Lower Bounds on U_{e3}

TL;DR

This paper calculates the minimal non-zero value of the lepton mixing parameter U_{e3} at 2-loop order, showing it can be extremely small but non-zero, with implications for neutrino physics and supernova models.

Contribution

It provides the first minimal estimates of U_{e3} at 2-loop level in an effective theory, extending previous 1-loop results and highlighting the non-zero nature of U_{e3}.

Findings

U_{e3} is generated at 2-loop order at levels of 10^{-12} to 10^{-14} for inverted hierarchy.

Normal hierarchy limits for U_{e3} are several orders of magnitude larger.

Results imply U_{e3} is generally expected to be non-zero.

Abstract

We give minimal values for the smallest lepton mixing parameter U_{e3}, applying 2-loop renormalization group equations in an effective theory approach. This is relevant in scenarios that predict an inverted neutrino mass spectrum with the smallest mass and U_{e3} being zero at tree level, a situation known to be preserved at 1-loop order. At 2-loop, U_{e3} is generated at a level of 10^{-12}-10^{-14}. Such small values are of interest in supernova physics. Corresponding limits for the normal mass ordering are several orders of magnitude larger. Our results show that U_{e3} can in general expected be to be non-zero.