Abstract
We obtain the distribution amplitude (DA) of the pion from its light-front wave functions in the basis light-front quantization framework. This light-front wave function of the pion is given by the lowest eigenvector of a light-front effective Hamiltonian consisting a three-dimensional confinement potential and the color-singlet Nambu--Jona-Lasinion interaction both between the constituent quark and antiquark. The quantum chromodynamics (QCD) evolution of the DA is subsequently given by the perturbative Efremov-Radyushkin-Brodsky-Lepage evolution equation. Based on this DA, we then evaluate the singly and doubly virtual transition form factors in the space-like region for $\pi^0\rightarrow \gamma^*\gamma$ and $\pi^0\rightarrow \gamma^*\gamma^*$ processes using the hard-scattering formalism. Our prediction for the pion-photon transition form factor agrees well with data reported by the Belle Collaboration. However, in the large $Q^2$ region it deviates from the rapid growth reported by the BaBar Collaboration. Meanwhile, our result on the $\pi^0\rightarrow \gamma^*\gamma^*$ transition form factor is also consistent with other theoretical approaches and agrees with the scaling behavior predicted by perturbative QCD.
Highlights
The parton distribution amplitudes (DAs) that play essential roles in describing the various hard exclusive processes of quantum chromodynamics (QCD) bound states [1–3] via the factorization theorem [4] are among the most basic structure functions
We have evaluated the valence-quark distribution amplitude from the light-front wave functions (LFWFs) of the pion in the framework of the basis light front quantization (BLFQ)
Our result is based on the wave functions as the eigenfunctions of an effective Hamiltonian which includes the confinement potentials and the color-singlet NambuJona-Lasinio interactions
Summary
The parton distribution amplitudes (DAs) that play essential roles in describing the various hard exclusive processes of quantum chromodynamics (QCD) bound states [1–3] via the factorization theorem [4] are among the most basic structure functions. [1,29], where TFFs are expected to follow the asymptotic behavior of, Q2FPγðQ2Þ → constant as Q2 → ∞ Unlike their results showing growth in Q2FπγðQ2Þ, the BABAR data [28] for the Q2Fðη;η0ÞγðQ2Þ appear consistent with the PQCD. The meson (M) TFFs for the doubly virtual M → γÃγà transitions have been studied within the Dyson-Schwinger and Bethe-Salpeter framework [52], the chiral perturbation theory [53], a light-front quark model [54], the anti–de Sitter (AdS)/QCD [55,56], and the lattice QCD [16,57–60]. The nonperturbative solutions for the LFWFs given by the recent BLFQ study of light mesons [67] have been applied successfully to predict the electromagnetic form factors and associated charge radii, PDFs, structure functions and generalized parton distributions of the pion [67–70]. We extend our investigations of the pion to compute its singly and doubly virtual photon TFFs
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