On high $Q^{2}$ behavior of the pion form factor for transitions $\gamma^{\ast} \gamma \to \pi^{0}$ and $\gamma ^{\ast} \gamma^{\ast} \to \pi^{0}$ within the nonlocal quark-pion model

We study the pion Distribution Amplitude (\pi DA) in the context of a nonlocal chiral quark model. The corresponding Lagrangian reproduces the phenomenological values of the pion mass and decay constant, as well as the momentum dependence of the quark propagator obtained in lattice calculations. It is found that the obtained \pi DA has two symmetric maxima, which arise from the new contributions generated by the nonlocal character of the interactions. This \pi DA is applied t...

Pion transition form factor for the process $\gamma*\gamma*\to \pi^0$ at space-like values of photon momenta is calculated within the effective quark-meson model with the interaction induced by instanton exchange. The leading and next-to-leading order power asymptotics of the form factor and the relation between the light-cone pion distribution amplitudes of twists 2 and 4 and the dynamically generated quark mass are found.

We report on the fully analytic calculation of the leading-power contribution to the photon-pion transition form factor $\gamma \, \gamma^{\ast} \to \pi^0$ at two loops in QCD. The applied techniques are based on hard-collinear factorization, together with modern multi-loop methods. We focus both, on the technical details such as the treatment of evanescent operators, and the phenomenological implications. Our results indicate that the two-loop correction is numerically compa...

We discuss the photon to meson transition form factor for virtual photons, which can be measured in e+ e- collisions. We demonstrate that this form factor is independent of the shape of the meson distribution amplitude over a wide kinematical range. This leads to a parameter-free prediction of perturbative QCD to leading twist accuracy, which has a status comparable to the famous leading-twist prediction of the cross section ratio R.

We consider the calculation of the pion-photon transition form factor $F^{\gamma^*\gamma\pi^0}(Q^2)$ within light-cone sum rules focusing attention to the low-mid region of momenta. The central aim is to estimate the theoretical uncertainties which originate from a wide variety of sources related to (i) the relevance of next-to-next-to-leading order radiative corrections (ii) the influence of the twist-four and the twist-six term (iii) the sensitivity of the results on auxili...

We analyze the pi -> gamma* gamma* amplitude in the framework of radial Regge models in the large-Nc limit. With the assumption of similarity of the asymptotic Regge rho and omega meson spectra we find that the pion distribution amplitude is constant in the large-$N_c$ limit at the scale Q0 where the QCD radiative corrections are absent -- a result found earlier in a class of chiral quark models. We discuss the constraints on the couplings from the anomaly and from the limit ...

BaBar's observation of significant deviations of the pion transition form factor (TFF) from the asymptotic expectation with $Q^2>9$ GeV$^2$ has brought a serious crisis to a fundamental picture established for such a simplest $q\bar{q}$ system by perturbative QCD, i.e. the dominance of collinear factorization at high momentum transfers for the pion TFF. We show that non-factorizable contributions due to open flavors in $\gamma\gamma^*\to\pi^0$ could be an important source tha...

We discuss different QCD approaches to calculate the form factor F^{\gamma^*\gamma\pi}(Q^2) of the \gamma^*\gamma\to\pi^{0} transition giving preference to the light-cone QCD sum rules (LCSR) approach as being the most adequate. In this context we revise the previous analysis of the CLEO experimental data on F^{\gamma^*\gamma\pi}(Q^{2}) by Schmedding and Yakovlev. Special attention is paid to the sensitivity of the results to the (strong radiative) \alpha_s-corrections and to...

An analysis of all available data (CELLO, CLEO, \babar) in the range $[1\div 40]$ GeV$^2$ for the pion-photon transition form factor in terms of light-cone sum rules with next-to-leading-order accuracy is discussed, including twist-four contributions and next-to-next-to-leading order and twist-six corrections---the latter two via uncertainties. The antithetic trend between the \babar data for the $\gamma^*\gamma\pi^0$ and those for the $\gamma^*\gamma\eta(\eta')$ transition i...

We calculate the pion transition form factor ${\cal F}_{\pi^0\gamma^*\gamma^*}(q_1^2,q_2^2)$, which describe the interaction of an on-shell pion with two off-shell photons, using lattice QCD simulations with two degenerate flavors of dynamical quarks. This form factor is the main ingredient in the calculation of the pion-pole contribution to hadronic light-by-light scattering in the muon $g-2$, $a_\mu^{\mathrm{HLbL}; \pi^0}$. We focus our study on the spacelike region with ph...