# Poster Summary: Determination of the Neutrino Mass Hierarchy with a New Statistical Method

(by Matteo Tenti) All the methods developed so far for establishing whether MO is normal (NH) or inverted (IH) are based on delta chi-squared evaluation.

Given the current uncertainties on the oscillations parameter value from few percents to more than 10%, the delta chi-squared computation leads to almost null the sensitivity on mass ordering. Therefore a more sophisticated test statistic should be introduced.

We studied the performance of a new test statistic, q. The new method takes into account the whole shape of probability density function of test statistic and exploits the intrinsic statistical fluctuations. The full details of the new method can be found in Phys. Rev. D 95, 053002.

The method has been applied to the recent release by NOvA in 2016 at Neutrino 2016 Conference. In Figure 1 the continuous line represents the significance of the exclusion of the inverted hierarchy obtained by the new method as function of the delta_CP value. For comparison the dot-dashed line corresponds to the delta chi-squared result.

The increase in significance obtained by our method leads to a decrease in the exposure needed to reach a given significance. So the power of the new method can be also settled comparing the isoline corresponding to different levels of significance in the n_NH vs n_IH plane, the predicted numbers of events in the NH and IH hypotheses, respectively, as shown in Figure 2.

In Fig.2, the black isolines for different significances are drawn. The region above each n-sigma line corresponds to the combinations of (n_NH, n_NH) that would give more than n-sigma significance in exclusion inverted hierarchy, if delta_CP is equals to 3/2 pi and the other oscillation parameters are given by the best fit value of global fit.

The top picture shows isolines for the delta chi-squared method, while in the bottom one isolines from the new method are drawn. The dashed-red lines indicate the median of the predicted number events assuming NH.

The inverted hiearchy is expected to be excluded at three sigma levels when red-dotted line crosses balck continuous line. This happens, for what concerns our method, when about 90 events are expected from NH hierarchy while there is no such cross in the delta chi-squared plot.