Useful relations and sum rules for PDFs and multiparton distribution functions of spin-1 hadrons

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 b₁) 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 = 2/3f_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. (author)