Exclusive neutrino-production of a charmed vector meson and transversity gluon GPDs

We calculate at the leading order in $\alpha_s$ the QCD amplitude for exclusive neutrino production of a $D^*$ or $D_s^*$ charmed vector meson on a nucleon. We work in the framework of the collinear QCD approach where generalized parton distributions (GPDs) factorize from perturbatively calculable coefficient functions. We include $O(m_c)$ terms in the coefficient functions and $O(m_D)$ term in the definition of heavy meson distribution amplitudes. The show that the analysis of the angular distribution of the decay $D_{(s)}^*\to D_{(s)} \pi$ allows to access the transversity gluon GPDs.