The Forward-Backward Asymmetry in $B\to D^{*}\ell\nu$: One more hint for Scalar Leptoquarks?

Abstract

Experimental data have provided intriguing hints for the violation of lepton flavour universality (LFU), including $B\to D^{(*)}\tau\nu/B\to D^{(*)}\ell\nu$, the anomalous magnetic moment of the muon and $b\!\to\! s\ell^+\ell^-$ with a significance of $\!>3\,\sigma$, $>\!4\,\sigma$ and $>\!5\,\sigma$, respectively. Furthermore, in a recent re-analysis of 2018 Belle data, it was found that the forward-backward asymmetry ($\Delta A_{\rm FB}$) of $B \to D^{*}\mu\bar \nu$ vs $B\to D^{*}e\bar \nu$ disagrees with the SM prediction by $\approx\!\!4\,\sigma$, providing an additional sign of LFU violation. We show that a tensor operator is necessary to significantly improve the agreement with data in $\Delta A_{\rm FB}$ while respecting the bounds from other $b\to c\ell\nu$ observables. Importantly, this tensor operator can only be induced (at tree-level within renormalizable models) by a scalar leptoquark. Furthermore, among the two possible representations, the $SU(2)_L$-singlet $S_1$ and the doublet $S_2$, which can interestingly both also account for the anomalous magnetic moment of the muon, only $S_1$ can provide a good fit. Even though the constraints from (differences of) other angular observables prefer a smaller value of $\Delta A_{\rm FB}$ than the current central one, this scenario is significantly preferred (nearly $4 \sigma$) over the SM hypothesis, and is compatible with constraints such as $B\to K^*\nu\nu$ and electroweak precision bounds. Therefore, if the $\Delta A_{\rm FB}$ anomaly is confirmed, it would provide circumstantial evidence for scalar leptoquarks and pave the way for a natural connection with all other anomalies pointing towards LFU violation.