Local-Duality QCD Sum Rules for Pion Elastic and (pi^0, eta, eta') to gamma gamma* Transition Form Factors Revisited

TL;DR

This paper revisits local-duality QCD sum rules to predict pion and pseudoscalar meson transition form factors, comparing with quantum-mechanical models and experimental data, highlighting reliable Q^2 ranges and discrepancies with BaBar results.

Contribution

It provides a comprehensive analysis of local-duality QCD sum rules for meson form factors, including uncertainty estimates and comparison with experimental data and quantum-mechanical models.

Findings

Reliable predictions for Q^2 > 5-6 GeV^2

Good agreement with eta and eta' form factors

Discrepancies between local-duality predictions and BaBar pi^0 data

Abstract

The local-duality formulation of QCD sum rules allows for the prediction of hadronic form factors without knowledge of the subtle details of their structure. With the aid of this formalism, we take a fresh look at the behaviours of the charged-pion elastic form factor and of the form factors entering in the transitions of the ground-state neutral unflavoured pseudoscalar mesons pi^0, eta, eta' to one real and one virtual photon within a broad range of momentum transfers Q^2. The uncertainties induced by the approximations inherent to this local-duality approach are estimated by studying, in parallel to QCD, quantum-mechanical potential models, where the exact form factors, obtained by solving the Schr\"odinger equation, may be compared with the corresponding local-duality sum-rule results. For Q^2 larger than 5-6 GeV^2, we judge the predictions of the simplest local-duality model to be reliable and expect their accuracy to improve very fast with increasing Q^2. The large-Q^2 prediction for the pion elastic form factor should be approached already at moderate momentum transfer squared of approximately 4-8 GeV^2; large deviations from its local-duality behaviour for Q^2 = 20-50 GeV^2, predicted by some hadron-structure models, seem rather unlikely. The (eta, eta') to gamma + gamma* form factors deduced from the simplest local-duality approach exhibit excellent agreement with experiment. In startling contrast, BaBar measurements of the pi^0 to gamma + gamma* form factor imply local-duality violations which even rise with Q^2.