Measurement of the strong coupling constant from inclusive jet production at the Tevatron pp collider

We report a measurement of the strong coupling constant, ${\ensuremath{\alpha}}_{s}({M}_{Z})$, extracted from inclusive jet production in $p\overline{p}$ collisions at $\sqrt{s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1800\mathrm{GeV}$. The QCD prediction for the evolution of ${\ensuremath{\alpha}}_{s}$ with jet transverse energy ${E}_{T}$ is tested over the range $40l{E}_{T}l450\mathrm{GeV}$ using ${E}_{T}$ for the renormalization scale. The data show good agreement with QCD in the region below 250 GeV. The value of ${\ensuremath{\alpha}}_{s}$ at the mass of the ${Z}^{0}$ boson averaged over the range $40l{E}_{T}l250\mathrm{GeV}$ is found to be ${\ensuremath{\alpha}}_{s}({M}_{Z})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.1178\ifmmode\pm\else\textpm\fi{}0.0001(\mathrm{stat}{)}_{\ensuremath{-}0.0095}^{+0.0081}(\mathrm{expt}.\mathrm{syst})$. The associated theoretical uncertainties are mainly due to the choice of renormalization scale $({+6%}{\ensuremath{-}4%})$ and input parton distribution functions $(5%)$.