Measurement of the $D^{*}$ longitudinal polarization in $B^0\to D^{*-}\tau^{+}\nu_{\tau}$ decays

International audience ; The longitudinal polarization fraction of the $D^{*}$ meson is measured in $B^0\to D^{*-}\tau^{+}\nu_{\tau}$ decays, where the $\tau$ lepton decays to three charged pions and a neutrino, using proton-proton collision data collected by the LHCb experiment at center-of-mass energies of 7, 8 and 13 TeV and corresponding to an integrated luminosity of 5 fb$^{-1}$. The $D^{*}$ polarization fraction $F_{L}^{D^{*}}$ is measured in two $q^{2}$ regions, below and above 7 GeV$^{2}/c^{4}$, where $q^{2}$ is defined as the squared invariant mass of the $\tau\nu_{\tau}$ system. The $F_{L}^{D^{*}}$ values are measured to be $0.51 \pm 0.07 \pm 0.03$ and $0.35 \pm 0.08 \pm 0.02$ for the lower and higher $q^{2}$ regions, respectively. The first uncertainties are statistical and the second systematic. The average value over the whole $q^{2}$ range is: $$F_{L}^{D^{*}} = 0.43 \pm 0.06 \pm 0.03.$$ These results are compatible with the Standard Model predictions.