Probing gluonic saturation in deeply virtual meson production beyond leading power

Exclusive diffractive meson production represents a golden channel for investigating gluonic saturation inside nucleons and nuclei. In this letter, we settle a systematic framework to deal with beyond leading power corrections at small-$x$, including the saturation regime, and obtain the $\gamma^{*} \rightarrow M (\rho, \phi, \omega)$ impact factor with both incoming photon and outgoing meson carrying arbitrary polarizations. This is of particular interest since the saturation scale at modern colliders, although entering a perturbative regime, is not large enough to prevents higher-twist effects to be sizable.