Novel azimuthal observables from two-photon collision at e⁺e⁻ colliders

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 γγ→ ππ as a benchmark process. As a direct consequence of the linearly polarized quasi-real photons emitted off the electron and positron beams, the cos 2φ azimuthal asymmetry in dipion production is predicted within the transverse-momentum-dependent (TMD) factorization framework. In numerical analysis, we take the helicity amplitudes of γγ→ ππ determined from the partial wave solutions in dispersion relation as input, and find that the predicted cos2φ 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.