Impact of polarization observables and $B_c\to \tau \nu$ on new physics explanations of the $b\to c\tau \nu$ anomaly

Abstract

The combined analysis of the BaBar, Belle, and LHCb data on $B\to D\tau \nu$, $B\to D^{\ast }\tau \nu$ and $B_c\to J/\Psi \tau \nu$ decay observables shows evidence of physics beyond the Standard Model (SM). In this article, we study all the one- and two-dimensional scenarios which can be generated by adding a single new particle to the SM. We put special emphasis on the model-discriminating power of $F_L(D^{\ast })$ and of the $\tau$ polarizations, and especially on the constraint from the branching fraction $\mathrm{BR}(B_c\to \tau \nu )$. We critically review this constraint and do not support the aggressive limit of $\mathrm{BR}(B_c\to \tau \nu )<10\%$ used in some analyses. While the impact of $F_L(D^{\ast })$ is currently still limited, the $\mathrm{BR}(B_c\to \tau \nu )$ constraint has a significant impact: depending on whether one uses a limit of $60\%$, $30\%$ or $10\%$, the pull for new physics (NP) in scalar operators changes drastically. More specifically, for a conservative $60\%$ limit a scenario with scalar operators gives the best fit to data, while for an aggressive $10\%$ limit this scenario is strongly disfavored and the best fit is obtained in a scenario in which only a left-handed vector operator is generated. We find a sum rule for the branching ratios of $B\to D\tau \nu$, $B\to D^{\ast }\tau \nu$ and ${\Lambda }_b\to {\Lambda }_c\tau \nu$ which holds for any NP contribution to the Wilson coefficients. This sum rule entails an enhancement of $\mathrm{BR}({\Lambda }_b\to {\Lambda }_c\tau \nu )$ over its SM prediction by $(24\pm 6)\%$ for the current $\mathcal{R}(D^{(\ast )})$ data.

Comments: 16 pages, 6 figures; v2: clarifying comments and few references added, matches version published in PRD; v3: typo corrected in eq. (28). Updated results based on the HFLAV average for spring 2019 are available in arXiv:1905.08253