Transverse-momentum-dependent parton distribution functions up to twist 4 for spin-1 hadrons

We show possible transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons including twist-3 and 4 in addition to the leading twist-2 ones by investigating all decomposition of a quark correlation function Lorentz-invariant way. The Hermiticity parity invariance are imposed decomposition; however, time-reversal is not used due an active role gauge links TMDs. Therefore, there exist time-reversal-odd even list up twist-4 level because were missing terms associated with lightcone vector $n$ previous works on part was no correlation-function study parts hadrons. that 40 TMDs tensor-polarized hadron twists 2, 3, 4. Some expressions structure modified from derivations new $n$, we find 30 3 this work. Since collinear should vanish after integrals over partonic transverse momentum, obtain sum rules functions, $ \int d^2 k_T h_{LT}= h_{LL} = h_{3LL} =0$. In addition, indicate fragmentation rare observables explicit color degrees freedom flow, which cannot be usually measured confined