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 $\gamma\gamma\to \pi\pi$ as a benchmark process. As a direct consequence of the linearly polarized quasi-real photons emitted off the electron and positron beams, the $\cos 2\phi$ azimuthal asymmetry in dipion production is predicted within the transverse-momentum-dependent (TMD) factorization framework. In numerical analysis, we take the helicity amplitudes of $\gamma\gamma\to \pi\pi$ determined from the partial wave solutions in dispersion relation as input, and find that the predicted $\cos2\phi$ azimuthal modulation may reach 40\% for the typical kinematical setup of {\tt Belle 2} and {\tt BESIII} experiments. 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.