Production of ${\nu }_{\tau }$ neutrinos and ${\bar{\nu }}_{t}au$ antineutrinos -- elaborate calculation for a fixed target experiment SHiP

We discuss cross sections for ${\nu }_{\tau }$ and ${\bar{\nu }}_{\tau }$ production from the direct $D_s^{\pm }\to {\nu }_{\tau }\mathrm{/}{\bar{\nu }}_{\tau }$ and chain $D_s^{\pm }\to {\tau }^{+}\mathrm{/}{\tau }^{-}\to {\nu }_{\tau }\mathrm{/}{\bar{\nu }}_{\tau }$ decays in $p\text{\hspace{0.17em}⁣}{+}^{96}\text{\hspace{0.17em}⁣}\mathrm{M}\mathrm{o}$ scattering with proton beam $E_{\mathrm{l}\mathrm{a}\mathrm{b}}$ = 400 GeV $\mathit{\text{i.e.}}$ at ${\sqrt{s}}_{NN}$ = 27.4 GeV. In our calculations we include $D_s^{\pm }$ from charm fragmentation $c \to D_s^{+}$and$\bar c \to D_s^-$ as well as those from subleading fragmentation of strange quarks/antiquarks $s\to D_s^{-}$ and $\bar{s}\to D_s^{+}$. The different contributions to $D_s^{\pm }$ and $\nu_{\tau} / {\overline \nu}{\tau}$ production rates are shown explicitly. Estimates of a number of observed ${\nu }_{\tau }\mathrm{/}{\bar{\nu }}_{\tau }$ in the $\nu{\tau} / \overline{\nu}_{\tau} +^{208}!$\mathrm{P}\mathrm{b}$$ reaction, with 2m long target are given.