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In this work we advocate a set of novel azimuthal-angle-related observables associated with exclusive hadron production from two-photon fusion at e^+ e^- colliders, taking the as a benchmark process. As a direct consequence of the linearly polarized quasi-real photons emitted off the electron and positron beams, the 2 azimuthal asymmetry in dipion production is predicted within the transverse-momentum-dependent (TMD) factorization framework. In numerical analysis, we take the helicity amplitudes of determined from the partial wave solutions in dispersion relation as input, and find that the predicted 2 azimuthal modulation may reach 40\% for the typical kinematical setup of Belle experiment. Future accurate measurement of this azimuthal asymmetry may facilitate the direct extraction of the relative phase between two helicity amplitudes with photon helicity configurations ++ and +-. This knowledge provides a valuable input for the dispersive determination of the hadronic light-by-light (Hlbl) contributions, which constitutes one of the largest theoretical uncertainties in predictions for the muon anomalous magnetic moment.
Yu et al. (Thu,) studied this question.
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