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

• Published in: arXiv.org
• Main Authors: Kumano, S, Qin-Tao, Song
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 01.09.2021
• Subjects: Distribution functions; Hadrons; Integrals; Mathematical analysis; Partons; Physics - High Energy Physics - Experiment; Physics - High Energy Physics - Lattice; Physics - High Energy Physics - Phenomenology; Physics - Nuclear Theory; Sum rules; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2106.15849

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 \(F_{LT}\), \(G_{LT}\), \(H_{LL}^\perp\), 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.