Probing new physics with $q^2$ distributions in $\overline{B}\to D^{(*)}\tau \overline{\nu }$

Recent experimental results for the ratios of the branching fractions of the decays $\overline{B}\to D^{(*)}\tau \overline{\nu }$ and $\overline{B}\to D^{(*)}\mu \overline{\nu }$ came as a surprise and lead to a discussion of possibility of testing new physics beyond the standard model through these modes. We show that these decay channels can provide us with good constraints on new physics and several new physics cases are favored by the present experimental data. In order to discriminate various new physics scenarios, we examine the $q^2$ distributions and estimate the sensitivity of this potential measurement at the SuperKEKB/Belle II experiment.

Figure 1

Constraints on the Wilson coefficients at the $m_b$ scale. The constraints are obtained from the ${\chi }^2$ fit of the measured $R(D)$ and $R(D^{*})$. The stars represent the optimal fitted values giving the smallest ${\chi }^2$.

Figure 2

The measured background-subtracted and efficiency-corrected $q^2$ distributions for $\overline{B}\to D\tau \overline{\nu }$ and $\overline{B}\to D^{*}\tau \overline{\nu }$ events, extracted from the BABAR data [2].

Figure 3

The differential branching fractions, predicted in the SM (black) and various NP scenarios listed in Sec. 2: $S_2$ (blue), $T$ (red), ${\mathrm{LQ}}_1$ (green), and ${\mathrm{LQ}}_2$ (cyan). The width of each curve is due to the theoretical errors in the hadronic form factor parameters and the uncertainty of $V_{cb}$.

Figure 4

The $R_{D^{(*)}}(q^2)$ distributions, predicted in the SM (black) and various NP scenarios listed in Sec. 2: $S_2$ (blue), $T$ (red), ${\mathrm{LQ}}_1$ (green), and ${\mathrm{LQ}}_2$ (cyan). The width of each curve is due to the theoretical errors in the hadronic form factor parameters.

Figure 5

Constraints on the Wilson coefficients at the $m_b$ scale. The constraints are obtained from the ${\chi }^2$ fit of binned $R_D(q^2)$ and $R_{D^{*}}(q^2)$ assuming the future experimental measurements at Belle II for the integrated luminosity $40{\mathrm{ab}}^{-1}$ to be perfectly consistent with the SM predictions. The red solid(dashed) lines correspond to the constraints at 68% (99.9%) C.L. coming from the $q^2$-integrated $R(D^{(*)})$.