We investigate models of charged lepton and neutrino masses and lepton mixing based on broken modular symmetry. The matter fields in these models are assumed to transform in irreducible representations of the finite modular group Γ₄ ≃ S ₄. We analyse the minimal scenario in which the only source of symmetry breaking is the vacuum expectation value of the modulus field. In this scenario there is no need to introduce flavon fields. Using the basis for the lowest weight modular forms found earlier, we build minimal phenomenologically viable models in which the neutrino masses are generated via the type I seesaw mechanism. While successfully accommodating charged lepton masses, neutrino mixing angles and mass-squared differences, these models predict the values of the lightest neutrino mass (i.e., the absolute neutrino mass scale), of the Dirac and Majorana CP violation (CPV) phases, as well as specific correlations between the values of the atmospheric neutrino mixing parameter sin² θ ₂₃ and i) the Dirac CPV phase δ, ii) the sum of the neutrino masses, and iii) the effective Majorana mass in neutrinoless double beta decay. We consider also the case of residual symmetries ℤ ₃ ^ST and ℤ ₂ ^S respectively in the charged lepton and neutrino sectors, corresponding to specific vacuum expectation values of the modulus.

In the framework of the modular symmetry approach to lepton flavour, we consider a class of theories where matter superfields transform in representations of the finite modular group Γ₅ ≃ A ₅. We explicitly construct a basis for the 11 modular forms of weight 2 and level 5. We show how these forms arrange themselves into two triplets and a quintet of A ₅. We also present multiplets of modular forms of higher weight. Finally, we provide an example of application of our results, constructing two models of neutrino masses and mixing based on the supersymmetric Weinberg operator.

The formalism of combined finite modular and generalised CP (gCP) sym-metries for theories of flavour is developed. The corresponding consistency conditions for the two symmetry transformations acting on the modulus τ and on the matter fields are derived. The implications of gCP symmetry in theories of flavour based on modular invariance described by finite modular groups are illustrated with the example of a modular S ₄ model of lepton flavour. Due to the addition of the gCP symmetry, viable modular models turn out to be more constrained, with the modulus τ being the only source of CP violation.

We explore the possibility that dark matter interactions with Standard Model particles are dominated by interactions with neutrinos. We examine whether it

We discuss fermion mass hierarchies within modular invariant flavour models. We analyse the neighbourhood of the self-dual pointτ=i, where modular invariant theories possess a residualZ₄invariance. In this region the breaking ofZ₄can be fully described by the spurionϵ≈τ − i, that flips its sign underZ₄. Degeneracies or vanishing eigenvalues of fermion mass matrices, forced by theZ₄symmetry atτ=i, are removed by slightly deviating from the self-dual point. Relevant mass ratios are controlled by powers of|ϵ|. We present examples where this mechanism is a key ingredient to successfully implement an hierarchical spectrum in the lepton sector, even in the presence of a non-minimal Kähler potential.

We study the phenomenology of the simplest renormalisable model that, at low energy, leads to the effective field theory of the Standard Model extended with right-handed neutrinos (νSMEFT). Our aim is twofold. First, to contextualise new collider signatures in models with sterile neutrinos so far studied only using the bottom-up approach. And second and more important, to provide a thorough example of one-loop matching in the diagrammatic approach, of which other matching techniques and automatic tools can benefit for cross-checks. As byproducts of this work, we provide for the first time: (i) a complete off-shell basis for the νSMEFT and explicit relations between operators linked by equations of motion; (ii) a complete basis for the low-energy effective field theory (νLEFT) and the tree-level matching onto the νSMEFT; (iii) partial one-loop anomalous dimensions in the νLEFT. This way, our work comprises a new step forward towards the systematisation of one-loop computations in effective field theories, especially if the SM neutrinos are Dirac.