High-mass dimuon production in<i>p¯N</i>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">−</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>N interactions at 125 GeV/<i>c</i>

We have studied muon pairs with an invariant mass between 4 and 9 GeV/${c}^{2}$ produced in p\ifmmode\bar\else\textasciimacron\fi{}N and ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$N interactions at an incident momentum of 125 GeV/c. The experiment was performed at Fermilab using a tungsten target and a special beam enriched to contain 18% antiprotons. We compare differential distributions as functions of the dimuon invariant mass, Feynman x, transverse momentum, and decay angles of the dimuon to the predictions of the Drell-Yan model including QCD corrections. Quark structure functions for the p\ifmmode\bar\else\textasciimacron\fi{} and ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$ are extracted. Comparisons of the antiproton data to the Drell-Yan model are significant because the cross sections depend principally on the valence-quark structure functions which are accurately determined by deep-inelastic scattering measurements. The measured absolute cross section (integrated over positive Feynman x and all transverse momenta) is 0.106\ifmmode\pm\else\textpm\fi{}0.005\ifmmode\pm\else\textpm\fi{}0.008 nb/nucleon for the p\ifmmode\bar\else\textasciimacron\fi{}N interaction and 0.107\ifmmode\pm\else\textpm\fi{}0.003\ifmmode\pm\else\textpm\fi{}0.009 nb/nucleon for the ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$N interaction, where the quoted errors are statistical and systematic, respectively. Normalization (K) factors that are required to bring the naive Drell-Yan and first-order QCD predictions into agreement with the measurements are extracted, and the uncertainties involved in such comparisons are examined.