Extracting the QCD ${\Lambda _{\overline {MS} }}$ parameter in Drell-Yan Process using Collins-Sopper-Sterman approach

In this work we directly fit the QCD dimensional transmutation parameter, ${\Lambda _{\overline {MS} }}$, to experimental data of Drell-Yan (DY) observables. For this purpose we first obtain the evolution of transverse momentum dependent parton distribution functions (TMDPDFs) up to the NNLO approximation based on Collins-Sopper-Sterman formalism. As is expecting the TMDPDFs are appearing at larger values of transvers momentum by increasing the energy scales and also the order of approximation. Then we calculate the cross section related to the TMDPDFs in the DY process. As a consequence of fitting to the E288 experimental data at center of mass energy $\sqrt{s}=23.8$ $GeV$, we obtain ${\Lambda _{\overline {MS} }} = 249 \pm 7 MeV$ corresponding to the renormalized coupling constant ${\alpha _s}(M_z^2) = 0.119 \pm 0.001$ which is within the acceptable range for this quantity. The results for DY cross section at different energy scales are in good agreement within the available data.