Can Randomness lead to non-anarchical mixing angles ?

Abstract

We study how disorder and graph connectivity affect neutrino masses and mixing in fermionic theory spaces. Extending the construction of Craig and Sutherland, we compare a nearest-neighbour chain, a non-local graph with distance-suppressed links, and a sparse Petersen-type graph, for Dirac and Majorana neutrinos. Strong site disorder suppresses boundary propagation through localisation. When the heavy mass matrix instead has a dominant approximately uniform diagonal, light masses can arise from cancellations in its inverse. A path expansion makes the dependence on graph connectivity explicit. Our benchmark ensembles display broad mixing distributions for some flavour couplings and peaked distributions for others, particularly with weak site disorder and structured flavour input. These observations do not establish a Haar distribution at strong disorder or a statistical preference over neutrino anarchy at weak disorder. The results identify conditions under which disorder can preserve structured mixing, while leaving its quantitative explanatory advantage to a controlled ensemble comparison.

arXiv commentEnlarged version with significantly modified discussion. 72 pages, 29 figures