Kinematical higher-twist corrections in $\gamma^* \gamma \to M \bar M $

Abstract

We estimate kinematical higher-twist (up to twist 4) corrections to the $\gamma^*(q_1) \gamma(q_2) \to M(p_1) \bar{M}(p_2)$ amplitudes at large $Q^2=-q_1^2$ and small $s=(q_1+q_2)^2$, where $M$ is a scalar or pseudoscalar meson. This process is known to factorize at leading twist into a perturbatively calculable coefficient function and generalized distribution amplitudes (GDAs). The kinematical higher-twist contributions of order $s/Q^2$ and $m^2/Q^2$ turn out to be important in the cross section, considering the kinematics accessible at Belle and Belle II. We present numerical estimates for the cross section for $\gamma^* \gamma \to \pi^0 \pi^0$ with the $\pi \pi$ GDA extracted from Belle measurements and with the asymptotic $\pi \pi$ GDA as inputs to study the magnitude of the kinematical corrections. To see how the target mass corrections of order $m^2/Q^2$ affect the cross section, we also perform the calculation for $\gamma^* \gamma \to \eta \eta$ by using a model $\eta \eta$ GDA.In the range $s> 1$ GeV$^2$, the kinematical higher-twist corrections account for $\sim 15 \%$ of the total cross section, an effect which is not negligible. Since $\pi \pi$ GDAs are the best way to access the pion energy-momentum tensor (EMT), our study demonstrates that an accurate evaluation of EMT form factors requires the inclusion of kinematical higher-twist contributions.