Charged-Higgs on $R_{D^{(\ast )}}$, $\tau$ polarization, and FBA

Abstract

We study the influence of a charged-Higgs on the excess of branching fraction ratio, $R_M=BR(\bar{B}\to M\tau {\bar{\nu }}_{\tau })/BR(\bar{B}\to M\ell {\bar{\nu }}_{\ell })$ $(M=D,D^{\ast })$, in a generic two-Higgs-doublet model. In order to investigate the lepton polarization, the detailed decay amplitudes with lepton helicity are given. When the charged-Higgs is used to resolve excesses, it is found that two independent Yukawa couplings are needed to explain the $R_D$ and $R_{D^{\ast }}$ anomalies. We show that when the upper limit of $BR(B_c\to \tau {\bar{\nu }}_{\tau })<30\%$ is included, $R_D$ can be significantly enhanced while $R_{D^{\ast }}<0.27$. With the $BR(B_c\to \tau {\bar{\nu }}_{\tau })$ constraint, we find that the $\tau$-lepton polarizations can be still affected by the charged-Higgs effects, where the standard model (SM) predictions are obtained as: $P_D^{\tau }\approx 0.324$ and $P_{D^{\ast }}^{\tau }\approx -0.500$, and they can be enhanced to be $P_D^{\tau }\approx 0.5$ and $P_{D^{\ast }}^{\tau }\approx -0.41$ by the charged-Higgs. The integrated lepton froward-backward asymmetry (FBA) is also studied, where the SM result is ${\bar{A}}_{FB}^{D^{(\ast )},\tau }\approx -0.359(0.064)$, and they can be enhanced (decreased) to be ${\bar{A}}_{FB}^{D^{(\ast )},\tau }\approx -0.33(0.02)$.

22 pages, 4 figures, version to be published in EPJC

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