Can Randomness lead to non-anarchical mixing angles ?

TL;DR

<3-5 sentence high-level summary> The paper investigates whether randomness in theory-space mass parameters can generate non-anarchical neutrino mixing, using three geometries and both Dirac and Majorana realizations. It identifies two regimes: in the strong-disorder limit, Anderson localization dominates, yielding hierarchical masses but anarchic mixing independent of geometry; in the weak-disorder limit, milder localization or quasi-degeneracies allow GIM-like cancellations that can produce structured, non-anarchical mixing, with geometry influencing the pattern of degeneracies and cancellations. The results map out when disorder-driven mechanisms naturally lead to realistic flavour structure and when they predict universal anarchy, clarifying how randomness and graph geometry jointly shape neutrino masses and mixings. These insights offer guidance for UV-complete models where disorder, deconstruction, or landscape-inspired randomness could underlie flavour hierarchies and mixing patterns.

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.

Figures (39)

• Figure 1: Figure shows mass mode distribution for the uniform case with $\epsilon_i$ = W $\&$$t_i = t$ (left) and the histogram for smallest, largest and a midrange mass value produced in various runs for random case (right) with W = 5 TeV, t = 0.2 TeV and N = 8 with $\epsilon_i \in [2t, 2t + W]$.
• Figure 2: Eigen modes $\chi_i$ of Local lattice with uniform sites $\epsilon_i$ = W = 5 TeV $\&$$t_i = t = 0.2$ TeV (left) and random sites $t_i = t = 0.2$ TeV $\&$$\epsilon_i \in$ [-2W, 2W] (right) for N = 8.
• Figure 3: Figure shows the median of the Log of Absolute minimum component 0-mode of RCW and lightest mode of disorder models $\xi_{0}$ achieved with N = 14 sites for 50 runs with 1000 trials (left) and with varying site N from 5 to 14 (right) with W = 5 TeV and t = 1 TeV.
• Figure 4: Long-range non-local lattice representation for N = 10 sites.
• Figure 5: Mass modes $\chi_i$ of Non-Local lattice having uniform sites $\epsilon_i = 2W$, $W = 5$ TeV, $t = 1$ TeV, $N = 8$ and increasing (left), constant (middle) and decreasing (right) non-neighbouring couplings with distance for $b = 0.7, 1$ and $2$ respectively.