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

TL;DR

This paper improves the theoretical description of gamma-gamma to pion-pion scattering amplitudes at high momentum transfer by deriving and estimating kinematical higher-twist corrections relevant for experimental conditions at Belle and Belle II.

Contribution

It applies the Braun-Manashov technique to derive higher-twist corrections of order s/Q^2 and m^2/Q^2 for gamma-gamma to pion-pion amplitudes, enhancing the accuracy of theoretical models.

Findings

Derived kinematical higher-twist contributions of order s/Q^2 and m^2/Q^2.

Estimated sizes of these corrections in Belle and Belle II kinematics.

Provided a framework for better understanding of pion GDAs and energy-momentum tensor form factors.

Abstract

We apply the Braun-Manashov technique to improve the description of $\gamma^*(q_1) \gamma(q_2) \to M(p_1) M(p_2)$ amplitudes at large $Q^2=-q_1^2$ and small $s=(q_1+q_2)^2$. We derive the kinematical higher-twist contributions of order $s/Q^2$ and $m^2/Q^2$ to the helicity amplitudes and estimate their sizes in the kinematics accessible at Belle and Belle II.Since pion GPDs cannot be directly measured by experiment, $\pi \pi$ GDAs are the best way to investigate the energy-momentum tensor form factors for pions.