Time-like pion electromagnetic form factors in $k_{T}$ factorization with the Next-to-leading-order twist-3 contribution

TL;DR

This paper computes the time-like pion electromagnetic form factor using $k_T$ factorization, incorporating NLO corrections to improve agreement with experimental data, especially highlighting the significance of twist-3 contributions.

Contribution

It introduces the calculation of NLO twist-3 contributions within $k_T$ factorization for the time-like pion form factor, enhancing the accuracy of theoretical predictions.

Findings

NLO corrections increase the form factor magnitude by 20-30%.

NLO corrections induce a strong phase of less than 15 degrees.

NLO twist-3 contributions help reconcile pQCD predictions with experimental data.

Abstract

We calculate the time-like pion electromagnetic form factor in the $k_T$ factorization formalism with the inclusion of the next-to-leading-order(NLO) corrections to the leading-twist and sub-leading-twist contributions. It's found that the total NLO correction can enhance (reduce) the magnitude (strong phase) of the leading order form factor by $20\% - 30\%$ ( $< 15^o$) in the considered invariant mass squared $q^2 > 5$ GeV$^2$, and the NLO twist-3 correction play the key role to narrow the gap between the pQCD predictions and the measured values for the time-like pion electromagnetic form factor.