A non-unitary solar constraint for long-baseline neutrino experiments
Long-baseline neutrino oscillation experiments require external constraints on $\sin^2θ_{12}$ and $Δm_{21}^2$ 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 ($α_{11}$) representing the magnitude of the mixing between the $ν_e$ 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 $(1-α_{11}) < 0.046$ at the $99\%$ credible interval and yields a strongly correlated constraint on the solar mass splitting and the magnitude of $ν_e$ non-unitary mixing.