2026/07/21 by Mitesh Kumar Behera, Jaydeb Das, Niloy Mondal
#hep-ph
We study a type-I seesaw framework based on non-holomorphic A4 modular symmetry, where polyharmonic Maaß forms construct the Yukawa couplings and right-handed neutrino (RHN) Majorana mass matrix. The use of non-holomorphic modular forms yields highly constrained neutral lepton mass matrices with a more restrictive lepton-sector structure and naturally generates a quasi-degenerate RHN mass spectrum, enabling resonant leptogenesis at an intermediate scale with RHN masses of O(103) TeV without requiring an ad hoc mass degeneracy. We further extend the model by introducing a complex scalar field (Φ) charged under ℤ3 symmetry. The spontaneous breaking of the discrete symmetry after the phase transition associated with Φ leads to domain-wall (DW) formation. A radiatively induced bias term associated with the RHN sector triggers DW annihilation, resolving the cosmological DW problem, and producing a stochastic gravitational wave (GW) signal that indirectly probes the RHN mass scale. The accompanying first-order phase transition produces a second GW peak, yielding a characteristic double-peaked spectrum with frequencies separated by several orders of magnitude and potentially observable by complementary future GW detectors.