Simone Marciano

We present a simple and broadly applicable extension of the Casas–Ibarra parametrization that captures the structure of all Majorana neutrino mass models. Building directly on the original formulation, our approach naturally accommodates additional degrees of freedom and provides a unified, minimal framework for parametrizing the Yukawa sector. It significantly simplifies both analytical treatments and numerical scans, and can be universally applied to any Majorana neutrino mass model, regardless of the underlying dynamics. The approach also offers a unified framework for classifying neutrino mass models according to the structure of the neutrino mass matrix, which naturally motivates the proposal of an extended version of the scotogenic model. This classification scheme yields tree-level (loop-level) representative models; the seesaw (scotogenic model), the linear seesaw (the generalized scotogenic model), and the linear plus inverse seesaw (the extended scotogenic model). We provide ready-to-use explicit expressions for several well-known scenarios, including the Zee model where one of the Yukawa matrices is antisymmetric.

A bstract: We build upon a simple U(2) _F model of flavor, in which all fermion masses and mixing hierarchies arise from powers of two small parameters controlling U(2) _F breaking. In the original formulation, an isomorphism to the discrete D ₆ × U(1) _F symmetry was invoked to generate a Majorana neutrino mass term. Here, we retain the successful features of that model for the charged leptons and quarks, while exploring alternative neutrino charge assignments within the U(2) _F framework. This approach allows us to generate Majorana neutrino masses via the see-saw mechanism without introducing any additional symmetries nor invoking any isomorphism. We further examine the implications of our models for Lepton Flavor Violating (LFV) decays, analyzing the processes μ → eγ , τ → μγ and τ → eγ and their connection with the leptonic anomalous magnetic moments. We show that within the Standard Model Effective Field Theory (SMEFT) approach the current limits on the branching ratios of μ → eγ LFV decays obtained in our U(2) _F models are not compatible with the central value of the recent measurement of the ( g − 2) _μ , thereby suggesting that either ( g − 2) _μ must be very close to the Standard Model predictions, as the latest experimental and theoretical results seem to suggest, or the invoked flavor symmetry is not appropriate to describe an anomalous muon magnetic moment.

The unique dimension-5 effective operator, LLHH, known as the Weinberg operator, generates tiny Majorana masses for neutrinos after electroweak spontaneous symmetry breaking. If there are new scalar multiplets that take vacuum expectation values (VEVs), they should not be far from the electroweak scale. Consequently, they may generate new dimension-5 Weinberg-like operators which in turn also contribute to Majorana neutrino masses. In this study, we consider scenarios with one or two new scalars up to quintuplet SU(2) representations. We analyse the scalar potentials, studying whether the new VEVs can be induced and therefore are naturally suppressed, as well as the potential existence of pseudo-Nambu-Goldstone bosons. Additionally, we also obtain general limits on the new scalar multiplets from direct searches at colliders, loop corrections to electroweak precision tests and the W-boson mass.

We propose a model for leptons based on the smallest modular finite group Γ₂ ≅ S ₃ that, for the first time, accounts for both the hints of large low-energy CP-violation in the lepton sector and the matter-antimatter asymmetry of the Universe, generated by only two heavy right-handed neutrinos. These same states are also employed in a Minimal seesaw mechanism to generate light neutrino masses. Besides the heavy neutrinos, our particle content is the same as the Standard Model (SM), with the addition of one single modulus τ, whose vacuum expectation value is responsible for both the modular and CP-symmetry breakings. We show that this minimalistic SM extension is enough to get an excellent fit to low energy neutrino observables and to the required baryon asymmetry η _B . Predictions for the neutrino mass ordering, effective masses in neutrinoless double beta decay and tritium decay as well as for the Majorana phases are also provided.

The Weinberg operator is the unique dimension-5 operator that generates Majorana masses for neutrinos after electroweak symmetry breaking. Thus, it seems natural that the way to have small neutrino masses is that they are Majorana particles, with their masses obtained at tree level suppressed by a heavy scale, i.e. the seesaw mechanism. We consider new dimension-5 operators with additional scalars that transform under higher representations R under SU(2), up to R ≤ 5. We analyse the constraints on the VEVs of the new scalar multiplets from the 𝜌 parameter, as well as the generation of dimension-6 operators and non-unitarity constraints