Lattice calculation of coordinate-space vector and axial-vector current correlators in QCD

We study the vector and axial-vector current correlators in perturbative and nonperturbative regimes of QCD. The correlators in Euclidean coordinate space are calculated on the lattice using the Möbius domain-wall fermion formulation at three lattice spacings covering 0.044-0.080 fm. The dynamical quark effects of 2 +1 light flavors are included. The sum V +A and the difference V -A of the vector (V ) and axial-vector (A ) current correlators calculated on the lattice after extrapolating to the physical point agree with those converted from the ALEPH experimental data of hadronic τ decays. The level of the agreement in the V +A channel is about 1.3 σ or smaller in the region of |x |≥0.4 fm , while that in the V -A channel is about 1.8 σ at |x |=0.74 fm and smaller at other distances. We also extract the chiral condensate from the short-distance correlators on the lattice using the partially conserved axial current relation. Its result extrapolated to the chiral and continuum limit is compatible with other estimates at low energies.