Pion to photon transition form factors with basis light-front quantization

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 ${\pi }^0\to {\gamma }^{\ast }\gamma$ and ${\pi }^0\to {\gamma }^{\ast }{\gamma }^{\ast }$ 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 ${\pi }^0\to {\gamma }^{\ast }{\gamma }^{\ast }$ transition form factor is also consistent with other theoretical approaches and agrees with the scaling behavior predicted by perturbative QCD.

15 pages, 5 figures, 3 tables; figure 3 and corresponding discussions added; version accepted by PRD

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• Basis light-front quantization approach to $\Lambda$ and ${\Lambda }_c$ and their isospin triplet baryons
• Pion spectroscopy and dynamics using the holographic light-front Schrödinger equation and the 't Hooft equation
• Dispersive derivation of the pion distribution amplitude
• The pion in the graviton soft-wall model: phenomenological applications