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

Abstract

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 $B\to D^{(\ast )}\tau \nu$. 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 $B\to D^{(\ast )}\tau \nu$ 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 $B\to D^{(\ast )}\tau {\nu }_s$ to a sterile neutrino is also argued to be viable.

22 pages, 9 figures; v.2: added references; v.3: incorporated large tau Yukawa coupling into RGEs and in UV model; published version

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• Flavor physics in the multi-Higgs doublet models induced by the left-right symmetry
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