Effective charge from lattice QCD

Using lattice configurations for quantum ​​​​​chromodynamics (QCD) generated with three domain-wall fermions at a physical pion mass, we obtain a parameter-free prediction of QCD's renormalisation-group-invariant process-independent effective charge, $\hat\alpha(k^2)$?--> . Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale, $m_0= 0.43(1)\;$?--> GeV, this coupling saturates at infrared momenta: $\hat\alpha(0)/\pi=0.97(4)$?--> . Amongst other things: $\hat\alpha(k^2)$?--> is almost identical to the process-dependent (PD) effective charge defined via the Bjorken sum rule; and also that PD charge which, employed in the one-loop evolution equations, delivers agreement between pion parton distribution functions computed at the hadronic scale and experiment. The diversity of unifying roles played by $\hat\alpha(k^2)$?--> suggests that it is a strong candidate for that object which represents the interaction strength in QCD at any given momentum scale; and its properties support a conclusion that QCD is a mathematically well-defined quantum field theory in four dimensions. * Our calculations benefited from the following resources: CINES, GENCI, IDRIS (Project ID 52271); and the IN2P3 Computing Facility. Work supported by National Natural ScienceFoundation of China (11805097), Jiangsu Provincial Natural Science Foundation of China (BK20180323). Jiangsu Province Hundred Talents Plan for Professionals; Generalitat Valenciana, under grant Prometeo/2019/087; Spanish Ministry of Economy and Competitiveness (MINECO) (FPA2017-84543-P)