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We calculate cross sections for the exclusive diffractive leptoproduction of$\rho$-mesons, $\gamma^*~p~\to~\rho~p$, within the framework of high-energyfactorization. Cross sections for longitudinally and transversally polarizedmesons are shown. We employ a wide variety of unintegrated gluon distributionsavailable in the literature and compare to HERA data. The resulting crosssections strongly depend on the choice of unintegrated gluon distribution. Wealso present predictions for the proton target in the kinematics of theBrookhaven EIC.

Exclusive production of $\rho$-mesons in high-energy factorization at HERA and EIC