Cubic Halo Bias in Eulerian and Lagrangian Space
  Predictions of the next-to-leading order, i.e. one-loop, halo power spectra
depend on local and non-local bias parameters up to cubic order. The linear
bias parameter can be estimated from the large scale limit of the halo-matter
power spectrum, and the second order bias parameters from the large scale,
tree-level, bispectrum. Cubic operators would naturally be quantified using the
tree-level trispectrum. As the latter is computationally expensive, we extent
the quadratic field method proposed in Schmittfull et al. 2014 to cubic fields
in order to estimate cubic bias parameters. We cross-correlate a basis set of
cubic bias operators with the halo field and express the result in terms of the
cross-spectra of these operators in order to cancel cosmic variance. We obtain
significant detections of local and non-local cubic bias parameters, which are
partially in tension with predictions based on local Lagrangian bias schemes.
We directly measure the Lagrangian bias parameters of the protohaloes
associated with our halo sample and clearly detect a non-local quadratic term
in Lagrangian space. We do not find a clear detection of non-local cubic
Lagrangian terms for low mass bins, but there is some mild evidence for their
presence for the highest mass bin. While the method presented here focuses on
cubic bias parameters, the approach could also be applied to quantifications of
cubic primordial non-Gaussianity.
