Gluon transversity in polarized proton-deuteron Drell-Yan process

Nucleon spin structure functions have been investigated mainly by longitudinally polarized ones for finding the origin of the nucleon spin. Other types of spin structure functions are transversely polarized ones. In particular, quark transversity distributions in the nucleons have very different properties from the longitudinally polarized quark distribution functions, especially in scaling violation, because they are decoupled from the gluon transversity, due to the fact that they are helicity-flip (chiral-odd) distributions. Such studies are valuable for finding not only the origin of the nucleon spin but also a signature on physics beyond the standard model, because the electric dipole moment of the neutron is proportional to the transversity distributions. Now, there is experimental progress on the quark transversity distributions; however, there is no experimental information on gluon transversity. In fact, the gluon transversity does not exist for the spin-1/2 nucleon due to the helicity-conservation constraint. One needs a hadron with spin more than or equal to one, so that the helicity flip of two units is allowed. A stable spin-1 target is, for example, the deuteron for studying the gluon transversity. In this work, we propose a possibility for finding the gluon transversity at hadron-accelerator facilities, especially in the proton-deuteron Drell-Yan process with the linearly polarized deuteron, by showing theoretical formalism and numerical results. In the experiment, the information on the angular distribution of the dimuon is necessary in the final state; however, the proton beam does not have to be polarized. We show the dependencies of the Drell-Yan cross section on the dimuon-mass squared M-mu mu(2), the dimuon transverse-momentum q(T), the dimuon rapidity y in the center-of-momentum frame, and the magnitude of the gluon transversity Delta(Tg). We also show typical spin asymmetries in the Drell-Yan process. Since the internal spin-1/2 nucleons within the deuteron cannot contribute directly to the gluon transversity, it could be a good observable to find a new non-nucleonic component beyond the simple bound system of nucleons in nuclei.