Luminosity dilution due to random offset beam-beam interaction

We consider beam-beam interaction in a collider for the case when the beams randomly displace around the equilibrium orbit at the interaction point. Due to the random part of the interaction, particles diffuse over the betatron amplitude causing an emittance growth of the beam. A Fokker-Planck equation is derived in which a diffusion coefficient is related with the spectral density of the noise. Estimations for the Superconducting Super Collider parameters give a tolerable level of the high-frequency beam offset at the interaction point.