Perturbed Lepton-Specific Two-Higgs-Doublet Model Facing Experimental Hints for Physics beyond the Standard Model

Abstract

BABAR, Belle, and LHCb Collaborations report evidence for new physics in $B\ensuremath{\rightarrow}D\ensuremath{\tau}\ensuremath{\nu}$ and $B\ensuremath{\rightarrow}{D}^{*}\ensuremath{\tau}\ensuremath{\nu}$ of approximately $3.8\ensuremath{\sigma}$. There is also the long lasting discrepancy of about $3\ensuremath{\sigma}$ in the anomalous magnetic moment of the muon, and the branching ratio for $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\nu}$ is $1.8\ensuremath{\sigma}$ ($2.4\ensuremath{\sigma}$) above the standard model expectation using the HFAG (PDG) values. Furthermore, CMS Collaboration finds hints for a nonzero decay rate of $h\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\tau}$. Interestingly, all these observations can be explained by introducing new scalars. In this Letter we consider these processes within a lepton-specific two-Higgs doublet model (i.e., of type X) with additional nonstandard Yukawa couplings. It is found that one can accommodate $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\nu}$ with modified Higgs--$\ensuremath{\tau}$ couplings. The anomalous magnetic moment of the muon can be explained if the additional neutral $CP$-even Higgs boson $H$ is light (below 100 GeV). Also $\mathcal{R}(D)$ and $\mathcal{R}({D}^{*})$ can be easily explained by additional $t$--$c$--Higgs couplings. Combining these $t$--$c$ couplings with a light $H$ the decay rate for $t\ensuremath{\rightarrow}Hc$ can be in a testable range for the LHC. Effects in $h\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\tau}$ are also possible, but in this case a simultaneous explanation of the anomalous magnetic moment of the muon is difficult due to the unavoidable $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$ decay.