The pion light-cone distribution amplitude from the pion electromagnetic form factor

Abstract

We suggest to probe the pion light-cone distribution amplitude, applying a dispersion relation for the pion electromagnetic form factor. Instead of the standard dispersion relation, we use the equation between the spacelike form factor $F_{\pi }(Q^2)$ and the integrated modulus of the timelike form factor. For $F_{\pi }(Q^2)$, the QCD light-cone sum rule with a dominant twist-2 term is used. Adopting for the pion twist-2 distribution amplitude a certain combination of the first few Gegenbauer polynomials, it is possible to fit their coefficients $a_{2,4,6,...}$ (Gegenbauer moments) from this equation, employing the measured pion timelike form factor. For the exploratory fit we use the data of the BaBar collaboration. The results definitely exclude the asymptotic twist-2 distribution amplitude. Also the model with a single $a_2\ne 0$ is disfavoured by the fit. Considering the models with $a_{n>2}\ne 0$, we find that the fitted values of the second and fourth Gegenbauer moments cover the intervals $a_2 (1 \mbox{GeV}) = (0.22 - 0.33) $, $a_4 (1 \mbox{GeV}) = (0.12 - 0.25) $. The higher moments starting from $a_8$ are consistent with zero, albeit with large uncertainties. The spacelike pion form factor obtained in two different ways, from the dispersion relation and from the light-cone sum rule, agrees, within uncertainties, with the measurement by the Jefferson Lab $F_{\pi }$ collaboration.

arXiv comment24 pages, 8 figures, 5 tables. Slightly modified version, published in Phys.Rev.D

References in corpus (35)

• RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses
• Two-pion contribution to hadronic vacuum polarization
• Higher-Twist Distribution Amplitudes of the K Meson in QCD
• Charged pion form factor between Q^2=0.60 and 2.45 GeV^2. II. Determination of, and results for, the pion form factor
• Precise Measurement of the e+ e- --> pi+ pi- (gamma) Cross Section with the Initial-State Radiation Method at BABAR
• High-Statistics Study of the tau^- -> pi^- pi^0 nu_tau Decay
• QCD-based pion distribution amplitudes confronting experimental data
• $B\to \pi \ell {\nu }_l$ Width and $|V_{ub}|$ from QCD Light-Cone Sum Rules
• Light Cone Sum Rules for the pi0-gamma*-gamma Form Factor Revisited
• Pion Form Factor in QCD at Intermediate Momentum Transfers
• Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD
• Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects
• Modeling the Pion and Kaon Form Factors in the Timelike Region
• Lattice Results for Low Moments of Light Meson Distribution Amplitudes
• A new Parameterization for the Pion Vector Form Factor
• Soft contribution to the pion form factor from light-cone QCD sum rules
• Kaon Distribution Amplitude from QCD Sum Rules
• The vector form factor of the pion from unitarity and analyticity: a model-independent approach
• Exploring Light-Cone Sum Rules for Pion and Kaon Form Factors
• Second Moment of the Pion Light-cone Distribution Amplitude from Lattice QCD
• Pion and Kaon Distribution Amplitudes in the Continuum Limit
• Pion distribution amplitude from Euclidean correlation functions
• Electromagnetic form factors at large momenta from lattice QCD
• BELLE Data on the ${\pi }^0\gamma \ast \gamma$ Form Factor: A Game Changer?
• Electromagnetic form factor of the pion
• Systematic estimation of theoretical uncertainties in the calculation of the pion-photon transition form factor using light-cone sum rules
• Pion form factor in large $N_c$ QCD
• The pseudoscalar meson electromagnetic form factor at high $Q^2$ from full lattice QCD
• Subleading power corrections to the pion-photon transition form factor in QCD
• Pion-photon transition form factor in LCSR and tests of asymptotics
• Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region
• Pion electromagnetic formfactor in the space-like region and $P$-phase ${\delta }_1^1(s)$ of $\pi \pi$ scattering from the value of the modulus of formfactor in the time-like region.
• Spacelike pion form factor from analytic continuation and the onset of perturbative QCD
• Higher twist distribution amplitudes of the pion and electromagnetic form factor $F_{\pi }(Q^2)$
• Electromagnetic form factor of pion in the field theory inspired approach

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