English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, by employing the $k_{T}$ factorization theorem, we calculatefirstly the next-to-leading-order (NLO) twist-3 contributions to the pionelectromagnetic form factors in the $\pi\gamma^* \to \pi$ process. From theanalytical and numerical calculations we find the following points: (a) For theleading order (LO) twist-2, twist-3 and the NLO twist-2 contributions, ourresults agree very well with those obtained in previous works; (b) We extractout two factors $F^{(1)}_{\rm T3}(x_i,t,Q^2)$ and $\ov{F}^{(1)}_{\rmT3}(x_i,t,Q^2)$, which describe directly the NLO twist-3 contributions to thepion electromagnetic form factors $F^+(Q^2)$; (c) The NLO twist-3 contributionis negative in sign and cancel partially with the NLO twist-2 part, the totalNLO contribution can therefore provide a roughly $\pm 20\%$ corrections to thetotal LO contribution in the considered ranges of $Q^2$; and (d) Thetheoretical predictions for $Q^2 F^+(Q^2)$ in the low-$Q^2$ region agree wellwith currently available data, this agreement can be improved by the inclusionof the NLO contributions.

The NLO twist-3 contribution to the pion electromagnetic form factors in $k_{T}$ factorization