# Phenomenology of Three-Neutrino Masses and Mixings

Egidio Lisi (see picture below) concluded the morning session today at Neutel XVII by giving an overview of the phenomenology of neutrinos using the data available at the beginning of this year. His work is based on a paper he published today on the Arxiv, 1703.04471. It is an update of a paper published last year.

What do we know and we do not know about the three-neutrino oscillations? To answer this question Lisi described the methodology of their analysis of the data. The data comes from many experiments. They start from long-baseline accelearator data, and solar plus kamland. These stabilize theta_13. In addition, in a second iteraction there are short-baseline reactor data to add, and lastly one may add atmospheric data. The latter is quite entangled so it is better to add it at the end. A chisquared analysis is employed in the analysis.

Lisi showed many graphs that describe the constraints on the neutrino mixing parameters brought by the different considered datasets. Notably, one sees a delta chisquared of 1.1 as an indication in favour of a normal mass ordering of neutrino states. Reactors do not add much to this notion, but atmospheric neutrino information enhance the favouring of normal hierarchy of masses, bringing the number to 3.6. This is a quite recent and strong advancement toward the solution of this puzzle: all indications are now in the same direction, something that was quite different only one year ago.

If one includes information from neutrinoless double-beta decay, this is dominated by KamLAND-Zen. One may obtain a chisquare curve as a function of m(double beta). The analysis results in a cutoff at high ordinate y of the allowed regions of the plane spanned by m(double beta) versus sum of neutrino masses.

In summary, there is a preference for the normal mass hierarchy at the level of two standard deviations, by considering all datasets and analysis of cosmological data. There is margin for improvement of all datasets, and there is room for reaching a three-sigma evidence in the near future.