Bias due to neutrinos must not uncorrect'd go
  In cosmologies with massive neutrinos, the galaxy bias defined with respect
to the total matter field (cold dark matter, baryons, and non-relativistic
neutrinos) depends on the sum of the neutrino masses $M_{\nu}$, and becomes
scale-dependent even on large scales. This effect has been usually neglected
given the sensitivity of current surveys, but becomes a severe systematic for
future surveys aiming to provide the first detection of non-zero $M_{\nu}$. The
effect can be corrected for by defining the bias with respect to the density
field of cold dark matter and baryons instead of the total matter field. In
this work, we provide a simple prescription for correctly mitigating the
neutrino-induced scale-dependent bias effect in a practical way. We clarify a
number of subtleties regarding how to properly implement this correction in the
presence of redshift-space distortions and non-linear evolution of
perturbations. We perform a MCMC analysis on simulated galaxy clustering data
that match the expected sensitivity of the \textit{Euclid} survey. We find that
the neutrino-induced scale-dependent bias can lead to important shifts in both
the inferred mean value of $M_{\nu}$, as well as its uncertainty. We show how
these shifts propagate to other cosmological parameters correlated with
$M_{\nu}$, such as the cold dark matter physical density $\Omega_{cdm} h^2$ and
the scalar spectral index $n_s$. In conclusion, we find that correctly
accounting for the neutrino-induced scale-dependent bias will be of crucial
importance for future galaxy clustering analyses. We encourage the cosmology
community to correctly account for this effect using the simple prescription we
present in our work. The tools necessary to easily correct for the
neutrino-induced scale-dependent bias will be made publicly available in an
upcoming release of the Boltzmann solver \texttt{CLASS}.
