Next-to-leading-order time-like pion form factors in $k_T$ factorization

TL;DR

This paper computes time-like pion form factors at NLO in $k_T$ factorization, showing moderate corrections and increasing phases with $Q^2$, supporting the framework's suitability for analyzing complex form factors.

Contribution

It provides the first NLO calculations of time-like pion form factors within the $k_T$ factorization formalism, including phase behavior and potential applications to B meson decays.

Findings

NLO corrections are below 30% for magnitude and 30° for phase at high $Q^2$.

The phase of the form factors increases with $Q^2$, aligning with experimental trends.

Supports $k_T$ factorization as effective for analyzing time-like form factors.

Abstract

We calculate the time-like pion-photon transition form factor and the pion electromagnetic form factor up to next-to-leading order (NLO) of the strong coupling constant in the leading-twist $k_T$ factorization formalism. It is found that the NLO corrections to the magnitude (phase) are lower than 30% ($30^\circ$) for the former, and lower than 25% ($10^\circ$) for the latter at large invariant mass squared $Q^2>30$ GeV$^2$ of the virtual photons. The increase of the strong phases with $Q^2$ is obtained, consistent with the tendency indicated by experimental data. This behavior is attributed to the inclusion of parton transverse momenta $k_T$, implying that the $k_T$ factorization is an appropriate framework for analyzing complex time-like form factors. Potential extensions of our formalism to two-body and three-body hadronic $B$ meson decays are pointed out.