Resummation of Large Logarithms in γ∗π0→γ\gamma^* \pi^0 \to \gamma

In the collinear factorization of the form factor for the transition $\gamma^* \pi^0 \to \gamma$ the hard part contains double log terms as $\ln^2 x$ with $x$ as the momentum fraction of partons from 0 to 1. A simple exponentiation for resummation leads to divergent results. We study the resummation of these $\ln^2 x$ terms. We show that the $\ln^2 x$ terms come partly from the light-cone wave function(LCWF) and partly from the form factor. We introduce a jet factor to factorize the $\ln^2 x$ term in the form factor. To handel the $\ln^2 x$ terms from the LCWF we introduce a nonstandard light-cone wave function(NLCWF) with the gauge links off the light-cone direction. An interesting relation between two wave function is found. With the introduced NLCWF and the jet factor we can re-factorize the form factor and obtain a new hard part which does not contain terms with $\ln^2 x$. Beside the renormalization scale $\mu$ the introduce NLCWF and jet factor have extra scales to characterize their $x$-behaviors. Using the evolutions of the extra scales and the relation we can do the resummation perturbatively in sense that the LCWF is the only nonpertubative object in the resumed formula. Our results with some models of LCWF show that there is a significant difference between numerical predictions with the resummation and that without the resummation, and the resummed predictions can describe the experimental data.Comment: one reference adde

Power corrections to the π0γ\pi^0\gamma transition form factor and pion distribution amplitudes

Employing the standard hard-scattering approach and the running coupling method we calculate a class of power-suppressed corrections $\sim 1/Q^{2n},n=1,2,3,...$ to the electromagnetic $\pi^0\gamma$ transition form factor (FF) $Q^2F_{\pi\gamma}(Q^2)$ arising from the end-point $x \to 0,1$ integration regions. In the investigations we use a hard-scattering amplitude of the subprocess $\gamma+\gamma^{*} \to q +\bar{q}$, symmetrized under exchange $\mu_R^2 \leftrightarrow \bar{\mu}_R^2$ important for exclusive processes containing two external photons. In the computations the pion model distribution amplitudes (DA's) with one and two non-asymptotic terms are employed. The obtained predictions are compared with the CLEO data and constraints on the DA parameters $b_2(\mu_0^2)$ and $b_4(\mu_0^2)$ at the normalization point $\mu_0^2=1 GeV^2$ are extracted. Further restrictions on the pion DA's are deduced from the experimental data on the electromagnetic FF $F_{\pi}(Q^2)$.Comment: 23 pages, 6 figures; the version published in Phys. Rev. D69, 094010 (2004

Next-to-next-to-leading order prediction for the photon-to-pion transition form factor

We evaluate the next-to-next-to-leading order corrections to the hard-scattering amplitude of the photon-to-pion transition form factor. Our approach is based on the predictive power of the conformal operator product expansion, which is valid for a vanishing $\beta$-function in the so-called conformal scheme. The Wilson--coefficients appearing in the non-forward kinematics are then entirely determined from those of the polarized deep-inelastic scattering known to next-to-next-to-leading accuracy. We propose different schemes to include explicitly also the conformal symmetry breaking term proportional to the $\beta$-function, and discuss numerical predictions calculated in different kinematical regions. It is demonstrated that the photon-to-pion transition form factor can provide a fundamental testing ground for our QCD understanding of exclusive reactions.Comment: 62 pages LaTeX, 2 figures, 9 tables; typos corrected, some references added, to appear in Phys. Rev.

Perturbative Effects in the Form Factor \gamma\gamma^*\to \pi and Extraction of the Pion Wave Function from CLEO Data

We study the pion form factor F^{\pi \gamma\gamma^*}(Q^2) in the light-cone sum rule approach, accounting for radiative corrections and higher twist effects. Comparing the results to the CLEO experimental data on F^{\pi \gamma\gamma^*}(Q^2), we extract the the pion distribution amplitude of twist-2. The deviation of the distribution amplitude from the asymptotic one is small and is estimated to be a_2(\mu) = 0.12 \pm 0.03 at \mu=2.4 GeV, in the model with one non-asymptotic term. The ansatz with two non-asymptotic terms gives some region of a_2 and a_4, which is consistent with the asymptotic distribution amplitude, but does not agree with some old models.Comment: 21 pages, LaTeX, 7 eps figures; (v2): Phys. Rev. D versio