Closing the Gap on $R_{D^*}$ by including longitudinal effects

Measurements of the $R_{D^*}equivmathrm{Br}(Brightarrow tau u D^*)/mathrm{Br}(Brightarrow e u D^*)$ parameter remain in tension with the standard model prediction, despite recent results helping to close the gap. The standard model prediction it is compared with considers the $D^*$ as an external particle, even though what is detected in experiments is a $Dpi$ pair it decays into, from which it is reconstructed. We argue that the experimental result must be compared with the theoretical prediction considering the full 4-body decay $(Brightarrow l u D^* to l u Dpi)$. We show that the longitudinal degree of freedom of the off-shell $D^*$ helps to further close the disagreement gap with experimental data. We find values for the ratio $R_{Dpi}^l equiv {mathrm{Br}(Brightarrow tau u_tau D pi)}/mathrm{Br}(Brightarrow l u_l Dpi)$ of $R_{Dpi}^e=0.274pm0.003$ and $R_{Dpi}^mu=0.275pm0.003$, where the uncertainty comes from the uncertainty of the form factors parameters. Comparing against $R_{Dpi}$ reduces the gap with the latest LHCb result from $1.1sigma$ to $0.48sigma$, while the gap with the latest Belle result is reduced from $0.42sigma$ to just $0.10sigma$ and with the world average results from $3.7sigma$ to $2.1sigma$. Erratum added at the end of the file.