Anomalous Action in Gauge Invariant, Nonlocal, Dynamical Quark Model

Anomalous sector of chiral Lagrangian is calculated in a gauge invariant, nonlocal, dynamical quark model. The Wess-Zumino term is proved coming from two kinds of sources, one is independent of and another dependent on dynamical quark self energy Σ(k2). p6 and more higher order anomalous sectors come only from Σ(k2) dependent source. After some cancellation, standard Wess-Zumino action is obtained. PACS number(s): 11.30.Rd, 12.38.Aw,12.38.Lg,12.39.Fe Chiral Lagrangian has successfully described low-energy hadronic process. Within context of chiral Lagrangian approach that incorporates symmetries of QCD, to a certain order in the low-energy expansion, the difference between different underlying theories with same spontaneously broken chiral symmetry is in the values of coefficients in the chiral Lagrangian. To test QCD in terms of chiral Lagrangian at quantitative level, we need to calculate values of these coefficients based on QCD and compare them with those from experiment data. Recently chiral Lagrangian is exactly derived from underlying QCD and coefficients in the chiral Lagrangian are formally expressed in terms of Green’s functions of underlying QCD [1]. Further it was shown that the coefficients for normal part with even intrinsic parity of pseudoscalar meson chiral Lagrangian is saturated by dynamical quark self energy Σ(k) [2]. While the anomaly contribution [3], conventionally taken as the main source of the coefficients, are completely cancelled, leaving the Σ(k) dependent coefficients which vanish when