Eur. Phys. J. C (2012) 72: 1813
https://doi.org/10.1140/epjc/s10052-011-1813-0

Regular Article - Theoretical Physics

Photon-to-pion transition form factor and pion distribution amplitude from holographic QCD

¹ Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China
² Theoretical Physics Research Center for Science Facilities, Chinese Academy of Sciences, Beijing, 100049, China
³ Istituto Nazionale di Fisica Nucleare, Secione di Bari, Bari, Italy

^* e-mail: zuof@ihep.ac.cn

Received: 6 October 2011
Revised: 26 October 2011
Published online: 20 January 2012

Abstract

We try to understand the recently observed anomalous behavior of the photon-to-pion transition form factor in the holographic QCD approach. First the holographic description of the anomalous γ ^∗ γ ^∗ π ⁰ form factor is reviewed and applied to various models. It is pointed out that the holographic identification of the pion mode from the 5D gauge field strength rather than the gauge potential, as first made by Sakai and Sugimoto, naturally reproduces the scaling behavior of various pion form factors. It is also illustrated that in describing the anomalous form factor, the holographic approach is asymptotically dual to the perturbative QCD (pQCD) framework, with the pion mode π(z)∼z corresponding to the asymptotic pion distribution amplitude. This indicates some inconsistency in light-front holography, since π(z)∼z would be dual to there. This apparently contradictory can be attributed to the fact that the holographic wave functions are effective ones, as observed early by Radyushkin. After clarifying these subtleties, we employ the relation between the holographic and the perturbative expressions to study possible asymptotic violation of the transition form factor. It is found that if one require that the asymptotic form factor possess a pQCD-like expression, the pion mode can only be ultraviolet-enhanced by logarithmic factors. The minimally deformed pion mode will then be of the form π(z)∼zln(zΛ)⁻¹. We suppose that this deformation may be due to the coupling of the pion with a nontrivial open string tachyon field, and then the parameter Λ will be related to the quark condensate. Interestingly, this pion mode leads immediately to Radyushkin’s logarithmic model, which fitted very well the experimental data in the large-Q ² region. On the other side, the pQCD interpretation with a flat-like pion distribution amplitude, proposed by Radyushkin and Polyakov, fails to possess a holographic expression.