A Lagrangian Perturbation Theory in the presence of massive neutrinos
  We develop a Lagrangian Perturbation Theory (LPT) framework to study the
clustering of cold dark matter (CDM) in cosmologies with massive neutrinos. We
follow the trajectories of CDM particles with Lagrangian displacements fields
up to third order in perturbation theory. Once the neutrinos become
non-relativistic, their density fluctuations are modeled as being proportional
to the CDM density fluctuations, with a scale-dependent proportionality factor.
This yields a gravitational back-reaction that introduces additional scales to
the linear growth function, which is accounted for in the higher order LPT
kernels. Through non-linear mappings from Eulerian to Lagrangian frames, we
ensure that our theory has a well behaved large scale behavior free of unwanted
UV divergences, which are common when neutrino and CDM densities are not
treated on an equal footing, and in resummation schemes that manifestly break
Galilean invariance. We use our theory to construct correlation functions for
both the underlying matter field, as well as for biased tracers using
Convolution-LPT. Redshift-space distortions effects are modeled using the
Gaussian Streaming Model. When comparing our analytical results to simulated
data from the Quijote simulation suite, we find good accuracy down to $r=20
\,\text{Mpc} \, h^{-1}$ at redshift $z=0.5$, for the real space and redshift
space monopole particle correlation functions with no free parameters. The same
accuracy is reached for the redshift space quadrupole if we additionally
consider an effective field theory parameter that shifts the pairwise velocity
dispersion. For modeling the correlation functions of tracers we adopt a simple
Lagrangian biasing scheme with only density and curvature operators, which we
find sufficient to reach down to $r=20 \,\text{Mpc} \, h^{-1}$ when comparing
to simulated halos.
