Photon-pion transition form factor and pion distribution amplitude

The pion distribution amplitude (DA) $\varphi_\pi (x)$ [1,2] is an important function accumulating information about momentum sharing between the quarks of the pion when the latter is in its valence $\bar q q$ configuration. It is an inherent element of perturbative QCD calculations of hard exclusive reactions involving the pion. A scenario is investigated in which the leading-twist pion DA $\varphi_\pi (x)$ is approximated by the pion decay constant $f_\pi$ for all essential values of the light-cone fraction $x$. A model for the light-front wave function $\Psi (x, k_\perp)$ is proposed that produces such a DA and has a rapidly decreasing (exponential for definiteness) dependence on the light-front energy combination $ k_\perp^2/x(1-x)$. It is shown that this model easily reproduces the fit of recent large-$Q^2$ {\sc BaBar} data [3] on the photon-pion transition form factor. Some aspects of scenario with flat pion distribution amplitude are discussed. \\[4pt] [1]~A.~V.~Radyushkin, JINR-P2-10717 (1977); English translation: arXiv:hep-ph/0410276.\\[0pt] [2] G.~P.~Lepage and S.~J.~Brodsky, Phys.\ Lett.\ B {\bf 87}, 359 (1979).\\[0pt] [3] B.~Aubert {\it et al.} [{\sc BaBar} Collaboration], arXiv:0905.4778 [hep-ex].