QCD condensates and the pion wave functions in the nonlocal chiral model

Abstract

We use the simple instanton motivated Nambu--Jona-Lasinio--type model to calculate a twist 3 pseudoscalar pion light cone wave function ${\ensuremath{\psi}}_{\ensuremath{\pi}}^{\mathrm{PS}}.$ Using the normalization condition for ${\ensuremath{\psi}}_{\ensuremath{\pi}}^{\mathrm{PS}}$ we calculate the quark condensate and also the gluon condensate, which agree with the phenomenological values for these quantities. Since we can compute also the ${k}_{T}^{2}$ dependence of the light cone wave functions, we calculate ${k}_{T}^{2}$ moments of the pseudoscalar and axial-vector wave functions which are related to the mixed vacuum condensates. This allows us to extract the condensates and compare them with existing estimates.