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We present numerical calculations of the partial width of the charged Higgsboson decay into a top quark, $H^- \rightarrow \bar{t} + b + X$, and thepartial width of the top quark decay into a light charged Higgs boson $t\rightarrow H^+ + b + X$ at next-to-next-to-leading order (NNLO) in QCD, basedon a factorization formula of the jet mass. The NNLO corrections significantlyreduce the renormalization scale dependence of the partial decay width in bothcases. We show relative size of the NNLO corrections for different chargedHiggs boson masses and for different renormalization scales. The NNLOcorrections are about 16% (1%) of the leading order widths for the chargedHiggs boson mass of 200GeV (2000GeV), while it is quite small for the top quarkdecay. Our analyses are independent of the detailed structure of the Yukawacouplings, and can be applied to various new physics models, as demonstrated bythe decay branching ratio in different types of the two-Higgs-doublet models.

Decay of the charged Higgs boson and the top quark in two-Higgs-doublet model at NNLO in QCD