On the ${\gamma }^{\ast }\gamma \to \pi (\eta ,{\eta }^{\prime })$ transition form factors

Abstract

The surprising results by the BarBar collaboration on the $\pi \gamma$ transition form factor require new thoughts about the high-$Q^2$ dependence of the form factors with virtual photons. We make use of the anomaly sum rule [J. Horejsi and O. Teryaev, Z. Phys. C65, 691 (1995).] which relates the hadron spectral density to the axial anomaly [S. Adler, Phys. Rev. 177, 2426 (1969); J. S. Bell and R. Jackiw, Nuovo Cimento A 60, 47 (1969).]. We study the quark-hadron duality relation for this sum rule and find out that the increase of the rescaled form factor $Q^2{F}_{\pi \gamma }(Q^2)\sim \log (Q^2)$ suggested by the BaBar data requires the presence of a $1/s$-correction term in the relation between the one-loop spectral density and the hadron-continuum spectral density.

Comments: 4 pages