The LFU ratio R π in the Standard Model and beyond

Abstract

We discuss the possibility of performing precise tests of $\mu /e$ universality in $B\to \pi {\ell }^{+}{\ell }^{-}$ decays. We show that in wide regions of the dilepton invariant mass spectrum the ratio between muonic and electronic decay widths can be predicted with high accuracy, both within and beyond the Standard Model. We present numerical expressions which can be used to extract precise information on short-distance dynamics if a deviation from universality is observed in the data.

Fig. 1

Dilepton spectrum in $B^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-}$ within the SM. The dotted-dashed line indicate the perturbative contribution (ignoring its parametric uncertainty). The gray error band represents the 68% interval after sampling over magnitudes and phases of the vector resonance contributions. The vertical dashed lines denote the three short-distance dominated regions where we provide precise estimates of $R_{\pi }$ (see text for details)

Fig. 2

Predictions for the parameters $b_V$ (left) and $b_L$ (right) in small $q^2$ bins in the low $q^2$ region (see main text). Numerical results for the different bins and their correlation matrix are given in Appendix 1