Deep exclusive meson production as a probe to the puzzle of $\Lambda$ hyperon polarization

In the 1970s, an unexpected transverse $\Lambda$ polarization in unpolarized proton-beryllium collisions was discovered, which initiated extensive studies on spin phenomena in high-energy physics. Over the past five decades, similar transverse $\Lambda$ polarization has been observed across various collision systems, including lepton-hadron deep-inelastic scattering, hadron-hadron collisions, and electron-positron collisions. Despite numerous promising theoretical models, the fundamental mechanism underlying this polarization phenomenon remains inconclusive to this day. However, in both longitudinally and transversely polarized lepton-hadron and hadron-hadron collisions, it is found that the $\Lambda$ hyperon is not polarized with respect to the initial parton spin direction. How the $\Lambda$ hyperon acquires its spin has become one of the most crucial questions to address in order to resolve this puzzle. In this paper, I propose to use an exclusive process that can be measured at the Electron-Ion Collider, the deep exclusive meson production, to explicitly test the mechanism of $\Lambda$ polarization. The outcomes of this experimental measurement are anticipated to unveil the dominant mechanism by which $\Lambda$ obtains its spin, eliminating many of the ambiguities that have been encountered in previous studies. Finally, experimental challenges and requirements are discussed.