Strong coupling constant from Adler function in lattice QCD

Abstract

We compute the QCD coupling constant, [Formula: see text], from the Adler function with vector hadronic vacuum polarization (HVP) function. On the lattice, Adler function can be measured by the differential of HVP at two different momentum scales. HVP is measured from the conserved-local vector current correlator using nf = 2 + 1 flavor Domain Wall lattice data with three different lattice cutoffs, up to a[Formula: see text] 3.14 GeV. To avoid the lattice artifact due to O(4) symmetry breaking, we set the cylinder cut on the lattice momentum with reflection projection onto vector current correlator, and it then provides smooth function of momentum scale for extracted HVP. We present a global fit of the lattice data at a justified momentum scale with three lattice cutoffs using continuum perturbation theory at [Formula: see text] to obtain the coupling in the continuum limit at arbitrary scale. We take the running to Z boson mass through the appropriate thresholds, and obtain [Formula: see text](MZ) = 0.1191(24)(37) where the first is statistical error and the second is systematic one.