Renormalized Halo Bias
  This paper provides a systematic study of renormalization in models of halo
biasing. Building on work of McDonald, we show that Eulerian biasing is only
consistent with renormalization if non-local terms and higher-derivative
contributions are included in the biasing model. We explicitly determine the
complete list of required bias parameters for Gaussian initial conditions, up
to quartic order in the dark matter density contrast and at leading order in
derivatives. At quadratic order, this means including the gravitational tidal
tensor, while at cubic order the velocity potential appears as an independent
degree of freedom. Our study naturally leads to an effective theory of biasing
in which the halo density is written as a double expansion in fluctuations and
spatial derivatives. We show that the bias expansion can be organized in terms
of Galileon operators which aren't renormalized at leading order in
derivatives. Finally, we discuss how the renormalized bias parameters impact
the statistics of halos.
