Contribution of the hybrid inflation waterfall to the primordial curvature perturbation

A contribution zeta(chi) to the curvature perturbation will be generated during the waterfall that ends hybrid inflation, that may be significant on small scales. In particular, it may lead to excessive black hole formation. We here consider standard hybrid inflation, where the tachyonic mass of the waterfall field is much bigger than the Hubble parameter. We calculate zeta(chi) in the simplest case, and see why earlier calculations of zeta(chi) are incorrect.