Uncertainties from metrology in the integrated luminosity measurement with the updated design of the very forward region of a detector at CEPC

At an e⁺e⁻ collider machine-detector interface includes, among others, a calorimeter dedicated for precision measurement of the integrated luminosity at a per mill level or better. Usually, such a device is placed at the outgoing beams, to keep the spatial symmetries of the head-on collisions at accelerators with a non-zero crossing angle. At CEPC it is currently proposed that the luminometer is placed on the z-axis. We review a feasibility of precision measurement of the integrated luminosity at the Z⁰ pole, from the point of view of systematic effects arising from metrology uncertainties, either concerning the luminometer position and alignment or the beam properties, with the luminometer centered around the z-axis.