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 consistently the pion's static observables and the elastic and \gamma*\gamma -> \pi^0 transition form factors within a light-front model. Consistency requires that all calculations are performed within a given model with the same and single adjusted length or mass-scale parameter of the associated pion bound-state wave function. Our results agree well with all extent data including recent Belle data on the \gamma*\gamma -> \pi^0 form factor at large q^2, yet the BaBa...

The structure of hadronic form factors at high energies and their deviations from perturbative quantum chromodynamics provide insight on nonperturbative dynamics. Using an approach that is consistent with dispersion relations, we construct a model that simultaneously accounts for the pion wave function, gluonic exchanges, and quark Reggeization. In particular, we find that quark Reggeization can be investigated at high energies by studying scaling violation of the form factor...

We analyze the radiative pion decay pi+ -> e+ nu_e gamma within nonlocal chiral quark models that include wave function renormalization. In this framework we calculate the vector and axial-vector form factors FV and FA at q^2=0 --where q^2 is the (e+ \nu_e) squared invariant mass-- and the slope a of FV(q^2) at q^2 -> 0. The calculations are carried out considering different nonlocal form factors, in particular those taken from lattice QCD evaluations, showing a reasonable ag...

The $\pi^0 \gamma\gamma$ vertex for virtual photons of squared masses $q_1^2$ and $q_2^2$ plays a vital r\^ole in several physical processes; for example for $q_1^2<0$, $q_2^2<0$, in the two-photon physics reaction $e^+ e^-\to e^+ e^- \pi^0$, and for $q_1^2>0$, $q_2^2>0$, in the annihilation process $e^+ e^-\to \pi^0 l^+ l^-$. It is also of interest because of its link to the axial anomaly. We suggest a new approach to this problem. We have obtained a closed analytic expressi...

Based upon a combined formalism of Schwinger-Dyson and Bethe-Salpeter equations in quantum chromodynamics (QCD), we propose a QCD kindred algebraic model for the dressed quark propagator, for the Bethe-Salpeter amplitude of the pion and the electromagnetic quark-photon interaction vertex. We then compute the $\gamma^{*}\pi^0\gamma$ transition form factor $G^{\gamma^{*}\pi^0\gamma}(Q^2)$ for a wide range of photon momentum transfer squared $Q^2$. The quark propagator is expand...

We discuss the relevance of a dedicated measurement of exclusive production of a pair of neutral pions in a hard gamma* gamma scattering at small momentum transfer. In this case, the virtuality of one photon provides us with a hard scale in the process, enabling us to perform a QCD calculation of this reaction rate using the concept of Transition Distribution Amplitudes (TDA). Those are related by sum rules to the pion axial form factor F^pi_A and, as a direct consequence, a ...

The QCD evolution of the pion distribution amplitude (DA) $\phi_\pi(x,Q^2)$ is computed for several commonly used models. Our analysis includes the nonperturbative form predicted by light-front holographic QCD, thus combining the nonperturbative bound state dynamics of the pion with the perturbative ERBL evolution of the pion distribution amplitude. We calculate the meson-photon transition form factors for the $\pi^0$, $\eta$ and $\eta^\prime$ using the hard-scattering formal...

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 contribut...

We accomplish the complete two-loop computation of the leading-twist contribution to the photon-pion transition form factor $\gamma \, \gamma^{\ast} \to \pi^0$ by applying the hard-collinear factorization theorem together with modern multi-loop techniques. The resulting predictions for the form factor indicate that the two-loop perturbative correction is numerically important. We also demonstrate that our results will play a key role in disentangling various models of the twi...

The elastic and $\gamma \to \pi$ transition form factors of the pion along with its usual static observables are calculated within a light-front field approach to the constituent quark model. The focus of this exercise in a simple model is on a unified description of all observables with one singly parametrized light-front wave function to detect possible discrepancies in experimental data, in particular the contentious large momentum-squared data on the transition factor as ...