Abstract
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 eV2 ≲ 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 mathcal{C} αβ of mathcal{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 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 mathcal{C} αβ, 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.
Highlights
Studies of neutrino oscillation entered into a “matured phase” after the structure of the three-flavour lepton mixing [1] is elucidated
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 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 sterile-sector model independent
Summary
Studies of neutrino oscillation entered into a “matured phase” after the structure of the three-flavour lepton mixing [1] is elucidated. In a previous paper [20], we have proposed a model-independent framework for testing low-scale unitarity violation It is based on the three active plus N sterile lepton (called neutrino) system, which is unitary in the whole (3 + N ) dimensional state space but restriction to observables in the active neutrino subspace renders the theory non-unitary in that subspace. The second goal of this paper is to utilize the oscillation probability formulas to uncover in which region of energies and baselines unitarity violating effect is large, and to examine the possibility of sizeable W 2 corrections which distinguishes between high- and low-scale unitarity violation These exercises may be useful in the application of our framework to some of the ongoing and generation neutrino oscillation experiments [16, 17, 46,47,48,49,50,51,52]. The framework can be used in dual modes: it serves (1) as a suitable framework for leptonic unitarity test in neutrino oscillation experiments, and (2) as a hunting tool for unitarity violation effects, which could serve for another way of distinguishing low-scale unitarity violation from high-scale one
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