The Role of Different Schemes in the QCD Analysis and Determination of the Strong Coupling

In this article, we present a Next-to-Leading Order (NLO) QCD analysis to study the role and influence of different schemes on simultaneous determination of the Parton Distribution Functions (PDFs) and strong coupling, $\alpha_s(M^2_Z)$. We perform our analysis based on three different data sets, HERA I and II combined data, H1-ZEUS charm combined data, and H1 and ZEUS beauty production cross sections data, in two different Thorne-Roberts (TR or RT) and Thorne-Roberts Optimal (RT OPT) schemes. We show in going from RT scheme to RT OPT scheme, in addition of reduction the uncertainty of some PDFs, specially for the gluon distribution, we get $\sim 0.4$~\% and $\sim 0.7$~\%~improvement in the fit quality and $\sim 0.9$~\% and $\sim 1.6$~\%~improvement for the strong coupling, $\alpha_s(M^2_Z)$, without and with heavy flavor contributions, respectively.