The reach of next-to-leading-order perturbation theory for the matter bispectrum

TL;DR

This study compares the accuracy of various perturbation theory models for the matter bispectrum against large N-body simulations, highlighting the influence of fitting procedures and systematic effects on the models' effective range.

Contribution

It provides a comprehensive comparison of next-to-leading-order perturbation theories for the matter bispectrum using extensive simulations, and analyzes the impact of fitting procedures and systematic uncertainties.

Findings

EFT models have the largest range of accuracy, but less than previously thought.

Setting three EFT counterterms to zero and fitting the fourth from the power spectrum is advantageous.

Systematic effects and fitting procedures significantly influence the estimated accuracy range.

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.