New physics couplings from angular coefficient functions of $\overline{B}\to D^{*}(D\pi )\ell {\overline{\nu }}_{\ell }$

The Belle Collaboration has recently measured the complete set of angular coefficient functions for the exclusive decays $\overline{B}\to D^{*}(D\pi )\ell {\overline{\nu }}_{\ell }$, with $\ell =e$, $\mu$, in four bins of the parameter $w=\frac{m_B^2+m_{D^{*}}^2-q^2}{2m_B{m}_{D^{*}}}$, with $q$ the lepton pair momentum [M. T. Prim et al. (Belle Collaboration), arXiv:2310.20286]. Under the assumption that physics beyond the Standard Model does not contribute to such modes, the measurements are useful to determine the hadronic form factors describing the $B\to D^{*}$ matrix elements of the Standard Model weak current, and to improve the determination of $|V_{cb}|$. On the other hand, they can be used to assess the impact of possible new physics contributions. In a bottom-up approach, we extend the Standard Model effective Hamiltonian governing this mode with the inclusion of the full set of Lorentz invariant $\mathrm{d}=6$ operators compatible with the gauge symmetry of the theory. The measured angular coefficient functions can tightly constrain the couplings in the generalized Hamiltonian. We present the first results of this analysis, discussing how improvements can be achieved when more complete data on the angular coefficient functions will be available.

Figure 1

Kinematics of $\overline{B}\to D^{*}(D\pi ){\ell }^{-}{\overline{\nu }}_{\ell }$.

Figure 2

NP couplings ${\epsilon }_V^{\mu },{\epsilon }_R^{\mu },{\epsilon }_P^{\mu },{\epsilon }_T^{\mu }$ obtained from the Belle measurement of the angular coefficient functions of $\overline{B}\to D^{*}(D\pi ){\mu }^{-}{\overline{\nu }}_{\mu }$. The light region corresponds to requiring that the theoretical results agree with the experimental data at $2.5\sigma$. The dark region corresponds to the values obtained minimizing the reduced ${\chi }^2$.

Figure 3

Angular coefficient functions in Eq. (2) for $\overline{B}\to D^{*}(D\pi ){\mu }^{-}{\overline{\nu }}_{\mu }$. The shaded regions correspond to the results obtained using the determined $\epsilon$ couplings, the points are the Belle measurements [19].

Figure 4

Ratio $R_{21s}$ in Eq. (8) for ${\epsilon }_T^{\mu }=0$ (dashed line) and varying ${\epsilon }_T^{\mu }$ in the range displayed in Fig. 2 (shaded region).

Figure 5

$|{\epsilon }_T^{\mu }|$ as a function of the position of the zero of the ratio ${\widehat{J}}_{2s}$ (blue curve) and ${\widehat{J}}_{2c}$ (magenta curve) for ${\epsilon }_V^{\mu }={\epsilon }_R^{\mu }=0$.

Figure 6

$\mathrm{Re}[{\epsilon }_T^{\mu }]$ as a function of the position of the zero of ${\widehat{J}}_{6c}$ for ${\epsilon }_V^{\mu }={\epsilon }_R^{\mu }={\epsilon }_P^{\mu }=0$, obtained from Eq. (9).