Transverse Lambda production at the future Electron-Ion Collider

We provide a comprehensive overview of transversely polarized $\mathrm{\ensuremath{\Lambda}}$ production at the future Electron-Ion Collider (EIC). In particular, we study both spontaneous transverse polarization as well spin transfer within momentum dependent (TMD) factorization region. To describe polarization, consider contribution from TMD polarizing fragmentation function (TMD PFF). Similarly, originating transversity FF). projections for statistical uncertainties in corresponding observables EIC. Using these uncertainties, characterize role that EIC will play constraining distributions. perform an impact semi-inclusive deep inelastic scattering process with proton beam. find projected experimental data leads to significant decrease $u$ and sea PFFs. Furthermore, access on FF, first extraction FF recent COMPASS data. compare theoretical our could have this distribution. Finally, also inside jets back-to-back electron-jet