$D^{\ast }$ polarization vs. $R_{D^{(\ast )}}$ anomalies in the leptoquark models

Abstract

Polarization measurements in $\bar{B}\to D^{(\ast )}\tau \overline{\nu }$ are useful to check consistency in new physics explanations for the $R_D$ and $R_{D^{\ast }}$ anomalies. In this paper, we investigate the $D^{\ast }$ and $\tau$ polarizations and focus on the new physics contributions to the fraction of a longitudinal $D^{\ast }$ polarization ($F_L^{D^{\ast }}$), which is recently measured by the Belle collaboration $F_L^{D^{\ast }}=0.60\pm 0.09$, in model-independent manner and in each single leptoquark model (${\mathrm{R}}_2$, ${\mathrm{S}}_1$ and ${\mathrm{U}}_1$) that can naturally explain the $R_{D^{(\ast )}}$ anomalies. It is found that $\mathcal{B}(B_c^{+}\to {\tau }^{+}\nu )$ severely restricts deviation from the Standard Model (SM) prediction of $F_{L,\text{SM}}^{D^{\ast }}=0.46\pm 0.04$ in the leptoquark models: [0.43, 0.44], [0.42, 0.48], and [0.43, 0.47] are predicted as a range of $F_L^{D^{\ast }}$ for the ${\mathrm{R}}_2$, ${\mathrm{S}}_1$, and ${\mathrm{U}}_1$ leptoquark models, respectively, where the current data of $R_{D^{(\ast )}}$ is satisfied at $1\sigma$ level. It is also shown that the $\tau$ polarization observables can much deviate from the SM predictions. The Belle II experiment, therefore, can check such correlations between $R_{D^{(\ast )}}$ and the polarization observables, and discriminate among the leptoquark models.

Comments: 24 pages, 3 figures, 1 table; references added, version published in JHEP