A benchmark model using genus-2 modular invariance generates quark mass hierarchies and CP violation via moduli VEVs near invariant points, with mass ratios vanishing in the symmetric limit and mixing angles reproduced.
Spontaneous breaking of CP symmetry by orbifold moduli
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abstract
CP-violating phases which contribute to the electric dipole moment(EDM) of the neutron are considered in the context of orbifold compactificationof the heterotic string. In particular, we study the situation where CP is spontaneously broken by moduli fields acquiring, in general, complex expectation values at the minimum of duality invariant low energy effective potentials. We show, by explicit minimization of such a potential in the case of the ${\bf Z}_{6}-{\rm IIb}$ orbifold, that it is the presence of so called Green-Schwarz anomaly coefficients $\delta_{\rm GS}^{i} $, that leads to significant CP violating expectation values of the moduli. By evaluating the soft supersymmetry breaking moduli dependent $A$ and $B$ terms in this model, we find that the experimental bounds $\Phi (A) $, $ \Phi (B) $ $\leq 5 \times 10^{-3} $ are exceeded for a particular range of values of the auxiliary field of the $S$ modulus.
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An exhaustive scan of Δ(96) Modular Littlest Seesaw models yields 35 viable residual-symmetry patterns with new fixed PMNS columns and sharp, testable predictions beyond TM1.
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Quark hierarchies and CP violation from the Siegel modular group
A benchmark model using genus-2 modular invariance generates quark mass hierarchies and CP violation via moduli VEVs near invariant points, with mass ratios vanishing in the symmetric limit and mixing angles reproduced.
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Lepton mixing from the $\Delta(96)$ Modular Littlest Seesaw
An exhaustive scan of Δ(96) Modular Littlest Seesaw models yields 35 viable residual-symmetry patterns with new fixed PMNS columns and sharp, testable predictions beyond TM1.