  Chiral-odd gluon transversity distribution could shed light on a new aspect
of hadron physics. Although we had much progress recently on quark transversity
distributions, there is no experimental measurement on the gluon transversity.
The gluon trasversity does not exist in the spin-1/2 nucleons and it exists in
the spin-1 deuteron. Therefore, it could probe new hadron physics in the
deuteron beyond the basic bound system of a proton and a neutron because the
nucleons cannot contribute directly. Here, we explain that the gluon
transversity can be measured at hadron accelerator facilities, such as Fermilab
and NICA, in addition to charged-lepton scattering measurements at lepton
accelerator facilities by showing cross sections of the proton-deuteron
Drell-Yan process as an example.
