Parton Distribution Amplitudes Research Articles

Pion Electromagnetic Form Factor at Spacelike Momenta

A novel method is employed to compute the pion electromagnetic form factor, F(π)(Q²), on the entire domain of spacelike momentum transfer using the Dyson-Schwinger equation (DSE) framework in QCD. The DSE architecture unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA). Using this PDA, the leading-order, leading-twist perturbative QCD result for Q²F(π)(Q²) underestimates the full computation by just 15% on Q²≳8 GeV², in stark contrast to the result obtained using the asymptotic PDA. The analysis shows that hard contributions to the pion form factor dominate for Q²≳8 GeV², but, even so, the magnitude of Q²F(π)(Q²) reflects the scale of dynamical chiral symmetry breaking, a pivotal emergent phenomenon in the standard model.

Light front distribution of the chiral condensate

The pseudoscalar projection of the pionʼs Poincaré-covariant Bethe–Salpeter amplitude onto the light-front may be understood to provide the probability distribution of the chiral condensate within the pion. Unlike the parton distribution amplitudes usually considered and as befitting a collective effect, this condensate distribution receives contributions from all Fock space components of the pionʼs light-front wave function. We compute this condensate distribution using the Dyson–Schwinger equation (DSE) framework and show the result to be a model-independent feature of quantum chromodynamics (QCD). Our analysis establishes that this condensate is concentrated in the neighbourhood of the boundaries of the distributionʼs domain of support. It thereby confirms the dominant role played by many-particle Fock states within the pionʼs light-front wave function in generating the chiral condensate and verifies that light-front longitudinal zero modes do not play a material role in that process.

Generalized parton distributions of the pion in chiral quark models and their QCD evolution

We evaluate Generalized Parton Distributions of the pion in two chiral quark models: the Spectral Quark Model and the Nambu-Jona-Lasinio model with a Pauli-Villars regularization. We proceed by the evaluation of double distributions through the use of a manifestly covariant calculation based on the alpha representation of propagators. As a result polynomiality is incorporated automatically and calculations become simple. In addition, positivity and normalization constraints, sum rules and soft pion theorems are fulfilled. We obtain explicit formulas, holding at the low-energy quark-model scale. The expressions exhibit no factorization in the t-dependence. The QCD evolution of those parton distributions is carried out to experimentally or lattice accessible scales. We argue for the need of evolution by comparing the Parton Distribution Function and the Parton Distribution Amplitude of the pion to the available experimental and lattice data, and confirm that the quark-model scale is low, about 320 MeV.

Complex conformal spin partial wave expansion of generalized parton distributions and distribution amplitudes

We introduce a new representation of generalized parton distributions and generalized distribution amplitudes that is based on the partial wave decomposition with respect to the complex collinear conformal spin. This decomposition leads us to a versatile parameterization of these non-perturbative functions in terms of conformal moments, which are measurable for integer value on the lattice. This new representation has several advantages: basic properties and crossing relations are automatically implemented, a rather flexible parameterization is possible, the numerical treatment of evolution is simple and analytic approximation of scattering amplitudes can be given. We demonstrate this for simple examples. In particular, phenomenological considerations indicate that the t-dependence of Mellin moments is governed by Regge trajectories. The new representation is vital to push the analysis of deeply virtual Compton scattering to next-to-next-to-leading order.

Probing quark-distribution amplitudes through generalized parton distributions at large momentum transfer.

In the large momentum transfer limit, generalized parton distributions can be calculated through a QCD factorization theorem which involves perturbatively calculable hard kernels and light-cone parton distribution amplitudes of hadrons. We illustrate this through the H(q)(x,xi,t) distribution for the pion and the proton, presenting the hard kernels at leading order. As a result, experimental data on the generalized parton distributions in this regime can be used to determine the functional form of the parton distribution amplitudes which has thus far been quite challenging to obtain. Our result can also be used as a constraint in phenomenological generalized parton distribution parametrizations.

Structure of the virtual Compton amplitude with an additional final-state meson in the extended Bjorken region

Using the framework of the nonlocal light-cone expansion a systematic study is performed for the structure of the twist-2 contributions to the virtual Compton amplitude in polarized deep-inelastic nonforward scattering for general nucleon spin with an additional scalar meson in the final state. A useful kinematic parametrization allowing for appropriate triple-valued off-forward parton distribution amplitudes is given. One-variable amplitudes being adapted to the fixed parameters of the extended Bjorken region are introduced by decomposing the Compton amplitude into collinear and noncollinear components. These amplitudes obey Wandzura-Wilczek- and Callan-Gross-like relations. The evolution equations for all the distribution amplitudes are determined showing that the additional meson momentum does not appear in the evolution kernels. The generalization to n outgoing mesons is given.

Hadron operators on the light-cone

Meson and baryon operators on the light cone are studied which reproduce the well-known parton distribution amplitudes as matrix elements between the vacuum and an one-meson (baryon) state. We extent our previous results to the case of the quark-gluon mixing which is relevan for the description of a flavour-singlet meson. The anomalous dimensions of the considered nonlocal light-cone operators are calculated explicity in the one-loop approximation. We thus recover the evolution kernels for meson and baryon wave functions derived earlier by other authors using different methods.