Rho-pion transition form factors in the $k_T$ factorization formulism revisited

TL;DR

This paper revisits the rho-pion transition form factors using the $k_T$ factorization approach, incorporating NLO QCD corrections, and compares predictions with lattice QCD results to improve understanding of meson interactions.

Contribution

It provides a detailed NLO analysis of rho-pion transition form factors within the $k_T$ factorization framework, including regularization of infrared divergences and comparison with lattice QCD data.

Findings

NLO corrections increase the spacelike form factor by up to 35%.

The timelike form factor remains well-behaved at large momentum transfer.

The rho-pion-photon coupling is estimated as 0.596 from combined analysis.

Abstract

We revisit the evaluations for the spacelike and timelike $\rho \pi$ transition form factors $F_{\rho\pi}(Q^2)$ and $G_{\rho\pi}(Q^2)$ with the inclusion of the the next-to-leading order (NLO) QCD contributions in the framework of the $k_T$ factorization theorem. The infrared divergence is regularized by the transversal momentum carried by external valence quarks, and ultimately absorbed into the meson wave functions. In the region of $ Q^2 \leqslant 2 \, \textrm{GeV}^2 $, where PQCD factorization apporach applicable, the NLO contribution can bring no larger than $ 35\%$ enhancement to the spacelike form factor $F_{\rho\pi}(Q^2)$. For the timelike form factor derived under the kinematic exchanging symmetry, this contribution is also under control when the momentum transfer squared is large enough. We also prolong our prediction into the small $Q^2$ region by taking the Lattice QCD results into account, and subsequently obtain the coupling $g_{\rho\pi\gamma} = G_{\rho\pi}(0)=0.596$.