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be determined using Equation 1 provided the parton distributions functions are known. This technique was used by the CDF collaboration to measure α$_{s}$ at different p$_{T}$ values and show its running with the hard scattering scale in Run I [59]. In Run II, the DØ collaboration has used the same principle but an improved technique to measure α$_{s}$ [60] from the data used to measure the inclusive jet cross section. The hadronization and underlying event corrections were determined using pythia and applied to theory predictions. The hadronization (underlying event) corrections vary between -15% (+30%) to -3% (+6%), for p$_{T}$ = 50 GeV /c to 600 GeV /c [48]. 

The perturbative results are the sum of O ( α 3 $_{s}$) pQCD calculation [16, 17], supplemented with O ( α 4 $_{s}$)(2-loop) corrections for the threshold effects [18]. The PDFs are taken from the MSTW2008 next-to-next-to-leading order (NNLO) parametrization and the renormaliza- tion and factorization µ$_{R}$ , µ$_{F}$ scales are set equal to the p$_{T}$ of the jet. The NNLO (NLO) MSTW2008 PDFs are available for 21 different values of α$_{s}$ ( M$_{Z}$ ) ranging from 0.107 - 0.117 (0.110 - 0.130) in steps of 0.001. This α$_{s}$ is used to evolve PDFs. 

Commonly available parton distributions from the MSTW and CTEQ groups include Tevatron jet data in the global fit. To avoid any correlation between the input PDFs and the extracted α$_{s}$ , only 22 of 110 available jet data points are used. These selected points contribute to the x region ( x ≤ 0 . 25) where PDFs in global fits are mainly determined by other experimental data and are not strongly influenced by Tevatron jet data. The jet data starts to affect g ( x ) at x ∼ 0 . 2. The change in g ( x ) due to inclusion of jet data is less than 5% for x ≲ 0 . 25 [55]. 

