[Paper Review] Photon-pion transition form factor: BABAR puzzle is cracked

A. E. Dorokhov|arXiv (Cornell University)|Mar 24, 2010

Quantum Chromodynamics and Particle Interactions1 references3 citations

TL;DR

This paper resolves the BABAR puzzle by demonstrating that nonperturbative QCD dynamics can lead to two distinct asymptotic regimes for the pion transition form factor: a standard 1/Q² behavior and a logarithmically enhanced ln(Q²)/Q² regime. Using nonlocal chiral quark models with dynamical quark mass Mq ≈ 125 MeV and small nonlocality scale Λ ∼ 0.01 GeV⁻², the model successfully describes CELLO, CLEO, and BABAR data, indicating a flat pion distribution amplitude consistent with frozen QCD evolution.

ABSTRACT

Recently, the BABAR collaboration published (arXiv:0905.4778) data for the photon-pion transition form factor $F_{πγγ^{\ast}}(Q^{2})$, which are in strong contradiction to the predictions of the standard factorization approach to perturbative QCD. Immediately afterwards, two mechanisms were suggested (A.E. Dorokhov, arXiv:0905.4577; A.V. Radyushkin, arXiv:0906.0323), that logarithmically enhance the form factor asymptotics and therefore provide a qualitatively satisfactory description of the BABAR data. However, the physics of the BABAR effect was not fully clarified. In the present work, based on a nonperturbative approach to the QCD vacuum and on rather universal assumptions, we show that there exists two asymptotic regimes for the pion transition form factor. One regime with asymptotics $F_{πγ^{\ast}γ}(Q^{2})\sim1/Q^{2}$ corresponds to the result of the standard QCD factorization approach, while other violates the standard factorization and leads to asymptotic behavior as $F_{πγ^{\ast}γ}(Q^{2})\sim\ln(Q^{2})Q^{2}$. Furthermore, considering specific nonlocal chiral quark models, we find the region of parameters, where the existing CELLO, CLEO and BABAR data for the pion transition form factor are successfully described.

Motivation & Objective

• To resolve the discrepancy between BABAR data and standard pQCD factorization predictions for the photon-pion transition form factor.
• To identify the nonperturbative QCD mechanisms responsible for the observed logarithmic enhancement in the form factor at high Q².
• To determine whether nonlocal chiral quark models can simultaneously describe data from CELLO, CLEO, and BABAR experiments.
• To clarify the role of the pion distribution amplitude and quark condensate in explaining the BABAR anomaly.
• To assess the impact of QCD evolution and the normalization scale in models fitting the high-momentum-transfer data.

Proposed method

• Develops a nonperturbative approach to the QCD vacuum based on universal assumptions about quark-antiquark interactions.
• Constructs nonlocal chiral quark models with two parameters: dynamical quark mass Mq and nonlocality scale Λ.
• Derives the pion transition form factor using α-representation and vertex functions that depend on Mq and Λ.
• Analyzes the behavior of the pion distribution amplitude φπ(x) under different endpoint suppression conditions (strong vs. weak).
• Compares the model predictions with experimental data from CELLO, CLEO, and BABAR in the Q² range 4–40 GeV².
• Fits the model parameters to reproduce the data, focusing on the regime where the form factor grows as ln(Q²)/Q².

Experimental results

Research questions

• RQ1 Can nonperturbative QCD dynamics explain the logarithmic enhancement in the pion transition form factor observed by BABAR at high Q²?
• RQ2 What conditions on the pion distribution amplitude lead to the ln(Q²)/Q² asymptotic behavior instead of the standard 1/Q² behavior?
• RQ3 Is there a specific parameter regime in nonlocal chiral quark models that can simultaneously describe CELLO, CLEO, and BABAR data?
• RQ4 Does the observed behavior imply a very low normalization scale, consistent with frozen QCD evolution?
• RQ5 What is the role of the quark condensate and dynamical quark mass in achieving a good fit to the BABAR data?

Key findings

• The model identifies two asymptotic regimes: standard 1/Q² behavior and a novel ln(Q²)/Q² behavior due to weak endpoint suppression in the pion distribution amplitude.
• The best fit to experimental data requires a dynamical quark mass Mq ≈ 125 MeV with very small uncertainty.
• The nonlocality parameter is found to be Λ ∼ 0.01 GeV⁻², indicating an almost local model with flat momentum-space regulators.
• The pion distribution amplitude is consistent with a flat or weakly suppressed shape, supporting the ln(Q²)/Q² asymptotics in the BABAR kinematic region.
• The model's success implies a very low normalization scale, consistent with frozen QCD evolution, as argued in prior works.
• The quark condensate is large, indicating strong chiral symmetry breaking at low momentum scales, which supports the nonperturbative nature of the solution.