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We investigate the singly virtual transition form factor (TFF) for the ⁰^* process in the space-like region using the hard-scattering formalism within the Basis Light-Front Quantization (BLFQ) framework. This form factor is expressed in terms of the perturbatively calculable hard-scattering amplitudes (HSAs) and the light-front wave functions (LFWFs) of the pion. We obtain the pion LFWFs by diagonalizing the light-front QCD Hamiltonian, which is determined for its constituent quark-antiquark and quark-antiquark-gluon Fock sectors with a three-dimensional confinement. We employ the HSAs up to next-to-leading order (NLO) in the quark-antiquark Fock sector and leading order (LO) in the quark-antiquark-gluon Fock sector. The NLO correction to the TFF in the quark-antiquark Fock sector is of the same order as the LO contribution to the TFF in the quark-antiquark-gluon Fock sector. We find that while the quark-antiquark-gluon Fock sector has minimal effect in the large momentum transfer (Q²) region, it has a noteworthy impact in the low-Q² region. Our results show that, after accounting for both Fock sectors, the TFF within the BLFQ framework aligns well with existing experimental data, particularly in the low Q² region.
Wu et al. (Tue,) studied this question.