  The chiral-odd transversity generalized parton distributions (GPDs) of the
nucleon can be accessed experimentally through the exclusive photoproduction
process gamma + N -> pi + rho + N', in the kinematics where the meson pair has
a large invariant mass and the final nucleon has a small transverse momentum,
provided the vector meson is produced in a transversally polarized state. We
calculate perturbatively the scattering amplitude at leading order in alpha_s.
We build a simple model for the dominant transversity GPD H_T(x,xi, t) based on
the concept of double distribution. We estimate the unpolarized differential
cross section for this process in the kinematics of the Jlab and COMPASS
experiments. Counting rates show that the experiment looks feasible with the
real photon beam characteristics expected at JLab@12 GeV, and with the quasi
real photon beam in the COMPASS experiment.
