We consider a new massive vector-boson Z that couples to leptons through the L_mu - L_tau current, and to quarks through an arbitrary set of couplings. We show that such a model can be obtained from a renormalizable field theory involving new heavy f
ermions in an anomaly-free representation. The model is a candidate explanation for the discrepancy observed recently by the LHCb collaboration in angular distributions of the final state particles in the rare decay B to K* mu^+ mu^-. Interestingly, the new vector-boson contribution to the decay tau to mu nu_tau bar nu_mu can also remove a small tension in the measurement of the corresponding branching ratio. Constraints from light flavor meson-mixing restrict the coupling to the up- and down-quarks to be very small and thus direct production of the vector-boson at hadron colliders is strongly suppressed. The most promising ways to test the model is through the measurement of the Z decay to four leptons and through its effect on neutrino trident production of muon pairs. This latter process is a powerful but little-known constraint, which surprisingly rules out explanations of (g-2)_mu based on Z gauge bosons coupled to muon number, with mass of at least a few GeV.
All current experiments searching for an electron EDM d_e are performed with atoms and diatomic molecules. Motivated by significant recent progress in searches for an EDM-type signal in diatomic molecules with an uncompensated electron spin, we provi
de an estimate for the expected signal in the Standard Model due to the CKM phase. We find that the main contribution originates from the effective electron-nucleon operator $bar{e} igamma_5 e bar{N}N$, induced by a combination of weak and electromagnetic interactions at $O(G_F^2alpha^2)$, and not by the CKM-induced electron EDM itself. When the resulting atomic P,T-odd mixing is interpreted as an {it equivalent} electron EDM, this estimate leads to the benchmark $d_e^{equiv}(CKM) sim 10^{-38}$ ecm.
