Search

Working within the Standard Model effective field theory approach, we examine the possibility to test charged lepton flavour violating (cLFV) new physics (NP) by angular measurements of the outgoing electron and positrons in the polarised $\mu^{+}\to e^{+}e^{+}e^{-}$ decay. This decay is planned to be studied with a sensitivity to the branching ratio of $B_{\mu\to3e}\sim 10^{-15}$ by the Mu3e experiment at PSI. To illustrate the potential of these measurements, we consider a set of eight effective operators generating the decay at the tree level, including dimension-five dipole operators and dimension-six scalar and vector four-fermion operators of different chiralities. We show that if the polarised $\mu^{+}\to e^{+}e^{+}e^{-}$ decay is observed and is induced by a single operator, data from three angular observables - two P-odd asymmetries and one T-odd asymmetry - can allow to discriminate between all considered operators with the exception of scalar and vector operators of opposite chirality. For these two types of operators, the P-odd asymmetry is maximal in magnitude; they can be distinguished, in principle, by measuring the helicities of the outgoing positrons. The observation of a non-zero T-odd asymmetry would indicate the presence in the decay rate of a dipole and vector operator interference term that is T (CP) violating., Comment: 22 pages, 2 figures, 3 tables

We develop the formalism of the finite modular group Γ4′≡S4′, a double cover of the modular permutation group Γ4≃S4, for theories of flavour. The integer weight k>0 of the level 4 modular forms indispensable for the formalism can be even or odd. We explicitly construct the lowest-weight (k=1) modular forms in terms of two Jacobi theta constants, denoted as ε(τ) and θ(τ), τ being the modulus. We show that these forms furnish a 3D representation of S4′ not present for S4. Having derived the S4′ multiplication rules and Clebsch-Gordan coefficients, we construct multiplets of modular forms of weights up to k=10. These are expressed as polynomials in ε and θ, bypassing the need to search for non-linear constraints. We further show that within S4′ there are two options to define the (generalised) CP transformation and we discuss the possible residual symmetries in theories based on modular and CP invariance. Finally, we provide two examples of application of our results, constructing phenomenologically viable lepton flavour models.

We construct phenomenologically viable models of lepton masses and mixing based on modular A4 invariance broken to residual symmetries Z3T or Z3ST and Z2S respectively in the charged lepton and neutrino sectors. In these models the neutrino mixing matrix is of trimaximal mixing form. In addition to successfully describing the charged lepton masses, neutrino mass-squared differences and the atmospheric and reactor neutrino mixing angles θ23 and θ13, 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 the existence of specific correlations between i) the values of the solar neutrino mixing angle θ12 and the angle θ13 (which determines θ12), ii) the values of the Dirac CPV phase δ and of the angles θ23 and θ13, iii) the sum of the neutrino masses and θ23, iv) the neutrinoless double beta decay effective Majorana mass and θ23, and v) between the two Majorana phases.

We study models of lepton masses and mixing based on broken modular invariance. We consider invariance under the finite modular group Γ4≃S4 and focus on the minimal scenario where the expectation value of the modulus is the only source of symmetry breaking, such that no flavons need to be introduced. After constructing a basis for the lowest weight modular forms, we build two minimal models, one of which successfully accommodates charged lepton masses and neutrino oscillation data, while predicting the values of the Dirac and Majorana CPV phases.

The observation of neutrinoless double beta decay would allow to establish lepton number violation and the Majorana nature of neutrinos. The rate of this process in the case of 3-neutrino mixing is controlled by the neutrinoless double beta decay effective Majorana mass |〈m〉|. For a neutrino mass spectrum with normal ordering, which is favoured over the spectrum with inverted ordering by recent global fits, |〈m〉| can be significantly suppressed. Taking into account updated data on the neutrino oscillation parameters, we investigate the conditions under which |〈m〉| in the case of spectrum with normal ordering exceeds 10−3(5×10−3)eV: |〈m〉|NO>10−3(5×10−3)eV. We analyse first the generic case with unconstrained leptonic CP violation Majorana phases. We show, in particular, that if the sum of neutrino masses is found to satisfy Σ>0.10eV, then |〈m〉|NO>5×10−3eV for any values of the Majorana phases. We consider also cases where the values for these phases are either CP conserving or are in line with predictive schemes combining flavour and generalised CP symmetries.

We show that the relatively large best fit value of sin2⁡2θ13=0.14(0.17) measured in the T2K experiment for fixed values of i) the Dirac CP violation phase δ=0, and ii) the atmospheric neutrino mixing parameters θ23=π/4, |Δm322|=2.4×10−3 eV2, can be reconciled with the Daya Bay result sin2⁡2θ13=0.090±0.009 if the effects of non-standard neutrino interactions (NSI) in the relevant ν¯e→ν¯e and νμ→νe oscillation probabilities are taken into account.

We investigate the generation of the baryon asymmetry of the Universe within a SUSY SU(5)×T′ model of flavour, which gives rise to realistic masses and mixing patterns for quarks and leptons. The model employs the see-saw mechanism for generation of the light neutrino masses and the baryon asymmetry is produced via leptogenesis. We perform detailed calculations of both the CP violating lepton asymmetries, originating from the decays of the heavy Majorana neutrinos operative in the see-saw mechanism, and of the efficiency factors which account for the lepton asymmetry wash-out processes in the Early Universe. The latter are calculated by solving numerically the system of Boltzmann equations describing the generation and the evolution of the lepton asymmetries. The baryon asymmetry in the model considered is proportional to the JCP factor, which determines the magnitude of CP violation effects in the oscillations of flavour neutrinos. The leptogenesis scale can be sufficiently low, allowing to avoid the potential gravitino problem.