Gravitational Waves in an A4 Neutrino Mass Model

TL;DR

This work presents an A4×Z4-flavored model in which cross couplings among flavons generate a natural vacuum bias, eliminating domain-wall degeneracy without explicit symmetry breaking. The model simultaneously yields realistic neutrino mixing from a corrected TBM structure and predicts a gravitational-wave signal from domain-wall annihilation, with amplitudes and peak frequencies that can approach near-future GW experiments and potentially explain PTA hints. By linking flavon dynamics to cosmological signatures, the paper offers a coherent framework where neutrino mass generation, flavor symmetry breaking, and gravitational waves are interconnected, and it highlights parameter regions around the TeV scale for flavor-breaking vevs and TeV-scale cross-couplings. These results motivate further numerical simulations of domain-wall evolution in A4-based setups to refine GW predictions and testability.

Abstract

The A4 flavor symmetry has provided tremendous insight into the flavor structure of the lepton sector of the Standard Model, predicting a very good approximation to neutrino mixing angles, Tri-Bimaximal Mixing. A4 is spontaneously broken by a scalar called the flavon, and when this happens a number of degenerate vacua can form, resulting in so-called domain walls. These objects are not observed and hence need to be annihilated. This is usually done by explicitly breaking A4 by adding a bias term to the scalar potential. In this paper, we construct a new model invariant under A4 and Z4, which creates cosmologically viable domain walls, lifts the degeneracy of the vacuum giving a natural mechanism for domain walls to annihilate, as well as predicts realistic neutrino mixing angles; all utilizing cross couplings between flavons. The annihilation of the domain walls, with proper choice of wall tension and the consequent bias term, leads to a gravitational wave signal that is potentially detectable in near future gravitational wave experiments, and interestingly intersects with the observed Pulsar Timing Array signal.

Figures (3)

• Figure 1: The $\chi^2$ difference vs $\theta_{\phi}$, showing the regions of best fit phases. We performed this $\chi^2$ fit to $\sin^2\,\theta_{13}$ and $\sin^2\,\theta_{23}$ to predict $\sin^2\,\theta_{12}$ from our derived sum rule \ref{['sumrule']}. Note the two values, the second valley corresponding to $\theta_{\phi}\approx298.5^{\circ}$, gives a more favorable range of $\sin^2\,\theta_{12}$.
• Figure 2: Gravitational-wave spectrum from domain wall annihilation with calculated $v_{\phi}\approx30~\text{TeV}, v_{\chi} \approx10$ TeV with appropriate domain wall tension. We see this could produce a GW signal that interestingly intersects with the observed Pulsar Timing Array signal.
• Figure 3: Gravitational Wave amplitude dependence on domain wall tension. We see that the greater the domain wall tension, the greater the amplitude of the gravitational waves which is intuitively expected. Note, the signal intersecting the Pulsar Timing Array signal NANOGrav:2023gor corresponds to a tension that gives a ratio in the bounds of eq. \ref{['eq:10']}.