Charm multiplicity and the branching ratios of inclusive charmless b quark decays in the general two-Higgs-doublet models

In the framework of general two-Higgs-doublet models, we calculate the branching ratios of various inclusive charmless b decays by using the low energy effective Hamiltonian including next-to-leading order QCD corrections, and examine the current status and the new physics effects on the determination of the charm multiplicity $n_c$ and semileptonic branching ratio $B_{SL}$. Within the considered parameter space, the enhancement to the ratio $BR(b \to s g)$ due to the charged-Higgs penguins can be as large as a factor of 8 (3) in the model III (II), while the ratio $BR(b \to no charm)$ can be increased from the standard model prediction of 2.49% to 4.91% (2.99%) in the model III (II). Consequently, the value of $B_{SL}$ and $n_c$ can be decreased simultaneously in the model III. The central value of $B_{SL}$ will be lowered slightly by about 0.003, but the ratio $n_c$ can be reduced significantly from the theoretical prediction of $n_c= 1.28 \pm 0.05$ in the SM to $n_c= 1.23 \pm 0.05$, $1.18 \pm 0.05$ for $m_{H^+}=200, 100$ GeV, respectively. We find that the predicted $n_c$ and the measured $n_c$ now agree within roughly one standard deviation after taking into account the effects of gluonic charged Higgs penguins in the model III with a relatively light charged Higgs boson.