Vishnu P. K.

The fermionic nature of neutrinos and the origin of their tiny masses remain unresolved issues in particle physics, intrinsically connected to lepton number symmetry-conserved for Dirac, violated for Majorana, and effectively pseudo-Dirac when global symmetries invoked for conservation are broken by quantum gravity. We investigate whether distinctive gravitational-wave (GW) signatures can illuminate the nature of neutrino masses and their underlying symmetries, particularly in scenarios where Yukawa couplings are not unnaturally small. To this end, we consider the minimal $B-L$ gauge extension of the Standard Model, where quantum numbers of beyond-SM states determine the neutrino nature and the scale of spontaneous $B-L$ breaking governs mass generation. In this framework, we show that neutrinos yield characteristic GW spectra: Majorana neutrinos with high-scale breaking ($\sim 10^{14}$ GeV) produce local cosmic strings and a flat spectrum across broad frequencies, Dirac neutrinos with low-scale breaking ($\sim 10^{7}$ GeV) generate peaked spectra from first-order phase transitions, and pseudo-Dirac scenarios give kink-like features from domain wall annihilation.

We investigate how neutrinos may acquire small electric charges within the Standard Model framework while preserving electromagnetic gauge invariance. Instead of gauging the standard hypercharge generator $Y$, a linear combination of $Y$ and a new generator $X$ from a gaugable global $U(1)_X$ symmetry is embedded, under which neutrinos transform non-trivially. We demonstrate that minimal scenarios based on flavor-dependent $U(1)_X$ symmetries, such as $X = L_α- L_β$, are incompatible with current neutrino oscillation data. In contrast, we have shown that only flavor-universal $U(1)_X$ symmetries-such as $U(1)_{B-L}$, which shifts both quark and lepton charges, and $U(1)_L$, which modifies only the lepton sector-can generate tiny neutrino charges consistent with observed masses and mixing. We also discuss the necessary connection between such charges and the Dirac nature of neutrinos. By analyzing the phenomenological implications in detail, our findings emphasize that constraints on neutrino charges should be evaluated within the specific framework of the $U(1)_X$ symmetry under consideration, rather than assuming a generic approach, as is often the case.

We propose a class of dark matter models based on a chiral $U(1)$ gauge symmetry acting on a dark sector. The chiral $U(1)$ protects the masses of the dark sector fermions, and also guarantees the stability of the dark matter particle by virtue of an unbroken discrete $\mathcal{Z}_N$ gauge symmetry. We identify 38 such $U(1)$ models which are descendants of a chiral $SU(3) \times SU(2)$ gauge symmetry, consisting of a minimal set of fermions with simple $U(1)$ charge assignments. We show how these models can also be utilized to generate small Majorana neutrino masses radiatively via the scotogenic mechanism with the dark sector particles circulating inside loop diagrams. We further explore the phenomenology of the simplest model in this class, which admits a Majorana fermion, Dirac fermion or a scalar field to be the dark matter candidate, and show the consistency of various scenarios with constraints from relic density and direct detection experiments.