Effective charge from lattice QCD

TL;DR

This paper uses lattice QCD with three domain-wall fermions at physical pion mass to predict a process-independent effective charge in QCD, revealing its infrared saturation and consistency with experimental data.

Contribution

It provides a parameter-free, lattice-based prediction of the QCD effective charge, demonstrating its infrared saturation and agreement with phenomenological effective charges.

Findings

Effective charge saturates at infrared momenta: $ ext{~}rac{ ilde{ ext{alpha}}(0)}{ ext{pi}}=0.97(4)$

$ ext{Effective charge}$ matches the process-dependent charge from the Bjorken sum rule

The effective charge aligns with experimental pion parton distribution functions

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, $\hat\alpha(k^2)$. Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale, 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.