NLO corrections and contribution of a tensor gluon operator to the process ${\gamma }^{\ast }\gamma \to \pi \pi$

Abstract

We have calculated the NLO corrections for the leading twist amplitude of the reaction ${\gamma }^{\ast }\gamma \to \pi \pi$ at large virtuality of the photon and at $W^2\ll Q^2$. With a simple model for the two-pion quark and gluon distribution amplitudes we have estimated that the NLO effects may reduce the leading-order amplitude by as much as 30%. We have found that besides the usual twist-2 quark and gluon operators the NLO amplitude receives contribution from a distribution associated with twist-2 tensor gluon operator. The new gluon distribution can be investigated by studying the azimuthal asymmetry of the cross section for $e+\gamma \to e^{\prime }+\pi \pi$.

12 pages, 5 figures, some misprints corrected, one new reference added, some improvements due to comments which we have received recently have been incorporated

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