First measurement of the decay-time-integrated $C\!P$ asymmetry in $B_s^0 \to D_s^- π^+$ decays

A measurement of the flavour-untagged decay-time-integrated ${C\!P}$ asymmetry in the flavour-specific decay ${B_s^0 \to D_s^-π^+}$, ${\langle A^s_{\rm untagged}\rangle}$, is performed using proton-proton collision data collected by the LHCb experiment between 2016 and 2018 at a center-of-mass energy of ${13\,{\rm TeV}}$, corresponding to a total integrated luminosity of ${5.4\,{\rm fb}^{-1}}$. The ${C\!P}$ asymmetry is measured in two $D_s^-$ meson decay modes, ${D_s^- \to K^-K^+π^-}$ and ${D_s^- \to π^-π^+π^-}$. The combined result, $\langle A^s_{\rm untagged}\rangle = ( -1.4 \pm 5.9\,\rm{(stat)} \pm 1.1\,\rm{(syst)}) \times 10^{-3}$, is consistent with the Standard Model expectation and provides a direct constraint on new physics in tree-level $b$-hadron decays.