Scalar doublet models confront $\tau$ and $b$ anomalies

There are indications of a possible breakdown of the standard model, suggesting that $\tau$ lepton interactions violate flavor universality. BABAR, Belle and LHCb report high ratios of $B\to D^{(*)}\tau\nu$. There are long-standing excesses in $B\to\tau\nu$ and $W\to\tau\nu$ decays, and a deficit in inclusive $\tau$ to strange decays. We investigate whether two Higgs doublet models with the most general allowed couplings to quarks, and a large coupling to $\tau$ leptons, can explain these anomalies while respecting other flavor constraints and technical naturalness. Fits to $B\to D^{(*)}\tau\nu$ data require couplings of the new Higgs doublet to down-type quarks, opening the door to many highly constrained flavor-changing neutral current (FCNC) processes. We confront these challenges by introducing a novel ansatz that relates the new up- and down-type Yukawa couplings, and demonstrate viable values of the couplings that are free from fine tuning. LEP and LHC searches for new Higgs bosons decaying via $H^0\to \tau^+\tau^-$ and $H^\pm\to\tau^\pm\nu$ allow a window of masses $m_H = [100$-$125]\,$GeV and $m_\pm\sim 100\,$GeV that is consistent with the predictions of our model. Contamination of the $W^+\to\tau^+\nu$ signal by $H^+\to\tau^+\nu$ decays at LEP could explain the apparent $W\to\tau\nu$ excess. We predict that the branching ratio for $B_s\to \tau^+\tau^-$ is not far below its current limit of several percent. An alternative model with decays of $B\to D^{(*)}\tau\nu_s$ to a sterile neutrino is also argued to be viable.