Efficiently evaluating loop integrals in the EFTofLSS using QFT integrals with massive propagators

Abstract

We develop a new way to analytically calculate loop integrals in the Effective Field Theory of Large Scale-Structure. Previous available methods show severe limitations beyond the one-loop power spectrum due to analytical challenges and computational and memory costs. Our new method is based on fitting the linear power spectrum with cosmology-independent functions that resemble integer powers of quantum field theory massive propagators with complex masses. A remarkable small number of them is sufficient to reach enough accuracy. Similarly to former approaches, the cosmology dependence is encoded in the coordinate vector of the expansion of the linear power spectrum in our basis. We first produce cosmology-independent tensors where each entry is the loop integral evaluated on a given combination of basis vectors. For each cosmology, the evaluation of a loop integral amounts to contracting this tensor with the coordinate vector of the linear power spectrum. The 3-dimensional loop integrals for our basis functions can be evaluated using techniques familiar to particle physics, such as recursion relations and Feynman parametrization. We apply our formalism to evaluate the one-loop bispectrum of galaxies in redshift space. The final analytical expressions are quite simple and can be evaluated with little computational and memory cost. We show that the same expressions resolve the integration of all one-loop $N$-point function in the EFTofLSS. This method, which is originally presented here, has already been applied in the first one-loop bispectrum analysis of the BOSS data to constraint $\Lambda$CDM parameters and primordial non-Gaussianities, see arXiv:2206.08327 and arXiv:2201.11518.