Understanding the degeneracies in NOνA data

Abstract The combined analysis of ν μ disappearance and ν e appearance data of NOνA experiment leads to three nearly degenerate solutions. This degeneracy can be understood in terms of deviations in νe appearance signal, caused by unknown effects, with respect to the signal expected for a reference set of oscillations parameters. We define the reference set to be vacuum oscillations in the limit of maximal θ 23 and no CP-violation. We then calculate the deviations induced in the ν e appearance signal event rate by three unknown effects: (a) matter effects, due to normal or inverted hierarchy (b) octant effects, due to θ 23 being in higher or lower octant and (c) CP-violation, whether δ CP ∼ −π/2 or δ CP ∼ π/2. We find that the deviation caused by each of these effects is the same for NOνA. The observed number of ν e events in NOνA is equivalent to the increase caused by one of the effects. Therefore, the observed number of ν e appearance events of NOνA is the net result of the increase caused by two of the unknown effects and the decrease caused by the third. Thus we get the three degenerate solutions. We also find that further data by NOνA can not distinguish between these degenerate solutions but addition of one year of neutrino run of DUNE can make a distinction between all three solutions. The distinction between the two NH solutions and the IH solution becomes possible because of the larger matter effect in DUNE. The distinction between the two NH solutions with different octants is a result of the synergy between the anti-neutrino data of NOνA and the neutrino data of DUNE