The pQCD analysis to extract PDFs and $\alpha_s^{{\rm NLO}}(M^2_Z)$ from inclusive jet-hadron production data

This perturbative Quantum Chromo Dynamics (pQCD) analysis attempts to present a simultaneous determination of parton distribution functions (PDFs) and the strong coupling $\alpha_s(M^2_Z)$ from inclusion of inclusive H1 and ZEUS jet, DiJets and TriJets production cross sections data on the HERA I and II combined data, as the central data sets for probing the internal structure of proton. To present an accurate pQCD analysis, we separate the role and influence of inclusion jet production cross sections data from inclusion of the strong coupling $\alpha_s(M^2_Z)$ as an extra fit parameter parameter on the gluon distribution. We show inclusion of jet, DiJets and TriJets production cross sections data improves the consistency between experiment and theory of cross sections for neutral current (NC) and charged current (CC) interactions of deep inelastic ${e^\pm}p$ scattering on proton up to $\sim 2.8$~\%. In addition, we show inclusion of jet production cross section data and considering $\alpha_s(M^2_Z)$ as a pQCD free parameter not only reduce dramatically the uncertainty band of gluon distribution but also improve the consistency between experiment and theory of NC and CC deep inelastic ${e^\pm}p$ scattering cross sections up to $\sim 3.6$~\%. Our simultaneous determination of PDFs and the strong coupling $\alpha_s(M^2_Z)$ with inclusion of jet production cross sections data leads to $\alpha_s^{{\rm NLO}}(M^2_Z) = 0.12041 \pm 0.00086$, which is in a good agreement with world average and other individual measurements.