Oct 4 – 8, 2021
University of Alcalá
Europe/Madrid timezone

Polarized PDFs and TMDs for spin-1 hadrons

Oct 6, 2021, 9:20 AM
20m
Colegio San Ildefonso (University of Alcalá)

Colegio San Ildefonso

University of Alcalá

Speaker

Shunzo Kumano (KEK/J-PARC)

Description

We explain possible transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons up to twist 4 by decomposing a quark correlation function with the conditions of the Hermiticity and parity invariance [1]. In the TMDs, there exist time-reversal-odd functions in addition to the time-reversal-even ones. We showed that 40 TMDs exist in the tensor-polarized spin-1 hadron in the twist 2, 3, and 4. In particular, we found 30 new structure functions in the twist 3 and 4 in our work. Since time-reversal-odd terms of the collinear correlation function should vanish after integrals over the partonic transverse momentum, we obtain new sum rules for the time-reversal-odd structure functions, $\int d^2 k_T g_{LT} = \int d^2 k_T h_{LL} = \int d^2 k_T h_{3LL} =0$. In addition, we indicated that new transverse-momentum-dependent fragmentation functions exist in tensor-polarized spin-1 hadrons.

Sum rules for structure functions and their twist-2 relations have important roles in constraining their magnitudes and $x$ dependencies and in studying higher-twist effects. The Wandzura-Wilczek (WW) relation and the Burkhardt-Cottingham (BC) sum rule are such examples for the polarized structure functions $g_1$ and $g_2$. Recently, new twist-3 and twist-4 parton distribution functions were proposed for spin-1 hadrons [1], so that it became possible to investigate spin-1 structure functions including higher-twist ones. We show in this work that an analogous twist-2 relation and a sum rule exist for the tensor-polarized parton distribution functions $f_{1LL}$ and $f_{LT}$ [2], where $f_{1LL}$ is a twist-2 function and $f_{LT}$ is a twist-3 one. Namely, the twist-2 part of $f_{LT}$ is expressed by an integral of $f_{1LL}$ (or $b_1$) and the integral of the function $f_{2LT} = (2/3) f_{LT} -f_{1LL}$ over $x$ vanishes. If the parton-model sum rule for $f_{1LL}$ ($b_1$) is applied by assuming vanishing tensor-polarized antiquark distributions, another sum rule also exists for $f_{LT}$ itself. These relations should be valuable for studying tensor-polarized distribution functions of spin-1 hadrons and for separating twist-2 components from higher-twist terms, as the WW relation and BC sum rule have been used for investigating $x$ dependence and higher-twist effects in $g_2$. In deriving these relations, we indicate that four twist-3 multiparton distribution functions $F_{LT}$, $G_{LT}$, $H_{LL}^¥perp$, and $H_{TT}$ exist for tensor-polarized spin-1 hadrons. These multiparton distribution functions are also interesting to probe multiparton correlations in spin-1 hadrons.

In the near future, we expect that physics of spin-1 hadrons will become a popular topic, since there are experimental projects to investigate spin structure of the spin-1 deuteron at the Jefferson Laboratory, the Fermilab, the nuclotron-based ion collider facility [3], the LHCspin, the electron-ion colliders in US and China in 2020's and 2030's.

[1] S. Kumano and Qin-Tao Song, Phys. Rev. D 103 (2021) 014025.
[2] S. Kumano and Qin-Tao Song, arXiv:2106.15849 (J. High Energy Phys. in press).
[3] A. Arbuzov et al. (S. Kumano, 16th author; Q.-T. Song, 27th author), Prog. Nucl. Part. Phys. 119 (2021) 103858.

Primary authors

Shunzo Kumano (KEK/J-PARC) Prof. Qin-Tao Song (Zhengzhou University)

Presentation materials