Charged Higgs boson contribution to Bq−→ℓν¯ and B¯→(P,V)ℓν¯ in a generic two-Higgs doublet model

Abstract

We comprehensively study the charged Higgs boson contributions to the leptonic ${B}_{q}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ ($q=u$, $c$) and semileptonic $\overline{B}\ensuremath{\rightarrow}{X}_{q}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ (${X}_{u}=\ensuremath{\pi}$, $\ensuremath{\rho}$; ${X}_{c}=D$, ${D}^{*}$) decays in the type-III two-Higgs doublet model. We employ the Cheng-Sher ansatz to suppress the tree-level flavor-changing neutral currents in the quark sector. When the strict constraints from the $\mathrm{\ensuremath{\Delta}}B=2$, $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$, and $pp(b\overline{b})\ensuremath{\rightarrow}H/A\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$ processes are considered, parameters ${\ensuremath{\chi}}_{tq}^{u}$ from the quark couplings and ${\ensuremath{\chi}}_{\ensuremath{\ell}}^{\ensuremath{\ell}}$ from the lepton couplings dictate the leptonic and semileptonic $B$ decays. It is found that, when the measured ${B}_{u}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\tau}\overline{\ensuremath{\nu}}$ and indirect bound of ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\tau}\overline{\ensuremath{\nu}}$ obtained by LEP1 data are taken into account, $R(D)$ and $R(\ensuremath{\pi})$ can have broadly allowed ranges; however, the values of $R(\ensuremath{\rho})$ and $R({D}^{*})$ are limited to approximately the standard model (SM) results. We also find that the same behaviors also occur in the $\ensuremath{\tau}$-lepton polarizations and forward-backward asymmetries (${A}_{FB}^{{X}_{q},\ensuremath{\tau}}$) of the semileptonic decays, with the exception of ${A}_{FB}^{{D}^{*},\ensuremath{\tau}}$, for which the deviation from the SM due to the charged Higgs boson effect is still sizable. In addition, the ${q}^{2}$-dependent ${A}_{FB}^{\ensuremath{\pi},\ensuremath{\tau}}$ and ${A}_{FB}^{D,\ensuremath{\tau}}$ can be very sensitive to the charged Higgs boson effects and have completely different shapes from the SM.