Weak dipole moments of the tau lepton in models with an extended scalar sector

We consider renormalizable couplings of neutral $\phi$, singly $\phi^\pm$, and doubly charged $\phi^{\pm\pm}$ scalar bosons to leptons and the $Z$ gauge boson and calculate the one-loop contributions to the anomalous weak magnetic dipole moment (AWMDM) $a_\tau^W$ and the weak electric dipole moment (WEDM) $d_\tau^W$ of a charged lepton in a model independent way. The analytic expressions are presented in terms of both parametric integrals and Passarino-Veltman scalar functions. Among the new contributions, there are those arising from the vertices of the type $\phi^\pm W^\mp Z$ and $Z \phi_i\phi_j$ ($i\ne j$), along with contributions from doubly charged scalar bosons. Both $a_\tau$ and $d_\tau^W$ are evaluated in several scenarios , first in a model independent way and then within some popular models, such as two-Higgs doublet models (THDMs), multiple-Higgs doublet models and Higgs triplet models. As far as $a_\tau^W$ is concerned, its real part reaches values as high as $10^{-10}-10^{-9}$ for masses of the new scalar bosons in the 200 GeV range, whereas the imaginary part is one or two orders of magnitude below. On the other hand, the most promising scenario for a nonvanishing WEDM is offered by a $CP$-violating THDM in a scenario where the heavy neutral scalar bosons are a mixture of $CP$ eigenstates. It is found that the real part of $d_\tau^W$ is of the order of $10^{-24}$ ecm and its imaginary part can reach the $10^{-26}$ ecm level for masses of the new scalar bosons of the order of a few hundred of GeVs. Both the tau AWMDM and WEDM decrease dramatically as the scalar boson masses increase.