A non-unitary solar constraint for long-baseline neutrino experiments

Long-baseline neutrino oscillation experiments require external constraints on ${\sin }^2{\theta }_{12}$ and $\mathrm{\Delta }{m}_{21}^2$ to make precision measurements of the leptonic mixing matrix. These constraints come from measurements of the Mikheyev-Smirnov-Wolfenstein (MSW) mixing in solar neutrinos. Here we develop an MSW large mixing angle approximation in the presence of heavy neutral leptons which adds a single new parameter (${\alpha }_{11}$) representing the magnitude of the mixing between the ${\nu }_e$ state and the heavy sector. We use data from the Borexino, SNO and KamLAND collaborations to find a solar constraint appropriate for heavy neutral lepton searches in long-baseline oscillation experiments. Solar data limits the magnitude of the non-unitary parameter to $(1-{\alpha }_{11})<0.046$ at the $99\mathrm{\%}$ credible interval and yields a strongly correlated constraint on the solar mass splitting and the magnitude of ${\nu }_e$ non-unitary mixing.