On the IR-Resummation in the EFTofLSS

TL;DR

The paper tackles accurate BAO modeling within the EFTofLSS by refining IR-resummation to include next-to-leading corrections from the long-displacement three-point function. It introduces a simplified, kernel-based resummation in Lagrangian space, extendable to redshift space, and recasts the result as a real-space convolution with a Gaussian-like kernel, enabling fast 1D FFT-based computation. The key findings show that the two-loop IR-resummed power spectrum aligns with the non-linear Dark Sky spectrum up to $k \,=\,0.34\,h\text{ Mpc}^{-1}$ at $z=0$, while the additional NLO terms modify the leading-order correlation function only marginally, indicating a robust BAO peak prediction. Overall, the method offers a practical, controllable approach to higher-precision LSS analyses with improved wiggle modeling and a public code release.

Abstract

We propose a simplification for the IR-resummation scheme of Senatore and Zaldarriaga, and also include its next-to-leading order corrections coming from the tree-level three-point function of the long displacement field. First we show that the new simplified formula shares the same properties of the resummation of Senatore and Zaldarriaga. In Fourier space, the IR-resummed power spectrum has no residual wiggles and the two-loop calculation matches the non-linear power spectrum of the Dark Sky simulation at $z=0$ up to $k\simeq0.34\,h\,\text{Mpc}^{-1}$ within cosmic variance. Then, we find that the additional subleading terms (although parametrically infrared-enhanced) modify the leading-order IR-resummed correlation function only in a marginal way, implying that the IR-resummation scheme can robustly predict the shape of the BAO peak.

Figures (4)

• Figure 1: Predictions of Eulerian PT for the correlation function around the BAO peak at zero-, one- and two-loop without IR-Resummation.
• Figure 2: (a) IR-resummed correlation function at zero-, one-, two-loop (respectively blue, orange, red) with and without the cubic terms discussed in the text (solid and dashed). (b) Relative difference normalized at $r=100 \,h^{-1}\text{Mpc}$. In both cases the cutoff is $\Lambda_{\text{IR}}=0.12\,h\,\text{Mpc}^{-1}$. We see that the effect of the inclusion of the NLO is not larger than the inclusion of the higher order terms in $\delta$, as expected from the estimates done in the text. Furthermore, the convergence of the perturbative treatment is quite rapid. The code that produces these plots is available on the http://stanford.edu/ senatore/.
• Figure 3: Relative change in the resummation when the cubic term is included, using a mix setting of infrared cutoffs: $\Lambda_{\text{IR}}=0.1\,h\,\text{Mpc}^{-1}$ for the LO term, $\Lambda_{\text{IR}}=0.5\,h\,\text{Mpc}^{-1}$ for the NLO term. The code that produces this plot is available on the http://stanford.edu/ senatore/.
• Figure 4: Power spectra at zero-, one- and two-loop, before and after the IR-resummation with $\Lambda_{\text{IR}}=0.12\,h^{-1}\text{Mpc}$. The IR-resummation improves the prediction for the wiggles in the power spectrum, leaving only an error in the broad band power. Data are taken from the ds14_arun of http://darksky.slac.stanford.edu.