Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules

Abstract

We revisit $F_{\pi }(Q^2)$ and $F_{P\gamma }(Q^2)$, $P=\pi ,\eta ,{\eta }^{\prime }$, making use of the local-duality (LD) version of QCD sum rules. We give arguments, that the LD sum rule provides reliable predictions for these form factors at $Q^2\ge 5-6$ GeV${}^2$, the accuracy of the method increasing with $Q^2$ in this region. For the pion elastic form factor, the well-measured data at small $Q^2$ give a hint that the LD limit may be reached already at relatively low values of momentum transfers, $Q^2\approx 4-8$ GeV${}^2$; we therefore conclude that large deviations from LD in the region $Q^2=20-50$ GeV${}^2$ seem very unlikely. The data on the ($\eta ,{\eta }^{\prime })\to \gamma {\gamma }^{\ast }$ form factors meet the expectations from the LD model. However, the {\sc BaBar} results for the ${\pi }^0\to \gamma {\gamma }^{\ast }$ form factor imply a violation of LD growing with $Q^2$ even at $Q^2\approx 40$ GeV${}^2$, at odds with the $\eta ,{\eta }^{\prime }$ case and with the general properties expected for the LD sum rule.

arXiv comment17 pages. arXiv admin note: substantial text overlap with arXiv:1103.3781 and arXiv:1110.6904

References in corpus (36)

• Mixing and Decay Constants of Pseudoscalar Mesons
• Light-Front Dynamics and AdS/QCD Correspondence: The Pion Form Factor in the Space- and Time-Like Regions
• Measurement of the gamma gamma* --> pi0 transition form factor
• Abelian anomaly and neutral pion production
• Light Cone Sum Rules for the pi0-gamma*-gamma Form Factor Revisited
• Pion Form Factor in QCD at Intermediate Momentum Transfers
• Evolved QCD predictions for the meson-photon transition form factors
• Measurement of the gamma gamma* --> eta and gamma gamma* --> eta' transition form factors
• Pseudovector components of the pion, pi^0 -> gamma gamma, and F_pi(q^2)
• Form Factors of Meson Decays in the Relativistic Constituent Quark Model
• Hard Constituent Quarks and Electroweak Properties of Pseudoscalar Mesons
• The form factors for the photon to pseudoscalar meson transitions - an update
• Pion-photon transition---the new QCD frontier
• The effective continuum threshold in dispersive sum rules
• Quark structure of the pion and pion form factor
• Pion in the Holographic Model with 5D Yang-Mills Fields
• Axial anomaly as a collective effect of meson spectrum
• Explicit Results for the Anomalous Three Point Function and Non-Renormalization Theorems
• Two-photon form factors of the pi0, eta and eta-prime mesons in the chiral theory with resonances
• Pion form factor at spacelike momentum transfers from local-duality QCD sum rule
• QCD sum rules with nonlocal condensates and the spacelike pion form factor
• Axial anomaly: the modern status
• Pion form factor and QCD sum rules: case of axial current
• Pion elastic and $({\pi }^0,\eta ,{\eta }^{\prime })\to \gamma {\gamma }^{\ast }$ transition form factors in a broad range of momentum transfers
• The puzzle of the π-> γγ* transition form factor
• How the recent BABAR data for P to γγ* affect the Standard Model predictions for the rare decays P to l+l-
• Quark-hadron duality and hadron properties from correlators of pseudoscalar and axial currents
• ${\pi }^0\to {\gamma }^{\ast }\gamma$ transition form factor within Light Front Quark Model
• On the ${\gamma }^{\ast }\gamma \to \pi (\eta ,{\eta }^{\prime })$ transition form factors
• Rigorous pion electromagnetic form factor behavior in the space-like region
• Semileptonic inclusive heavy meson decay: duality in a nonrelativistic potential model in the Shifman-Voloshin limit
• Accuracy of the pion elastic form factor extracted from a local-duality sum rule
• The Pion-Photon Transition Form Factor and New Physics in the Tau Sector
• Non-local anomaly of the axial-vector current for bound states
• Selected topics in e^+e^- collisions
• Quark-binding effects in inclusive decays of heavy mesons