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We calculate the cross section for diffractive hadron production in deepinelastic scattering off heavy nuclei in the framework of gluonsaturation/color glass condensate. We analyze the kinematic region of thefuture Electron-Ion Collider. We argue that coherent and incoherent diffractivechannels are very sensitive to the structure of the nuclear matter at low $x$.This expresses itself in a characteristic dependence of the cross sections onrapidity and transverse momentum of the produced hadron and on the nuclearweight. We also discuss dependence on the scattering angle and argue that bothcoherent and incoherent cross sections may be within experimental reach at EIC.

Diffractive hadron production in DIS off heavy nuclei and gluon saturation