Deeply virtual meson production at HERA and at the EIC within the Color Glass Condensate EFT

Continuing our previous study of Deeply Virtual Meson Production (DVMP) at twist-3 accuracy, we derive compact expressions for all helicity amplitudes. We perform a phenomenological analysis of the helicity-amplitude ratio $\mathcal{A}^{11}/\mathcal{A}^{00}$ and of the spin-density matrix element $r_{00}^{04}$ within the Color Glass Condensate framework. Small-$x$ evolution is incorporated by numerically solving the running-coupling-and-collinearly-improved Balitsky-Kovchegov and Balitsky-Fadin-Kuraev-Lipatov equations with the McLerran-Venugopalan model as the initial condition. By capturing a relevant subset of next-to-leading order corrections, we provide the most theoretically accurate description of these observables to date. Our results are compared to HERA data, and predictions are presented for electron-lead collisions at the future Electron-Ion Collider. We discuss the impact of non-linear effects at low photon virtuality and the role of genuine higher-twist contributions associated with light vector meson distribution amplitudes, corresponding to higher-Fock-state components of the projectile.