Revisiting the one leptoquark solution to the $R(D^{(\ast)})$ anomalies and its phenomenological implications

It has been shown recently that the anomalies observed in $\bar B\to D^{(\ast)}τ\barν_τ$ and $\bar B\to \bar K\ell^+\ell^-$ decays could be resolved with just one scalar leptoquark. Fitting to the current data on $R(D^{(\ast)})$ along with acceptable $q^2$ distributions in $\bar B\to D^{(\ast)}τ\barν_τ$ decays, four best-fit solutions for the operator coefficients have been found. In this paper, we explore the possibilities of how to discriminate these four solutions. Firstly, we find that two of them are already excluded by the decay $B_c^-\to τ^-\barν_τ$, because the predicted decay widths have already overshot the total width $Γ_{B_c}$. It is then found that the remaining two solutions result in two effective Hamiltonians governing $b\to c τ\barν_τ$ transition, which differ by a sign and enhance the absolute value of the coefficient of $\bar c_Lγ_μb_L\,\bar τ_Lγ^μ{ν_τ}_L$ operator by about $12\%$. However, they give nearly the same predictions as in the SM for the $D^\ast$ and $τ$ longitudinal polarizations as well as the lepton forward-backward asymmetries in $\bar B\to D^{(\ast)}τ\barν_τ$ decays. For the other observables like $\mathcal B(B_c^-\to τ^-\barν_τ)$, $\mathcal B(B_c^- \to γτ^-\barν_τ)$, $R_{D^{(\ast)}}(q^2)$, ${\rm d}\mathcal B(\bar B\to D^{(\ast)}τ\barν_τ)/{\rm d}q^2$ and $\mathcal B(\bar B\to X_cτ\barν_τ)$, on the other hand, the two solutions give sizable enhancements relative to the SM predictions. With measurement of $B_c^-\to τ^-\barν_τ$ at LHCb and refined measurements of observables in $\bar B\to D^{(\ast)}τ\barν_τ$ at both LHCb and Belle-II, such a specific NP scenario could be further deciphered.

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