The bias of weighted dark matter haloes from peak theory

We give an analytical form for the weighted correlation function of peaks in a Gaussian random eld. In a cosmological context, this approach strictly describes the formation bias and is the main result here. Nevertheless, we show its validity and applicability to the evolved cosmological density eld and halo eld, using Gaussian random eld realisations and dark matter N-body numerical simulations. Using this result from peak theory we compute the bias of peaks (and dark matter halos) and show that it reproduces results from the simulations at the O(10%) level. Our analytical formula for the bias predicts a scale-dependent bias with two characteristics: a broad band shape which, however, is most aected by the choice of weighting scheme and evolution bias, and a more robust, narrow feature localised at the BAO scale, an eect that is conrmed in simulations. This scale-dependent bias smooths the BAO feature but, conveniently, does not move it. We provide a simple analytic formula to describe this eect. We envision that our analytic solution will be of use for galaxy surveys that exploit galaxy clustering.