Twist-3 contribution to the ${\gamma }^{\ast }\gamma \to \pi \pi$ amplitude in the Wandzura-Wilczek approximation

Abstract

We have calculated the Wandzura-Wilczek contribution to the twist-3 part of ${\gamma }^{\ast }\gamma \to 2\pi$ amplitude. It describes interaction of the longitudinally polarized virtual photon with the real one, and it is suppressed by 1/Q, where $Q^2$ is the virtuality of the ${\gamma }^{\ast }$, as compared to the twist-2 contribution. We have found that, in the Wandzura-Wilczek approximation, factorization applies to the twist-3 amplitude.

Comments: 13 pages, 4 figures