Twist-2 relation and sum rule for tensor-polarized parton distribution functions of spin-1 hadrons

Abstract

Abstract 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 tensor-polarized parton distribution functions f 1LL and f LT , 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 ⊥ $$ {H}_{LL}^{\perp } $$ , 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, the electron-ion colliders in US and China in 2020’s and 2030’s.

Keywords

• Deep Inelastic Scattering (Phenomenology)