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We discuss cross sections for $\nu_{\tau}$ and ${\overline \nu}_{\tau}$production from the direct $D_s^{\pm} \to \nu_{\tau}/{\overline \nu}_{\tau}$and chain $D_s^{\pm} \to \tau^+/\tau^- \to \nu_{\tau}/{\overline \nu}_{\tau}$decays in $p\!+^{96}\!\mathrm{Mo}$ scattering with proton beam$E_{\mathrm{lab}}$ = 400 GeV \textit{i.e.} at $\sqrt{s}_{NN}$ = 27.4 GeV. Inour calculations we include $D_s^{\pm}$ from charm fragmentation $c \toD_s^{+}$ and $\bar c \to D_s^-$ as well as those from subleading fragmentationof strange quarks/antiquarks $s \to D_s^-$ and $\bar s \to D_s^+$. Thedifferent contributions to $D_s^{\pm}$ and $\nu_{\tau} / {\overline\nu}_{\tau}$ production rates are shown explicitly. Estimates of a number ofobserved $\nu_{\tau} / \overline{\nu}_{\tau}$ in the $\nu_{\tau} /\overline{\nu}_{\tau} +^{208}\!\mathrm{Pb}$ reaction, with 2m long target aregiven.

Production of $\nu_\tau$ neutrinos and $\overline{\nu}_tau$ antineutrinos -- elaborate calculation for a fixed target experiment SHiP