Abstract: In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus tau and its conjugate, (tau) over bar. We point out that certain combinations of observables depend only on tau , i.e. are meromorphic, and in some cases even holomorphic functions of tau. These functions, which we dub “invariants” in this Letter, are highly constrained, renormalization group invariant, and allow us to derive many of the models' features without the need for extensive parameter scans. We illustrate the robustness of these invariants in two existing models in the literature based on modular symmetries, Gamma(3) and Gamma(5). We find that, in some cases, the invariants give rise to robust relations among physical observables that are independent of tau. Furthermore, there are instances where additional symmetries exist among the invariants. These symmetries are relevant phenomenologically and may provide a dynamical way to realize symmetries of mass matrices.

Abstract: We analyze the recent experimental evidence for an excess of tau-lepton production in several exclusive semileptonic B-meson decays in the context of two-Higgs-doublet models. These decay modes are sensitive to the exchange of charged scalars and constrain strongly their Yukawa interactions. While the usual Type-II scenario cannot accommodate the recent BaBar data, this is possible within more general models in which the charged-scalar couplings to up-type quarks are not as suppressed. Both the B -> D-(*)tau nu(tau) and the B -> tau nu(tau) data can be fitted within the framework of the Aligned Two-Higgs-Doublet Model, but the resulting parameter ranges are in conflict with the constraints from leptonic charm decays. This could indicate a departure from the family universality of the Yukawa couplings, beyond their characteristic fermion mass dependence. We discuss several new observables that are sensitive to a hypothetical charged-scalar contribution, demonstrating that they are well suited to distinguish between different scenarios of new physics in the scalar sector, and also between this group and models with different Dirac structures; their experimental study would therefore shed light on the relevance of scalar exchanges in semileptonic b -> c tau(-)(nu) over bar (tau) transitions.

Abstract: Motivated by the measured large branching ratio of (B) over bar (0) --> pi(0)pi(0) (the so-called pi pi puzzle), we investigate the effects of a family nonuniversal Z' model on the tree-dominated B --> pi pi decays. We find that the Z' coupling parameter zeta(LR)(d) similar to 0.05 with a nontrivial new weak phase phi(L)(d) similar to -50 degrees, which is relevant to the Z' contributions to the QCD penguin sector Delta C-5, is needed to reconcile the observed discrepancy. Combined with the recent fitting results from B --> pi K, pi K* and rho K decays, the Z' parameter spaces are severely reduced but still not excluded entirely, implying that both the “pi pi” and “pi K” puzzles could be accommodated simultaneously within such a family nonuniversal Z' model.