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→Dτν and B→D*τν of approximately 3.8σ. There is also the long lasting discrepancy of about 3σ in the anomalous magnetic moment of the muon, and the branching ratio for τ→μνν is 1.8σ (2.4σ) above the standard model expectation using the HFAG (PDG) values. Furthermore, CMS Collaboration finds hints for a nonzero decay rate of h→μτ. 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 τ→μνν with modified Higgs--τ 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→μτ are also possible, but in this case a simultaneous explanation of the anomalous magnetic moment of the muon is difficult due to the unavoidable τ→μγ decay.