Understanding the Degenerate Solutions of NOvA

A combined analysis of disappearance and appearance data of NOvA experiment gives three nearly degenerate solutions. This degeneracy can be understood by the following argument: We first consider νe \nu_e appearance signal due to vacuum oscillations in the limit of maximal θ23 \theta_{23} and no CP-violation. We then calculate the deviations induced in the signal event rate by (a) matter effects (NH or IH), (b) θ23 \theta_{23} octance effects (HO or LO) and CP-violation (δC=−π/2 or π/2) (\delta_{C} = - \pi/2 \ {\rm or} \ \pi/2) . We find that the deviation caused by each of these effects is the same for NOvA. The three fold degeneracy arises because the data of NOvA is equal to the increase caused by two of the effects and the decrease caused by the third effect. We also find that further data by NOvA can not distinguish between these degenerate solutions but addition of one year of neutrino run of DUNE can make a distinction at 3σ 3 \sigma confidence level between all three solutions