المؤلفون: Novichkov, P.P., Penedo, J.T., Petcov, S.T.

المصدر: Nuclear Physics

الوصف: 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.

الوصول الحر: https://explore.openaire.eu/search/publication?articleId=od______3000::d25b3a61b270af1bf7cd08d4316a233bTest
http://repo.scoap3.org/apiTest

المؤلفون: Penedo, J.T., Petcov, S.T.

المصدر: Nuclear Physics

الوصف: 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.

الوصول الحر: https://explore.openaire.eu/search/publication?articleId=od______3000::892f69dc380f38b2f272a36ecbe5b95dTest
http://repo.scoap3.org/apiTest