Useful relations and sum rules for PDFs and multiparton 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 17.01.2022
• Subjects: Distribution functions; Gluons; Hadrons; Mathematical analysis; Operators (mathematics); Particle accelerators; Physics - High Energy Physics - Lattice; Physics - High Energy Physics - Phenomenology; Physics - Nuclear Theory; Protons; Sum rules; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2201.06557

There are two types of polarizations in spin-1 hadrons, and they are vector and tensor polarizations. The latter is a unique one since it does not exist in the spin-1/2 proton. The vector-polarized PDFs are the same for both the proton and spin-1 hadrons; therefore, we mainly investigate the unique PDFs in tensor-polarized hadrons. By using the operator product expansion, the twist-3 PDF \(f_{LT}\) can be expressed by two terms in the same way with \(g_T\) of the proton. The first term is determined by the twist-2 PDF \(f_{1LL}\) (or \(b_1\)) which was measured by an experiment, and the second term is expressed by twist-3 quark-gluon distributions. If we neglect the higher-twist effects, \(f_{LT}\) is simply given by \(f_{1LL}\), and this relation is similar to the Wandzura-Wilczek relation of \(g_T\). Furthermore, a new sum rule is also obtained for \(f_{2LT}=2/3 f_{LT}- f_{1LL}\), which is analogous to the Burkhardt-Cottingham sum rule, in the tensor-polarized spin-1 hadrons. In future, these interesting relations could be studied at accelerator facilities, such as the Jefferson Laboratory, the Fermilab, the nuclotron-based ion collider facility in Russia, the proposed electron-ion colliders in US and China.