On the pion distribution amplitude. Derivation, properties, predictions

We provide an in-depth analysis of the $\pi$ distribution amplitude in terms of two different Gegenbauer representations. Detailed predictions for the $\pi -\gamma$ transition form factor are presented, obtained with light-cone sum rules. Various $\pi$ distribution amplitudes are tested and the crucial role of their endpoint behavior in the form-factor analysis is discussed. Comparison with the data is given.