Pion form factor in QCD sum rules, local duality approach, and O(A_2) fractional analytic perturbation theory

Using the results on the electromagnetic pion Form Factor (FF) obtained in the $O(\alpha_s)$ QCD sum rules with non-local condensates \cite{BPS09} we determine the effective continuum threshold for the local duality approach. Then we apply it to construct the $O(\alpha_s^2)$ estimation of the pion FF in the framework of the fractional analytic perturbation theory.Comment: 4 pages, 2 figures, invited talk at the 3rd Joint International Hadron Structure'09 Conference, Tatranska Strba (Slovak Republic), Aug. 30--Sept. 3, 200

New vistas of the meson structure in QCD from low to high energies

This talk presents issues pertaining to the quark structure of the pion within QCD, both from the theoretical and from the experimental point of view. We review and discuss the pion-photon transition form factor and the pion's electromagnetic form factor vs. corresponding experimental data from the CLEO Collaboration and the JLab. We also examine the extent to which recent high-precision lattice computations of the second moment of the pion's distribution amplitude conform with theoretical models. Finally, we include predictions for the azimuthal asymmetry of the $\mu^+$ distribution in the polarized $\mu$-pair-induced DY production employing various pion distribution amplitudes.Comment: 6 pages, 7 figures, 2 tables. Talk presented at International Workshop on e^+e^- collisions from Phi to Psi, Frascati, Italy, 7-10 April 2008. V2 is an exclusive HEP version which includes predictions from AdS/QCD. V3: typo in title correcte

Nonlocal Condensate Model for QCD Sum Rules

We include effects of nonlocal quark condensates into QCD sum rules (QSR) via the K$\ddot{\mathrm{a}}$ll$\acute{\mathrm{e}}$n-Lehmann representation for a dressed fermion propagator, in which a negative spectral density function manifests their nonperturbative nature. Applying our formalism to the pion form factor as an example, QSR results are in good agreement with data for momentum transfer squared up to $Q^2 \approx 10$ GeV$^2$. It is observed that the nonlocal quark condensate contribution descends like $1/Q^2$, different from the exponential decrease in $Q^2$ obtained in the literature, and contrary to the linear rise in the local-condensate approximation.Comment: 8 pages, 8 figure

Deep inside the pion. Reconciling QCD theory with data

Recent developments in the QCD description of the pion structure are reviewed. The CLEO pion-photon transition data analysis favors a distribution amplitude for the pion that is double-humped but endpoint-suppressed. After a short outline of the derivation of this amplitude from QCD sum rules with nonlocal condensates, we present the fully fledged analysis of the CLEO data prefaced by predictions for the $F^{\gamma\rho\pi}$ form factor and commenting on the inherent theoretical uncertainties due to higher twists and NNLO perturbative corrections. We supplement our discussion by considering within QCD factorization theory, the electromagnetic pion form factor at NLO accuracy on one hand, and diffractive di-jets production on the other, comparing our predictions with the respective experimental data from JLab and the Fermilab E791 collaboration. In all cases, the agreement is impressive.Comment: 10 pages, 5 figures consisting of 8 eps files. Contribution to the Festschrift on the occasion of Klaus Goeke's 60th birthday, to appear in Annalen der Physi

Pion form factor analysis using NLO analytic perturbation theory

I present results for the pion's electromagnetic form factor in the spacelike region, which implement the most advanced perturbative information currently available for this observable in conjunction with a pion distribution amplitude that agrees with the CLEO data on the pion-photon transition form factor at the $1\sigma$ level. I show that using for the running strong coupling and its powers their analytic versions in the sense of Shirkov and Solovtsov, the obtained predictions become insensitive to the renormalization scheme and scale setting adopted. Joining the hard contribution with the soft part on account of local duality and respecting the Ward identity at $Q^2=0$, the agreement with the available experimental data, including expectations from planned experiments at JLab, is remarkable both in trend and magnitude. I also comment on Sudakov resummation within the analytic approach.Comment: 5 pages, 3 figures embedded; uses espcrc2.tex. Invited talk presented at QCD04, 5-9 July 2004, Montpellier, Franc

Transition form factors of the pion in light-cone QCD sum rules with next-to-next-to-leading order contributions

The transition pion-photon form factor is studied within the framework of Light-Cone QCD Sum Rules. The spectral density for the next-to-leading order corrections is calculated for any Gegenbauer harmonic. At the level of the next-to-next-to-leading (NNLO) radiative corrections, only that part of the hard-scattering amplitude is included that is proportional to the $\beta$-function, taking into account the leading zeroth-order harmonic. The relative size of the NNLO contribution in the prediction for the form factor $F^{\gamma^{*}\gamma\pi}(Q^2)$ has been analyzed, making use of the BLM scale-setting procedure. In addition, predictions for the form factor $F^{\gamma^{*}\rho\pi}$ are obtained that turn out to be sensitive to the endpoint behavior of the pion distribution amplitude, thus providing in connection with experimental data an additional adjudicator for the pion distribution amplitude. In a note added, we comment on the preliminary high-$Q^2$ BaBar data on $F^{\gamma^{*}\gamma\pi}$ arguing that the significant growth of the form factor between 10 and 40 GeV$^2$ cannot be explained in terms of higher-order perturbative corrections at the NNLO.Comment: 36 pages, 8 figures, 1 table. v2 new entry in Table I with reference added and replaced Fig. 6. v3 extended discussion of BaBar data (added 1 figure and references). v4 double reference removed; matches version published in Nucl. Phys. B. v5 corrected Ref. [62]; v6 corrects several errors (all boldfaced) and extended acknowledgment