An attempt to construct pion distribution amplitude from the PCAC relation in the nonlocal chiral quark model

Abstract

Using the PCAC relation, we derive a compact formula for the pion decay constant $F_π$ in the nonlocal chiral quark model. For practical calculations this formula may be used both in the Minkowski and in the Euclidean space. For the pion momentum $P_μ\to0$ it reduces to the well known expression derived earlier by other authors. Using a generalized dipole Ansatz for the momentum dependence of the constituent quark mass in the Minkowski space, we express $F_π^{2}$ in terms of a single integral over the quark momentum fraction $u$. We interpret the integrand as a pion distribution amplitude $ϕ(u)$. We discuss its properties and compare with the $π$DA's obtained in other models.