Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules
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ELEMENTARY PARTICLES AND FIELDS Theory
Elastic and Transition Form Factors of Light Pseudoscalar Mesons from QCD Sum Rules* I. A. Balakireva1)** , W. Lucha2)*** , and D. I. Melikhov1), 2), 3)**** Received December 21, 2011
Abstract—We revisit Fπ (Q2 ) and FP γ (Q2 ), P = π, η, η , 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 Q2 ≥ 5−6 GeV2 , the accuracy of the method increasing with Q2 in this region. For the pion elastic form factor, the well-measured data at small Q2 give a hint that the LD limit may be reached already at relatively low values of momentum transfers, Q2 ≈ 4−8 GeV2 ; we therefore conclude that large deviations from LD in the region Q2 = 20−50 GeV2 seem very unlikely. The data on the (η, η ) → γγ ∗ form factors meet the expectations from the LD model. However, the BaBar results for the π 0 → γγ ∗ form factor imply a violation of LD growing with Q2 even at Q2 ≈ 40 GeV2 , at odds with the η, η case and with the general properties expected for the LD sum rule. DOI: 10.1134/S106377881302004X
1. INTRODUCTION In spite of the long history of theoretical investigations of the pion, its properties are still not fully understood. At asymptotically large values of the momentum transfer, Q2 → ∞, the pion elastic and the πγ transition form factors obey perturbative QCD (pQCD) factorization theorems [1, 2] Fπ (Q2 ) → 8παs (Q2 )fπ2 /Q2 , √ Fπγ (Q2 ) → 2fπ /Q2 , fπ = 130 MeV.
(1)
Subleading logarithmic and power corrections modify the behavior (1) at large but finite Q2 . In early applications of QCD to the pion elastic form factor, Fπ (Q2 ), one hoped that power corrections vanish rather fast with Q2 ; however, later investigations revealed that nonperturbative power corrections dominate the form factor Fπ (Q2 ) up to relatively high Q2 ≈ 10−20 GeV2 . This picture has arisen from different approaches [3–8]. It was found that even at Q2 as large as Q2 = 20 GeV2 the O(1) ∗
The text was submitted by the authors in English. SINP, Moscow State University, Russia. 2) Institute for High Energy Physics, Austrian Academy of Sciences, Vienna, Austria. 3) Faculty of Physics, University of Vienna, Austria. ** E-mail: [email protected] *** E-mail: [email protected] **** E-mail: [email protected] 1)
term provides about half of the form factor; the pQCD formula based on factorization starts to work well only at Q2 ≥ 50−100 GeV2 . For the pion–photon transition form factor, Fπγ (Q2 ), the axial anomaly [9, 10] fixes its value at Q2 = 0. Lepage and Brodsky proposed a simple interpolating formula between the known value of the form factor at Q2 = 0 and its asymptotic behavior (1) −1 1 Q2 2 , (2) 1+ 2 2 Fπγ (Q ) = √ 4π fπ 2 2π 2 fπ which was believed to describe well the transition form factor in a broad range of Q2 . Surprisingly, some of the recent studies of the pion elastic form factor in the region Q2 ≈ 5−50 GeV2 [11– 14] reported much larger values of the pion elastic form factor than expected b
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