TMDs for spin-1 hadrons

Abstract

Transverse-momentum-dependent parton distribution functions (TMDs) were investigated at the twists 3 and 4 for spin-1 hadrons in addition to the twist-2 ones. They were found by studying all the possible decomposition of a quark correlation function in a Lorentz-invariant way with the Hermiticity and parity invariance. The time-reversal invariance was not imposed for the TMDs due to an active role of gauge links; however, they were used for collinear parton distribution functions (PDFs) by integrating the TMDs over the transverse momentum. We found that 30 TMDs exist in the tensor-polarized spin-1 hadron at the twists 3 and 4, whereas there are 10 TMDs at the twist 2. We also showed that there are 3 collinear PDFs at the twists 3 and 4. The corresponding TMD fragmentation functions exist sat the twists 2, 3, and 4 simply by changing function names and variables. Since the time-reversal invariance is valid in the collinear PDFs, the integrals of time-reversal-odd TMDs over the transverse momentum should vanish. It leads to the sum rules $\int d^2{k}_T{h}_{1LT}(x,k_T^2)=\int d^2{k}_T{g}_{LT}(x,k_T^2)=\int d^2{k}_T{h}_{LL}(x,k_T^2)=\int d^2{k}_T{h}_{3LL}(x,k_T^2)=0$ on the time-reversal odd TMDs at the twists 3 and 4.

arXiv comment5 pages, LaTeX, 24th International Spin Symposium, October 18-22, 2021, (In person/Online) Matsue, Japan

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