Lattice measurements of nonlocal quark condensates, vacuum correlation length, and pion distribution amplitude in QCD

Abstract

Recent data of lattice measurements of the gauge-invariant nonlocal scalar quark condensates are analyzed to extract the short--distance correlation length, 1/\lambda_q, and to construct an admissible Ansatz for the condensate behaviour in a coordinate space. The correlation length values for both the quenched and full-QCD cases appear in a good agreement with the well-known QCD SR estimates of the mixed quark-gluon condensate, 2 \lambda_q^2 = <\bar{q}(ig\sigma^{\mu\nu}G_{\mu\nu})q>/<\bar{q}q> = 0.8 - 1.1 GeV^2. We test two different Ansatzes for a nonlocal quark condensate and trace their influence on the twist-2 pion distribution amplitude by means of QCD SRs. The main features of the pion distribution amplitude are confirmed by the CLEO experimental results.