Transverse spin physics programs at colliders

Transversely polarized proton-proton collisions provide a unique opportunity to improve our understanding of transverse spin structure of the proton. The complex spin structure of the proton leads to emergent properties such as spin-momentum and spin-spin correlations analogous to the fine and hyperfine structure of atoms. These correlations in protons are experimentally accessible through observables known as transverse single-spin asymmetries (TSSAs). TSSAs quantify azimuthal modulations of particle production in collisions of transversely polarized nucleons with unpolarized particles, and have been measured to reach magnitudes up to 40% in hadron-hadron collisions. Two complementary theoretical frameworks have been developed for describing large TSSAs in which contributions arise from nonperturbative elements of the factorized cross section 1) transverse-momentum-dependent (TMD) factorization, and 2) twist-3 factorization. Both frameworks have demonstrated success in modeling TSSAs in complementary regions of transverse momentum, and are relevant for constraining orbital angular momentum of quarks and gluons in protons

In order to disentangle these underlying mechanisms of the transverse spin structure of proton, TSSAs were measured for various observables in transversely polarized proton+proton collisions at the Relativistic Heavy Ion Collider (RHIC). In this talk, I will present latest results from STAR and PHENIX experiments as well as future prospects in the sPHENIX experiment.