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

Recent data from lattice measurements of 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 behavior in a coordinate space. The correlation length values for both the quenched and full-QCD cases appear in good agreement with the well-known QCD sum-rule (SR) estimates of the mixed quark-gluon condensate $2{\lambda }_q^2=〈\overline{q}\left(ig{\sigma }_{\mu \nu }{G}_{\mu \nu }\right)q〉/〈\overline{q}q〉=0.8\mathrm{}–1.1{\mathrm{GeV}}^2.$ We test two different Ansätze for a nonlocal quark condensate and trace their influence on the twist-2 pion distribution amplitude by means of QCD SR’s. The main features of the pion distribution amplitude are confirmed by the CLEO experimental results.