Inverted Mass Hierarchy from Scaling in the Neutrino Mass Matrix: Low and High Energy Phenomenology

TL;DR

This paper proposes the 'scaling' hypothesis in the Majorana neutrino mass matrix, naturally explaining observed neutrino mixing patterns, predicting an inverted hierarchy, and exploring implications for high-energy astrophysical neutrinos and leptogenesis.

Contribution

It introduces the scaling hypothesis in the neutrino mass matrix, offering a novel explanation for neutrino mixing and hierarchy, and connects low-energy neutrino properties with high-energy phenomena and leptogenesis.

Findings

Scaling predicts an inverted neutrino mass hierarchy.

The hypothesis naturally explains large solar mixing and non-maximal atmospheric mixing.

A specific ratio of mu -> e gamma to tau -> e gamma decay rates is derived in supersymmetric models.

Abstract

Best-fit values of recent global analyzes of neutrino data imply large solar neutrino mixing, vanishing U_{e3} and a non-maximal atmospheric neutrino mixing angle theta_{23}. We show that these values emerge naturally by the hypothesis of "scaling" in the Majorana neutrino mass matrix, which states that the ratios of its elements are equal. It also predicts an inverted hierarchy for the neutrino masses. We point out several advantages and distinguishing tests of the scaling hypothesis compared to the L_e - L_mu - L_tau flavor symmetry, which is usually assumed to provide an understanding of the inverted hierarchy. Scenarios which have initially vanishing U_{e3} and maximal atmospheric neutrino mixing are shown to be unlikely to lead to non-maximal theta_{23} while keeping simultaneously U_{e3} zero. We find a peculiar ratio of the branching ratios mu -> e gamma and tau -> e gamma in supersymmetric seesaw frameworks, which only depends on atmospheric neutrino mixing and results in tau -> e gamma being unobservable. The consequences of the scaling hypothesis for high energy astrophysical neutrinos at neutrino telescopes are also investigated. Then we analyze a seesaw model based on the discrete symmetry D_4 times Z_2 leading to scaling in the low energy mass matrix and being capable of generating the baryon asymmetry of the Universe via leptogenesis. The relevant CP phase is identical to the low energy Majorana phase and successful leptogenesis requires an effective mass for neutrinoless double beta decay larger than 0.045 eV.