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

BABAR, Belle, and LHCb Collaborations report evidence for new physics in B -> D tau nu and B -> D* tau nu of approximately 3.8 sigma. There is also the long lasting discrepancy of about 3 sigma in the anomalous magnetic moment of the muon, and the branching ratio for tau -> mu nu nu is 1.8 sigma (2.4 sigma) above the standard model expectation using the HFAG (PDG) values. Furthermore, CMS Collaboration finds hints for a nonzero decay rate of h -> mu 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 tau -> mu nu nu with modified Higgs-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 R(D) and 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 -> Hc can be in a testable range for the LHC. Effects in h -> mu 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 t -> mu gamma decay.