On the Pion Distribution Amplitude Shape

Abstract

We argue that the recent BaBar data on $\gamma \to \pi$ e.m. transition form factor at large photon virtuality supports the idea that pion distribution amplitude (DA) is close to unity with ${\varphi }_{\pi }^{\prime }(0)/6\gg 1$ at a normalization point of $\mu =0.6÷0.8$ GeV. Such pion DA can be obtained in the effective chiral quark model. The possible flat shape of the pion DA implies that the standard expansion of the DA in Gegenbauer polynomials can be divergent. On basis of chiral models we predict that the two-pion DA should exhibit anomalous endpoint behaviour for pions in the S-wave and that such feature is absent for higher partial waves. The latter implies that the $\rho ,f_2$, etc. meson DAs have no anomalous endpoint behaviour. Possible implications of such pion DA for other hard exclusive processes are shortly discussed.

Refernces and more discussion are added. Version published in JETP Letters, v 90 p. 250 (2009)

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