Third Family Corrections to Tri-bimaximal Lepton Mixing and a New Sum Rule

TL;DR

This paper analyzes the stability of tri-bimaximal neutrino mixing predictions under third family wave-function corrections, deriving a new stable sum rule relating deviations in mixing angles and the CP phase.

Contribution

It introduces a universal parameter to account for third family corrections and derives a new stable lepton mixing sum rule applicable to hierarchical neutrinos.

Findings

The sum rule 's = r cos delta + 2/3 a' remains stable under leading order corrections.

Third family wave-function corrections can be unified into a single parameter.

The results provide a testable relation for neutrino mixing deviations.

Abstract

We investigate the theoretical stability of the predictions of tri-bimaximal neutrino mixing with respect to third family wave-function corrections. Such third family wave-function corrections can arise from either the canonical normalisation of the kinetic terms or renormalisation group running effects. At leading order both sorts of corrections can be subsumed into a single universal parameter. For hierarchical neutrinos, this leads to a new testable lepton mixing sum rule 's = r cos delta + 2/3 a' (where s, r, a describe the deviations of solar, reactor and atmospheric mixing angles from their tri-bimaximal values, and 'delta' is the observable Dirac CP phase) which is stable under all leading order third family wave-function corrections, as well as Cabibbo-like charged lepton mixing effects.