Neutrino Oscillation Probabilities in Matter with Direct and Indirect Unitarity Violation in the Lepton Mixing Matrix

TL;DR

This paper derives comprehensive formulas for neutrino oscillation probabilities in matter considering both direct and indirect unitarity violations in the lepton mixing matrix, with detailed analysis of their accuracy and effects.

Contribution

It provides the first complete series expansion formulas for neutrino oscillations with combined unitarity violations, including numerical validation and analysis of their impact.

Findings

Series expansion formulas accurately describe oscillation probabilities.

Unitarity violation effects significantly alter summed neutrino transition probabilities.

Numerical analysis highlights differences between direct and indirect unitarity violations.

Abstract

In the presence of both direct and indirect unitarity violation in the lepton mixing matrix, we derive a complete set of series expansion formulas for neutrino oscillation probabilities in matter of constant density. Expansions in the mass hierarchy parameter $\alpha \equiv \Delta m_{21}^{2} / \Delta m_{31}^{2}$ and those unitarity violation parameters $s^{2}_{ij}$ (for i = 1, 2, 3 and j = 4, 5, 6) up to the first order are studied in this paper. We analyse the accuracy of the analytical series expansion formulas in different regions of L / E. A detailed numerical analysis is also performed, of which the different effects of the direct and the indirect unitarity violation are particularly emphasized. We also study in this paper the summed $\nu^{}_{\alpha} \rightarrow \nu^{}_{e, \nu, \tau}$ probabilities, whose deviation from the unity provides a definite signal of the unitarity violation.