We study the nonsinglet evolution for the twist-three quark-gluon correlation functions associated with the transverse momentum odd quark distributions. Different from that for the leading-twist quark distributions, these evolution equations involve more general twist-three functions beyond the correlation functions themselves. They provide important information on nucleon structure and can be studied in the semi-inclusive hadron production in deep inelastic scattering and Drell-Yan lepton pair production in the $pp$ scattering process.

Transverse polarization in the hyperon ($\Lambda$) production in the unpolarized deep inelastic scattering and $pp$ collisions is studied in the twist-three approach, considering the contribution from the quark-gluon-antiquark correlation distribution in nucleon. We further compare our results for deep inelastic scattering to a transverse momentum dependent factorization approach, and find consistency between the two approaches in the intermediate transverse momentum region. We also find that in $pp$ collisions, there are only derivative terms contributions, and the nonderivative terms vanish.

We apply collinear expansion to inclusive hadron production in ${e}^{+}{e}^{$-${}}$ annihilation and derive a formalism suitable for systematic study of leading as well as higher-twist contributions to fragmentation functions at the tree level. We make the calculations for hadrons with spin-0, spin-$1/2$ as well as spin-1 and obtain the results in terms of different components of fragmentation functions for the hadronic tensors, the differential cross section as well as hadron polarizations in different cases. The results show a number of interesting features such as the existence of transverse polarization for spin-$1/2$ hadrons at the twist-3 level, the quark polarization independence of the spin alignment of vector mesons.

The observation of the vector meson’s global spin alignment by the STAR Collaboration reveals that strong spin correlations may exist for quarks and antiquarks in relativistic heavy-ion collisions in the normal direction of the reaction plane. We propose a systematic method to describe such correlations in the quark matter. We classify them as local and long range quark spin correlations in the system. We show in particular that the effective quark spin correlations contain the genuine spin correlations originated directly from the dynamical process as well as those induced by averaging over other degrees of freedom. We also show that such correlations can be studied by measuring the vector meson’s spin density matrix and hyperon-hyperon and hyperon-anti-hyperon spin correlations. We present the relationships between these measurable quantities and spin correlations of quarks and antiquarks. Published by the American Physical Society 2024