Effective charge from lattice QCD

Abstract

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, α(k2). Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale, m0 = 0.43(1) GeV, this coupling saturates at infrared momenta: α(0)/π = 0.97(4) . Amongst other things:α(k2)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 α(k2) 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 welldefined quantum field theory in four dimensions.