Evolved QCD predictions for the meson-photon transition form factors

Abstract

The QCD evolution of the pion distribution amplitude (DA) φ π (x, Q 2 ) is computed for several commonly used models. Our analysis includes the nonperturbative form predicted by light-front holographic QCD, thus combining the nonperturbative bound state dynamics of the pion with the perturbative ERBL evolution of the pion DA. We calculate the meson-photon transition form factors for the π 0 , η and η using the hard-scattering formalism. We point out that a widely-used approximation of replacing φ (x, (1 − x)Q) with φ(x, Q) in the calculations will unjustifiably reduce the predictions for the meson-photon transition form factors. It is found that the four models of the pion DA discussed give very different predictions for the Q 2 dependence of the meson-photon transition form factors in the region of Q 2 > 30 GeV 2 . More accurate measurements of these transition form factors at the large Q 2 region will be able to distinguish different models of the pion DA. The rapid growth of the large Q 2 data for the pion-photon transition form factor reported by the BABAR Collaboration is difficult to explain within the current framework of QCD. If the BABAR data for the meson-photon transition form factor is confirmed, it could indicate physics beyondthe-standard model, such as a weakly-coupled elementary C = + axial vector or pseudoscalar z 0 in the few GeV domain, an elementary field which would provide the coupling γ * γ → z 0 → π 0 at leading twist. Our analysis thus indicates the importance of additional measurements of the pion-photon transition form factor at large Q 2 .

Pion-Photon Transition Form Factor and Pion Distribution Amplitude in QCD: Facing the Enigmatic Behavior of the BaBar Data

“…[28]. [17], whereas the dotted and the double-dotted-dashed lines denote two independent predictions derived from AdS/QCD in [29] and [30], respectively. The experimental data are taken from various experiments, referenced in the text.…”

“…2 the two broken (blue) lines represent the independent findings of two such approaches for Q 2 F γ * γπ 0 (Q 2 ). The dotted line denotes the prediction derived in [29], using a dressed electromagnetic current and taking into account the twisttwo and the twist-four hadronic AdS components of the pion wave function (Eq. (43) in [29]) within a softwall holographic approach.…”

“…The dotted line denotes the prediction derived in [29], using a dressed electromagnetic current and taking into account the twisttwo and the twist-four hadronic AdS components of the pion wave function (Eq. (43) in [29]) within a softwall holographic approach. The combination of the nonperturbative bound-state dynamics, predicted by the holographic AdS/QCD correspondence, with the perturbative Efremov-Radyushkin-Brodsky-Lepage evolution [3,39] was treated in detail in [40].…”

“…(43) in [29]) within a softwall holographic approach. The combination of the nonperturbative bound-state dynamics, predicted by the holographic AdS/QCD correspondence, with the perturbative Efremov-Radyushkin-Brodsky-Lepage evolution [3,39] was treated in detail in [40]. The doubledotted-dashed line shows an analogous result [30], obtained by an extension of the hard-wall AdS/QCD model which includes the Chern-Simons term, required to reproduce the chiral anomaly of QCD.…”

“…The calculation of the π 0 , η, and η ′ TFFs has been carried out within holographic approaches of AdS/QCD, e.g., [29], [30], and [38]. In Fig.…”