Time-like pion electromagnetic form factors in kTkT factorization with the next-to-leading-order twist-3 contribution

We calculate the time-like pion electromagnetic form factor in the kTkT factorization formalism with the inclusion of the next-to-leading-order (NLO) corrections of 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%20%–30% (<15°<15°) in the considered invariant mass squared q2>5 GeV2q2>5 GeV2, and the NLO twist-3 correction plays the key role to narrow the gap between the pQCD predictions and the measured values for the time-like pion electromagnetic form factor.