Luminosity limit due to the beam-beam interactions with or without crossing angle

In recent high luminosity colliders, the finite crossing angle scheme becomes popular to gain the luminosity with multibunch or long bunch operation. Success of the KEKB factory showed that the finite crossing angle scheme has no problem achieving beam-beam parameters up to 0.05. We have studied the beam-beam interactions with and without crossing angle toward higher luminosity. We discuss how the crossing angle affects the beam-beam parameter and luminosity in the present KEKB using computer simulations. The simulations showed that crab cavities, which realize the head-on collision effectively, can be expected to double the luminosity.