Perturbative determination of O(a\,m) improvement on the QCD running coupling

We present the perturbative results of the discretization errors proportional to the quark mass (O(a m)) on the QCD running coupling within lattice perturbation theory. Our analysis involves calculating the 2-loop renormalization factor Zg using improved lattice actions for the SU(Nc) gauge group and Nf multiplets of fermions with a finite quark mass. We employ the background field method to compute Zg, by calculating quantum corrections on both the background and quantum gluon propagator, respecting the O(a) improvement. This allows us to evaluate the perturbative O(a m) lattice errors which affect the determination of the running coupling. Eliminating these O(a m) effects is crucial for the nonperturbative studies of precision determinations of the strong coupling constant using lattice field theory.