Measurement of the Strong Coupling Constant from Inclusive Jet Production at the Tevatron $\overline{p}\mathit{p}$ Collider

We report a measurement of the strong coupling constant, ${\alpha }_s\left(M_Z\right)$, extracted from inclusive jet production in $p\overline{p}$ collisions at $\sqrt{s}=1800\mathrm{}\mathrm{GeV}$. The QCD prediction for the evolution of ${\alpha }_s$ with jet transverse energy $E_T$ is tested over the range $40<\mathrm{}{E}_T<450\mathrm{}\mathrm{GeV}$ using $E_T$ for the renormalization scale. The data show good agreement with QCD in the region below 250 GeV. The value of ${\alpha }_s$ at the mass of the $Z^0$ boson averaged over the range $40<\mathrm{}{E}_T<250\mathrm{}\mathrm{GeV}$ is found to be ${\alpha }_s\left(M_Z\right)=0.1178\mathrm{}\pm 0.0001\left(\mathrm{stat}{)}_{-0.0095\mathrm{}}^{+0.0081\mathrm{}}\right(\mathrm{expt}.\mathrm{syst})$. The associated theoretical uncertainties are mainly due to the choice of renormalization scale $\left(\{+6\mathrm{}\%\}\{-4\mathrm{}\%\}\right)$ and input parton distribution functions $\left(5\%\right)$.