Optimal-observable analysis of possible new physics in $B\to D^{(*)}\tau {\nu }_{\tau }$

We study all possible observables in $B\to D^{(*)}\tau {\nu }_{\tau }$ with new physics (NP), including new vector, scalar and tensor interactions, and investigate the prospects of extracting NP Wilson coefficients with optimal observables. The analysis shows that, overall, the full $q^2$ integrated observables in $B\to D\tau {\nu }_{\tau }$ are more sensitive towards the scalar current, whereas the bin-by-bin analysis of $q^2$ distribution of the differential branching fraction points to regions of $q^2$ sensitive to tensor interactions. Interestingly, the observables in $B\to D^{*}\tau {\nu }_{\tau }$ are more sensitive to tensor interactions, and bin-by-bin analysis of this mode shows the distinct regions of $q^2$ sensitive to vector or scalar interactions. In addition to that, the $\tau$ polarization asymmetry is found to be more sensitive to NP compared to the other observables, in both decay modes.

Figure 1

Surfaces of constant ${\chi }^2=1$ for a few selected cases of different observables in $B\to D\tau {\nu }_{\tau }$.

Figure 2

Surfaces of constant ${\chi }^2=1$ for a few selected cases of different observables shown in $B\to D^{*}\tau {\nu }_{\tau }$.

Figure 3

The variations of $\delta C_i$ with the $q^2$ for a few selected cases in $B\to D\tau {\nu }_{\tau }$, here, $\overline{C_i}=\delta C_i/N_{\mathrm{norm}}$.

Figure 4

The variations of $\delta C_i$ with the $q^2$ for a few selected cases in $B\to D^{*}\tau {\nu }_{\tau }$, here, $\overline{C_i}=\delta C_i/N_{\mathrm{norm}}$.

Figure 5

Measured $q^2$ distribution of the events in $B\to D\tau {\nu }_{\tau }$ (left) and $B\to D^{*}\tau {\nu }_{\tau }$ (right) decays [2]. The black lines represent the $q^2$ distribution predicted in the SM, obtained from the respective differential branching fractions.