The NLO twist-3 contribution to the pion electromagnetic form factors in $k_T$ factorization

Abstract

In this paper, by employing the $k_T$ factorization theorem, we calculate firstly the next-to-leading-order (NLO) twist-3 contributions to the pion electromagnetic form factors in the $\pi {\gamma }^{\ast }\to \pi$ process. From the analytical and numerical calculations we find the following points: (a) For the leading order (LO) twist-2, twist-3 and the NLO twist-2 contributions, our results agree very well with those obtained in previous works; (b) We extract out two factors $F_{T3}^{(1)}(x_i,t,Q^2)$ and $\text{ov}{F}_{T3}^{(1)}(x_i,t,Q^2)$, which describe directly the NLO twist-3 contributions to the pion electromagnetic form factors $F^{+}(Q^2)$; (c) The NLO twist-3 contribution is negative in sign and cancel partially with the NLO twist-2 part, the total NLO contribution can therefore provide a roughly $\pm 20\%$ corrections to the total LO contribution in the considered ranges of $Q^2$; and (d) The theoretical predictions for $Q^2{F}^{+}(Q^2)$ in the low-$Q^2$ region agree well with currently available data, this agreement can be improved by the inclusion of the NLO contributions.

Comments: 26 pages, 10 ps figures and 2 Tables, minor corrections