The Determination of $\alpha_S$ at Hadron Colliders

Hadron colliders offer a unique opportunity to test perturbative QCD because, rather than producing events at a specific beam energy, the dynamics of the hard scattering is probed simultaneously at a wide range of momentum transfers. This makes the determination of $\al$ and the parton density functions (PDF) at hadron colliders particularly interesting. In this paper we restrict ourselves to extracting $\al$ for a given PDF at a scale which is directly related to the transverse energy produced in the collision. As an example, we focus on the single jet inclusive transverse energy distribution and use the published '88-'89 CDF data with an integrated luminosity of 4.2 pb$^{-1}$. The evolution of the coupling constant over a wide range of scales (from 30~GeV to 500~GeV) is clearly shown and is in agreement with the QCD expectation. The data to be obtained in the current Tevatron run (expected to be well in excess 100 pb$^{-1}$ for both the CDF and D\O\ experiments) will significantly decrease the experimental errors.