Twist-2 relation and sum rule for tensor-polarized parton distribution functions of 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, 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 tensorpolarized parton distribution function f(1LL) and fL(T,) 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(perpendicular to), 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, the electron ion colliders in US and China in 2020's and 2030's.

Automated summary

This work explores the twist-2 relation and sum rule for tensor-polarized parton distribution functions, providing valuable insights for studying spin-1 hadrons and separating twist-2 components from higher-twist terms. The existence of twist-3 multiparton distribution functions for tensor-polarized spin-1 hadrons is also highlighted, showcasing the potential for probing multiparton correlations in these particles. Furthermore, upcoming experimental projects focusing on spin-1 hadrons' spin structure indicate a growing interest in this area of physics.