Can Randomness lead to non-anarchical mixing angles ?

TL;DR

This paper investigates how randomness in fermion mass parameters and the geometry of the mass graph can influence neutrino mixing angles, showing that strong disorder leads to anarchical mixing while weak disorder can produce structured patterns.

Contribution

It extends previous work by analyzing multiple geometries and disorder regimes, revealing conditions for hierarchical or structured neutrino mixing from disordered theory spaces.

Findings

Strong disorder causes localization and anarchical mixing angles.

Weak disorder allows for structured mixing due to eigenmode degeneracies.

Different geometries influence the transition between hierarchical and anarchical mixing.

Abstract

We revisit the proposal of Craig and Sutherland that Anderson localization in a disordered fermion theory space can generate small neutrino masses from TeV scale physics \citecraig2018exponential}. Building on this idea, we ask a broader question: can randomness in fermion mass parameters also give rise to nonanarchical neutrino mixing angles, and how does the answer depend on the geometry of the mass graph? To explore this, we analyse three representative geometries a nearest neighbour chain, a fully connected non local model, and the Petersen graph in both Dirac and Majorana neutrino realisations. In the regime of strong diagonal disorder, all geometries display robust localization and naturally generate the observed neutrino mass scale, with the corresponding flavour mixing angles reflecting the random localization centres and thus taking an anarchical form. In the regime of weak disorder, where localization is milder, and eigenmodes can exhibit quasidegeneracies, light neutrino masses can emerge through GIM-mechanismlike cancellations among the heavy states. The weak disorder with geometry dependent weak localization constitutes a distinct pathway to structured mixings within disordered theory spaces. Overall, our results delineate the regimes in which disorder driven mechanisms produce hierarchical masses and identify the conditions under which structured flavour mixing can arise.