Prospects of transverse $\Lambda$ and $\bar{\Lambda}$ polarization measurements at LHCb

Transverse $\Lambda$ polarization observed over four decades ago contradicted expectations from early leading-order perturbative QCD calculations. Measurements of $\Lambda$ polarization from unpolarized $pp$ and $p$A collisions have been previously observed to increase as a function of $x_F$ and $p_T$ up to a few GeV range and approximately independent of beam energy. Recent studies have linked polarization to the process of hadronization, which describes how particular hadrons are formed from scattered quarks and gluons. The high energy of the LHC and the coverage and precision measurement possibilities from LHCb forward geometry are ideal for studying hyperon polarization as a function of both $p_T$ and $x_F$. This contribution presents the status and prospects of hyperon polarization measurements in $pp$, $p$Pb, Pb$p$, and fixed-target $p$A collisions at LHCb.