Non-unitary evolution of neutrinos in matter and the leptonic unitarity test

Understand

We present a comprehensive study of the three-active plus $N$ sterile neutrino model as a framework for constraining leptonic unitarity violation induced at energy scales much lower than the electroweak scale.

• We formulate a perturbation theory with expansion in small unitarity violating matrix element $W$ while keeping (non-$W$ suppressed) matter effect to all orders.
• We show that under the same condition of sterile state masses $0.1\, \text{eV}^2 \lesssim m^2_{J} \lesssim (1-10)\, \text{GeV}^2$ as in vacuum, assuming typical accelerator based long-baseline neutrino oscillation experiment, one can derive a very simple form of the oscillation probability which consists only of zeroth-order terms with the unique exception of probability leaking term $\mathcal{C}_{\alpha \beta}$ of $\mathcal{O} (W^4)$.
• We argue, based on our explicit computation to fourth-order in $W$, that all the other terms are negligibly small after taking into account the suppression due to the mass condition for sterile states, rendering the oscillation probability {\em sterile-sector model independent}.