Octupole parton structure of spin-3/2 targets

Abstract

In spin-$3/2$ targets, octupole polarization can reveal quark and gluon correlations beyond those probed by vector polarization and quadrupole alignment. Here, we construct the complete leading-twist gluon transverse-momentum-dependent distribution basis, with 32 independent coefficients for each specified Wilson-line and color structure. Fourteen of these describe octupole dependence in gluon number, helicity, and linear polarization. In heavy-quark-pair leptoproduction at small, nonzero pair imbalance, comparing target states with opposite octupoles and identical lower moments isolates the octupole contribution. Beam-helicity reversal and joint angular projections in target orientation and pair-imbalance azimuth can then separate all fourteen gluon octupole responses at leading-power Born order. We also derive the incoming-target quark responses in semi-inclusive deep-inelastic scattering and Drell-Yan production. Time-reversal relations between distributions remain valid under symmetry-preserving renormalization and evolution, while predictions across processes require factorization formulas connecting those distributions to scattering observables. Finally, we connect this framework to polarized ${}^7$Li through its collinear limits and nuclear spin-orbital correlations.

Comments: 32 pages, 2 figures