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

Abstract

Experimental data have provided intriguing hints for the violation of lepton flavour universality (LFU), including $B\to D^{(\ast )}\tau \nu /B\to D^{(\ast )}\ell \nu$, 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 ($\Delta A_{\mathrm{FB}}$) of $B\to D^{\ast }\mu \bar{\nu }$ vs $B\to D^{\ast }e\bar{\nu }$ 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 $\Delta A_{\mathrm{FB}}$ 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 $\Delta A_{\mathrm{FB}}$ than the current central one, this scenario is significantly preferred (nearly $4\sigma$) over the SM hypothesis, and is compatible with constraints such as $B\to K^{\ast }\nu \nu$ and electroweak precision bounds. Therefore, if the $\Delta A_{\mathrm{FB}}$ 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.

Comments: 7 pages, 3 figures, 1 table, matches journal version