Azimuthal $B\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$ angular distribution with tensor operators

In a recent paper we performed a comprehensive study of the impact of new-physics operators with different Lorentz structures on $\overline{B}\to D^{*+}{l}^{-}\overline{{\nu }_{\ell }}$ decays, $\ell =e^{-}$, ${\mu }^{-}$, ${\tau }^{-}$, involving the $b\to cl{\nu }_{\ell }$ transition. In this work we extend the previous calculation by including tensor operators. In the case of $\overline{B}\to D^{*+}{\tau }^{-}\overline{{\nu }_{\tau }}$, we present the full three-angle and $q^2$ angular distribution with tensor new-physics operators with complex couplings. The impact of the tensor operators on various observables in the angular distribution, specially the azimuthal observables including the $CP$ violating triple product asymmetries are discussed. It is shown that these azimuthal observables are very useful in discriminating different new-physics operators. Finally we consider new-physics leptoquark models with tensor interactions and show how the presence of additional scalar operators modify the predictions of the tensor operators.

Figure 1

The description of the angles ${\theta }_{l,D^{*}}$ and $\chi$ in the angular distribution of $\overline{B}\to D^{*}(\to D\pi )l^{-}{\nu }_l$ decay.

Figure 2

The allowed region for the complex coupling $T_L$ for case (a) at 95% C.L.

Figure 3

The predictions for the observables $F_L^{D^{*}}(q^2)$, differential branching ratio, $R_{D^{*}}(q^2)$, and $A_{\mathrm{FB}}^{D^{*}}(q^2)$ for the decay ${\overline{B}}^0\to D^{*+}\tau {\nu }_{\tau }$ in the presence of only $T_L$ coupling. The green band corresponds to the SM prediction and its uncertainties. The values of the coupling $T_L$ are chosen to show the maximum and minimum deviations from the SM expectations.

Figure 4

The correlation plots between $⟨A_C^{(1,2,3)}⟩$ ($⟨A_T^{(1,2,3)}⟩$) and $⟨A_{\mathrm{FB}}^{D^{*}}⟩$ in the presence of complex NP couplings. The red, orange and blue scatter points correspond to pure vector NP couplings $(V_L,V_R)$, pure scalar NP couplings $(S_L,S_R)$, and pure tensor NP coupling $(T_L)$. The scatter points are allowed by measurements of $R_D$ and $R_{D^{*}}$ at 95% C.L. The green points correspond to the SM predictions for these quantities.

Figure 5

The allowed regions for the leptoquark effective couplings $S_L$ and $T_L$ at ${\mu }_b=4.2\mathrm{GeV}$. The constraints on these NP couplings are from the measured $R(D)$ and $R(D^{*})$ within the $2\sigma$ level. The red (blue) scatter points correspond to $S_1(R_2)$ leptoquark models.

Figure 6

The correlations between $⟨A_C^{(1,2,3)}⟩$ ($⟨A_T^{(2)}⟩$) and $R_{D^{*}}$ for three different NP scenarios: only $S_L$ coupling (green), $R_2$ leptoquark coupling (red), and $S_1$ leptoquark coupling (blue). The black points correspond to the SM predictions for these quantities. The vertical bands correspond to $R_{D^{*}}$ data with $\pm 1\sigma$ (green) or $\pm 2\sigma$ (yellow) errors.

Figure 7

The correlation plots between $⟨A_C^{(1,2,3)}⟩$, $⟨A_T^{(2)}⟩$, and $⟨A_{\mathrm{FB}}^{D^{*}}⟩$ in the presence of leptoquark contributions. The red (blue) scatter points correspond to $R_2(S_1)$ leptoquarks. These scatter points satisfy the current measurements of $R_D$ and $R_{D^{*}}$ within the 2 $\sigma$ level. The green points in each panel correspond to the SM predictions for these quantities.