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 1.3σ or smaller in the region of |x|≥0.4 fm, while that in the V−A channel is about 1.8σ 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.