Azimuthal asymmetries in $D$-meson and jet production at the EIC

We study the azimuthal asymmetries in back-to-back leptoproduction of $D$-meson and jet to probe the gluon TMDs in an unpolarized and transversely polarized electron-proton collision at the kinematics of EIC. We give predictions for unpolarized cross-sections within the TMD factorization framework. In $D$-meson and jet formation, the only leading order contribution comes from the photon gluon fusion process. We give numerical estimates of the upper bound on the azimuthal asymmetries with the saturation of positivity bounds; also, we present the asymmetries using a Gaussian parameterization of TMDs. We obtain sizable asymmetries in the kinematics that will be accessible at EIC.