Deep exclusive meson production as a probe to the puzzle of Λ hyperon polarization

In the 1970s, an unexpected transverse <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi mathvariant="normal">Λ</a:mi></a:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi mathvariant="normal">Λ</c:mi></c:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi mathvariant="normal">Λ</e:mi></e:math> hyperon is polarized with respect to the initial parton spin direction. How the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi mathvariant="normal">Λ</g:mi></g:math> 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 <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mi mathvariant="normal">Λ</i:mi></i:math> polarization. The outcomes of this experimental measurement are anticipated to unveil the dominant mechanism by which <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mi mathvariant="normal">Λ</k:mi></k:math> obtains its spin, eliminating many of the ambiguities that have been encountered in previous studies. Finally, experimental challenges and requirements are discussed.