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 0.1eV2≲mJ2​≲(1−10)GeV2 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
Cαβ​ of O(W4). 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}. Then, we identify a limited energy region in
which this suppression is evaded and the effects of order W2 corrections may
be observable. Its detection would provide another way, in addition to
detecting Cαβ​, to distinguish between low-scale and
high-scale unitarity violation. We also solve analytically the zeroth-order
system in matter with uniform density to provide a basis for numerical
evaluation of non-unitary neutrino evolution.Comment: 35 content pages + 12 appendix pages, 4 figures; Several clarifying
modifications to match the published versio