  We address the issue of the cosmological bias between matter and galaxy
distributions, looking at dark-matter haloes as a first step to characterize
galaxy clustering. Starting from the linear density field at high redshift, we
follow the centre of mass trajectory of the material that will form each halo
at late times (proto-halo). We adopt a fluid-like description for the evolution
of perturbations in the proto-halo distribution, which is coupled to the matter
density field via gravity. We present analytical solutions for the density and
velocity fields, in the context of renormalized perturbation theory. We start
from the linear solution, then compute one-loop corrections for the propagator
and the power spectrum. Finally we analytically resum the propagator and we use
a suitable extension of the time-renormalization-group method (Pietroni 2008)
to resum the power spectrum. For halo masses M<10^{14} Msol/h our results at
z=0 are in good agreement with N-body simulations. Our model is able to predict
the halo-matter cross spectrum with an accuracy of 5 per cent up to k = 0.1
h/Mpc approaching the requirements of future galaxy redshift surveys.
