (forsterite) surface, one of the most common minerals in Universe, Earth, Mars, cometary and interstellar dust. We propose three regolith models to simulate the principal phases of titanium oxide (TiO, TiO and TiO). The models show different adsorption processes i.e. physisorption and chemisorption. Our results suggest that the TiO is the most reactive phase and produces a strong exothermic effect. Besides, we have detailed, from a theoretical point of view, the effect that has the adsorption process in the electronic properties such as electronic density of states (DOS) and oxide reduction process (redox). This theoretical study can be important to understand the formation of new materials that can be used as support in the catalytic processes that occur in the Earth, Mars and Moon. Also, it may be important to interpret the present day photochemistry and interaction of regolith and airborne aerosols in the atmosphere on Mars or to define possible catalytic reactions of the volatiles captured on the Moon regolith.Authors acknowledges the Spanish MINECO projects CGL2014-55230-R, PCIN-2017-098, and FIS2016--77692-C2-2-P co-financed with European FEDER funds. We also would like to thank the generous support of Kempe and Wallenberg Foundations. MPZ, JMT, and EER recognize the ESA/Airbus/Air Liquide and Merck Space Exploration Masters challenge 2018 finalist award for Moon ISRU solutions for the Moon Alchemist proposal that uses Moon regolith with TiO2 for methane production

Self-Assembled Structures Formed in CO2-Enriched Atmospheres: A Case-Study for Martian Biomimetic Forms

The aim of this study was to investigate the biomimetic precipitation processes that follow the chemical-garden reaction of brines of CaCl2 and sulfate salts with silicate in alkaline conditions under a Mars-type CO2-rich atmosphere. We characterize the precipitates with environmental scanning electron microscope micrography, micro-Raman spectroscopy, and X-ray diffractometry. Our analysis results indicate that self-assembled carbonate structures formed with calcium chloride can have vesicular and filamentary features. With magnesium sulfate as a reactant a tentative assignment with Raman spectroscopy indicates the presence of natroxalate in the precipitate. These morphologies and compounds appear through rapid sequestration of atmospheric CO2 by alkaline solutions of silica and salts.The authors acknowledge the contribution of the European COST Action CA17120 supported by the EU Frame work Programme Horizon 2020 and the Spanish MINECO projects FIS2016-77692-C2 and PCIN-2017-098. M.P.Z. acknowledges the partial support of the Spanish State Research Agency (AEI) Project No. MDM-2017-0737 and of the Spanish Ministry of Science and Innovation project PID2019-104205GB-C21