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

TL;DR

This paper calculates the pion's distribution amplitude and transition form factors using basis light-front quantization, achieving good agreement with Belle data and providing insights into QCD dynamics.

Contribution

It introduces a novel approach to compute pion transition form factors via basis light-front quantization and effective Hamiltonian, connecting nonperturbative wave functions with QCD evolution.

Findings

Predicted pion-photon transition form factor matches Belle data.

Deviates from BaBar's large $Q^2$ growth in the transition form factor.

Results are consistent with perturbative QCD scaling.

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.