Precise measurement of dimuon production cross sections in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="normal">Fe</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="normal">Fe</mml:mi></mml:math>deep inelastic scattering at the Fermilab Tevatron

We present measurements of the semi-inclusive cross sections for ${\ensuremath{\nu}}_{\ensuremath{\mu}}$- and ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$-nucleon deep inelastic scattering interactions with two oppositely charged muons in the final state. These events dominantly arise from the production of a charm quark during the scattering process. The measurement was obtained from the analysis of 5102 ${\ensuremath{\nu}}_{\ensuremath{\mu}}$-induced and 1458 ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$-induced events collected with the NuTeV detector exposed to a sign-selected beam at the Fermilab Tevatron. We also extract a cross-section measurement from a reanalysis of 5030 ${\ensuremath{\nu}}_{\ensuremath{\mu}}$-induced and 1060 ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$-induced events collected from the exposure of the same detector to a quad-triplet beam by the Chicago Columbia Fermilab Rochester (CCFR) experiment. The results are combined to obtain the most statistically precise measurement of neutrino-induced dimuon production cross sections to date. These measurements should be of broad use to phenomenologists interested in the dynamics of charm production, the strangeness content of the nucleon, and the Cabibbo-Kobayashi-Maskawa matrix element ${V}_{\mathrm{cd}}.$