Measurement of the $D^{\ast }$ longitudinal polarization in $B^0\to D^{\ast -}{\tau }^{+}{\nu }_{\tau }$ decays

The longitudinal polarization fraction of the $D^{\ast }$ meson is measured in $B^0\to D^{\ast -}{\tau }^{+}{\nu }_{\tau }$ 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 $D^{\ast }$ polarization fraction $F_L^{D^{\ast }}$ is measured in two $q^2$ regions, below and above 7 GeV${}^2\mathrm{/}{c}^4$, where $q^2$ is defined as the squared invariant mass of the $\tau {\nu }_{\tau }$ system. The $F_L^{D^{\ast }}$ values are measured to be $0.52\pm 0.07\pm 0.04$ and $0.34\pm 0.08\pm 0.02$ 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: $$F_L^{D^{\ast }}=0.41\pm 0.06\pm \mathrm{0.03.}$$ These results are compatible with the Standard Model predictions.