Measurement of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ν</mml:mi><mml:mi>μ</mml:mi></mml:msub></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mover accent="true"><mml:mi>ν</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>μ</mml:mi></mml:msub></mml:math>induced neutral current single<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math>production cross sections on mineral oil at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>E</mml:mi><mml:mi>ν</mml:mi></mml:msub><mml:mo>∼</mml:mo><mml:mi mathvariant="script">O</mml:mi></mml:math>(1 GeV)

MiniBooNE reports the first absolute cross sections for neutral current single ${\ensuremath{\pi}}^{0}$ production on ${\mathrm{CH}}_{2}$ induced by neutrino and antineutrino interactions measured from the largest sets of NC ${\ensuremath{\pi}}^{0}$ events collected to date. The principal result consists of differential cross sections measured as functions of ${\ensuremath{\pi}}^{0}$ momentum and ${\ensuremath{\pi}}^{0}$ angle averaged over the neutrino flux at MiniBooNE. We find total cross sections of $(4.76\ifmmode\pm\else\textpm\fi{}{0.05}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.76}_{\mathrm{sys}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{cm}}^{2}/\mathrm{\text{nucleon}}$ at a mean energy of $⟨{E}_{\ensuremath{\nu}}⟩=808\text{ }\text{ }\mathrm{MeV}$ and $(1.48\ifmmode\pm\else\textpm\fi{}{0.05}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.23}_{\mathrm{sys}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{cm}}^{2}/\mathrm{\text{nucleon}}$ at a mean energy of $⟨{E}_{\ensuremath{\nu}}⟩=664\text{ }\text{ }\mathrm{MeV}$ for ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ and ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ induced production, respectively. In addition, we have included measurements of the neutrino and antineutrino total cross sections for incoherent exclusive NC $1{\ensuremath{\pi}}^{0}$ production corrected for the effects of final state interactions to compare to prior results.