Gluon transversity and TMDs for spin-1 hadrons


  • Shunzo Kumano KEK/J-PARC
  • Qin-Tao Song



QCD, quark, gluon, spin-1 hadron, structure function, transversity


We explain a gluon transversity, transverse-momentum-dependent parton distribution functions (TMDs), and parton distribution functions (PDFs) for spin-1 hadrons. The gluon transversity exists in hadrons with spin more than or equal to one, and it does not exist in the spin-1/2 nucleons. Since there is no direct contribution from the nucleons, it is an appropriate quantity to probe an exotic component in the spin-1 deuteron beyond a simple bound system of the nucleons. We show how the gluon transversity can be measured at hadron accelerator facilities by the Drell-Yan process in addition to lepton-accelerator experiments. Next, possible TMDs are explained for the spin-1 hadrons at the twists 3 and 4 in addition to twist-2 ones by considering tensor polarizations. We found that 30 TMDs exist in the tensor-polarized spin-1 hadron at the twists 3 and 4 in addition to 10 TMDs at the twist 2. There are 3 collinear PDFs at the twists 3 and 4. We also indicate that the corresponding TMD fragmentation functions exist at the twists 3 and 4. Due to the time-reversal invariance in the collinear PDFs, there are new sum rules on the time-reversal odd TMDs. In addition, we obtained a useful twist-2 relation, a sum rule, and relations with multiparton distribution functions by using the operator product expansion and the equation of motion for quarks. These findings are valuable for experimental investigations on polarized deuteron structure functions in 2020's and 2030's at world accelerator facilities.


A. Airapetian et al. (HERMES Collaboration), Phys. Rev. Lett. 95 (2005) 242001; S. Kumano, Phys. Rev. D 82 (2010) 017501; S. Kumano and Qin-Tao Song, Phys. Rev. D 94 (2016) 054022; W. Cosyn, Yu-Bing Dong, S. Kumano, and M. Sargsian, Phys. Rev. D 95 (2017) 074036.

(JLab) J.-P. Chen et al., Proposal to Jefferson Lab PAC-38, PR12-11-110 (2011); M. Jones et al., A Letter of Intent to Jefferson Lab PAC 44, LOI12-16-006 (2016); (Fermilab) D. Geesaman et al., Proposal to Fermilab PAC, P-1039 (2013); D. Keller et al., proposal to be submitted to Fermilab in 2022; (NICA) A. Arbuzov et al., Prog. Nucl. Part. Phys. 119 (2021) 103858; (LHCspin) C. A. Aidala et al., arXiv:1901.08002; (EIC) R. Abdul Khalek et al., arXiv:2103.05419; (EicC) D. P. Anderle et al., Front. Phys. 16 (2021) 64701.

S. Kumano, Qin-Tao Song, Phys. Rev. D 101 (2020) 054011; D 101 (2020) 094013.

S. Hino and S. Kumano, Phys. Rev. D 59 (1999) 094026; 054018 60 (1999) 054018.

J. P. Ma, C. Wang, and G. P. Zhang, arXiv:1306.6693 (unpublished, 2013).

S. Kumano and Qin-Tao Song, Phys. Rev. D 103 (2021) 014025.

K. Goeke, A. Metz and M. Schlegel, Phys. Lett. B 618 (2005) 90; A. Metz, P. Schweitzer and T. Teckentrup, Phys. Lett. B 680 (2009) 141.

A. Bacchetta and P. Mulders, Phys. Rev. D 62 (2000) 114004.

S. Kumano and Qin-Tao Song, 141 JHEP 09 (2021) 141.

S. Kumano and Qin-Tao Song, arXiv:2112.13218, submitted for publication. X. Ji, Phys. Rev. D 49 (1994) 114.

F. E. Close and S. Kumano, Phys. Rev. D 42 (1990) 2377; S. Kumano, J. Phys.: Conf. Series 543 (2014) 012001.




How to Cite

Kumano S, Song Q-T. Gluon transversity and TMDs for spin-1 hadrons. Supl. Rev. Mex. Fis. [Internet]. 2022 May 24 [cited 2022 Dec. 9];3(3):0308097 1-6. Available from: