In presence of non standard interactions, the solar neutrino data is consistent with two solutions, one close to the standard LMA solution with $\sin^2\theta_{ 12} \simeq 0.3$ and another with $\sin^2\theta_{ 12}^D \simeq 0.7(=\cos^2\theta_{ 12})$. The latter has been called the Dark LMA (DLMA) solution in the literature. This issue is hard to resolve via oscillations because of the existence of the so-called "generalised mass hierarchy" degeneracy of the neutrino mass matrix in presence of NSI. However, if the mass hierarchy is independently determined in a non-oscillation experiment such as neutrino-less double beta decay, the invariance of neutrino oscillation probabilities under $\sin^2\theta_{ 12} \leftrightarrow \cos^2\theta_{ 12}$ is lost and the possibility of resolving the LMA vs DLMA opens up. We point out that the $P_{ \mu\mu}$ channel can distinguish $\theta_{ 12}$ from $\theta_{ 12}^D$ and study the corresponding difference in long-baseline experiments. We show that a key ingredient required is the input from the $P_{ ee}$ channel measured at a reactor experiment. We find that if the mass hierarchy is determined by neutrino-less double beta decay, then a combined measurement of the effective mass squared differences in long-baseline experiments such as T2HK and DUNE and reactor experiment such as JUNO can resolve the DLMA conundrum to better than $3\sigma$ within 1 year for T2HK and little more than 3 years for DUNE.
Categories: hep-ph