Final tau-neutrino results from the DONuT experiment

The DONuT experiment collected data in 1997 and published first results in 2000 based on four observed ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ charged-current (CC) interactions. The final analysis of the data collected in the experiment is presented in this paper, based on $3.6\ifmmode\times\else\texttimes\fi{}{10}^{17}$ protons on target using the 800 GeV Tevatron beam at Fermilab. The number of observed ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ CC events is 9 with an estimated background of 1.5 events, from a total of 578 observed neutrino interactions. We calculate the ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ CC cross section as a function of one parameter. Assuming ${\mathrm{D}}_{\mathrm{s}}$ mesons are the sole source for ${\ensuremath{\nu}}_{\ensuremath{\tau}}$, the energy-independent part of the total CC cross section can be parametrized as ${\ensuremath{\sigma}}^{\mathrm{const}}({\ensuremath{\nu}}_{\ensuremath{\tau}})=2.51{n}^{1.52}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{cm}}^{2}\text{ }{\mathrm{GeV}}^{\ensuremath{-}1}$ for $n\ensuremath{\ge}4$, where $n$ is the parameter controlling the longitudinal part of the ${\mathrm{D}}_{\mathrm{s}}$ differential cross section of the form $d\ensuremath{\sigma}/d{x}_{F}\ensuremath{\propto}(1\ensuremath{-}|{x}_{F}|{)}^{n}$. The analysis could not distinguish between ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ and ${\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$. The value of $n$ obtained from Pythia simulations, $n=6.1$, gives an estimated value of ${\ensuremath{\sigma}}^{\mathrm{const}}({\ensuremath{\nu}}_{\ensuremath{\tau}})=(0.39\ifmmode\pm\else\textpm\fi{}0.13\ifmmode\pm\else\textpm\fi{}0.13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}38}\text{ }\text{ }{\mathrm{cm}}^{2}\text{ }{\mathrm{GeV}}^{\ensuremath{-}1}$.