Transverse $\mathrm{\Lambda }$ polarization in $e^{+}{e}^{-}$ annihilations and in SIDIS processes at the EIC within TMD factorization

We present a phenomenological study on the role of charm contribution and $SU(2)$ isospin symmetry in the extraction of the $\mathrm{\Lambda }$ polarizing fragmentation functions from $e^{+}{e}^{-}\to {\mathrm{\Lambda }}^{\uparrow }({\bar{\mathrm{\Lambda }}}^{\uparrow })h+X$ annihilation processes. We adopt the well-established transverse-momentum-dependent factorization formalism, within the Collins-Soper-Sterman evolution scheme at next-to-leading logarithm accuracy, carefully exploiting the role of the nonperturbative component of the polarizing fragmentation function. We then discuss the impact of these results on the predictions for transverse $\mathrm{\Lambda }$, $\bar{\mathrm{\Lambda }}$ polarization in semi-inclusive deep inelastic scattering processes at typical energies of the future Electron-Ion Collider.