Abstract
We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. We show that for genus g\ge 3g≥3 the definition of CP is unique, while two independent possibilities are allowed when g\le 2g≤2. We discuss the transformation properties of moduli, matter multiplets and modular forms in the Siegel upper half plane, as well as in invariant subspaces. We identify CP-conserving surfaces in the fundamental domain of moduli space. We make use of all these elements to build a CP and symplectic invariant model of lepton masses and mixing angles, where known data are well reproduced and observable phases are predicted in terms of a minimum number of parameters.
Highlights
Fermion masses, mixing angles and conserving points satisfying (CPs) violating phases are tightly linked together in the present picture of particle interactions
We examine thoroughly all candidate CP definitions, arising as non-trivial automorphisms of the Siegel modular group Γ = S p(2g, ), which coincides with S L(2, ) when g = 1
We show that for genus g ≥ 3 there is a unique automorphism suitable to be interpreted as CP, coinciding with the one identified in refs. [55, 56]
Summary
Fermion masses, mixing angles and CP violating phases are tightly linked together in the present picture of particle interactions. In the previously discussed class of theories, CP properties depend on the chosen point in moduli space, which simultaneously controls particle masses and mixing angles. In this context most of the observed features of the fermion spectrum might be determined mostly by the vacuum, rather than by Lagrangian parameters. Within the more general case of a multidimensional moduli space, consistent CP definitions have been examined recently in the context of symplectic modular invariant theories, where the relevant flavour group is the Siegel modular group [55, 56].
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