Integrated trispectrum detection from BOSS DR12 NGC CMASS

Abstract: We present the first detection of the integrated trispectrum ($\mathit{i}$-trispectrum) monopole and quadrupoles signal from BOSS CMASS NGC DR12. Extending the FKP estimators formalism to the Fourier transform of the four-point correlation function, we test shot-noise subtraction, Gaussianity of the i-trispectrum data-vector, significance of the detection and similarity between the signal from the data and from the galaxy mock catalogues used to numerically estimate the covariance matrix. Using scales corresponding to modes from minimum $k_\mathrm{min}=0.03\,h/\mathrm{Mpc}$ to maximum $k_\mathrm{min}=0.15\,h/\mathrm{Mpc}$, we find a detection in terms of distance from the null hypothesis of $(10.4,5.2,8.3,1.1,3.1)$ $\sigma$-intervals for the i-trispectrum monopole and quadrupoles respectively. This quantifies the presence of the physical signal of the four-points statistics on BOSS data. For completeness the same analysis is also performed for power spectrum and bispectrum, both monopoles and quadrupoles.