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 $F_{\pi}$ 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 $P_{\mu}\to0$ 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 $F_{\pi}^{2}$ in terms of a single integral over the quark momentum fraction $u$. We interpret the integrand as a pion distribution amplitude $\phi(u)$. We discuss its properties and compare with the $\pi$DA's obtained in other models.Comment: To appear in the special issue of Acta Physica Polonica to celebrate the 65th Birthday of Professor Jan Kwiecinski. 14 pages, 4 figure