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, . Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale, GeV, this coupling saturates at infrared momenta: . Amongst other things: 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 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.
Highlights
quantum chromodynamics (QCD) fascinates for many reasons, with the feature of confinement looming large amongst them
The QCD running coupling lies at the heart of many attempts to define and understand confinement because, Received 6 January 2020, Revised 3 April 2020, Published online 29 June 2020 * Our calculations benefited from the following resources: CINES, GENCI, IDRIS (Project ID 52271); and the IN2P3 Computing Facility
The coupling is process-independent: one obtains precisely the same result, independent of the scattering process considered, whether gluon+gluon → gluon+gluon, quark+quark → quark+quark, etc. This clean connection between the coupling and the gluon vacuum polarisation relies on another particular feature of QCD, viz. in Landau gauge the renormalisation constant of the gluon-ghost vertex is unity [19], in consequence of which the effective charge obtained from the pinch technique (PT)-background field method (BFM) gluon vacuum polarisation is directly connected with that deduced from the gluon-ghost vertex [21,22,23], sometimes called the “Taylor coupling”, αT [24, 25]
Summary
QCD fascinates for many reasons, with the feature of confinement looming large amongst them. In Landau gauge the renormalisation constant of the gluon-ghost vertex is unity [19], in consequence of which the effective charge obtained from the PT-BFM gluon vacuum polarisation is directly connected with that deduced from the gluon-ghost vertex [21,22,23], sometimes called the “Taylor coupling”, αT [24, 25]. These observations underly the RGI PI effective coupling, α (k2), introduced in Ref.
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