Misc,
The reach of next-to-leading-order perturbation theory for the matter bispectrum
(2021)cite arxiv:2107.08054Comment: 20 pages, 13 figures.
Abstract
We provide a comparison between the matter bispectrum derived with different
flavours of perturbation theory at next-to-leading order and measurements from
an unprecedentedly large suite of $N$-body simulations. We use the $\chi^2$
goodness-of-fit test to determine the range of accuracy of the models as a
function of the volume covered by subsets of the simulations. We find that
models based on the effective-field-theory (EFT) approach have the largest
reach, standard perturbation theory has the shortest, and `classical' resummed
schemes lie in between. The gain from EFT, however, is less than in previous
studies. We show that the estimated range of accuracy of the EFT predictions is
heavily influenced by the procedure adopted to fit the amplitude of the
counterterms. For the volumes probed by galaxy redshift surveys, our results
indicate that it is advantageous to set three counterterms of the EFT
bispectrum to zero and measure the fourth from the power spectrum. We also find
that large fluctuations in the estimated reach occur between different
realisations. We conclude that it is difficult to unequivocally define a range
of accuracy for the models containing free parameters. Finally, we
approximately account for systematic effects introduced by the $N$-body
technique either in terms of a scale- and shape-dependent bias or by boosting
the statistical error bars of the measurements (as routinely done in the
literature). We find that the latter approach artificially inflates the reach
of EFT models due to the presence of tunable parameters.
