A First Detection of the Connected 4-Point Correlation Function of
  Galaxies Using the BOSS CMASS Sample
  We present an $8.1\sigma$ detection of the non-Gaussian 4-Point Correlation
Function (4PCF) using a sample of $N_{\rm g} \approx 8\times 10^5$ galaxies
from the BOSS CMASS dataset. Our measurement uses the $\mathcal{O}(N_{\rm
g}^2)$ NPCF estimator of Philcox et al. (2021), including a new modification to
subtract the disconnected 4PCF contribution (arising from the product of two
2PCFs) at the estimator level. This approach is unlike previous work and
ensures that our signal is a robust detection of gravitationally-induced
non-Gaussianity. The estimator is validated with a suite of lognormal
simulations, and the analytic form of the disconnected contribution is
discussed. Due to the high dimensionality of the 4PCF, data compression is
required; we use a signal-to-noise-based scheme calibrated from theoretical
covariance matrices to restrict to $\sim$ $100$ basis vectors. The compression
has minimal impact on the detection significance and facilitates traditional
$\chi^2$-like analyses using a suite of mock catalogs. The significance is
stable with respect to different treatments of noise in the sample covariance
(arising from the limited number of mocks), but decreases to $4.7\sigma$ when a
minimum galaxy separation of $14 h^{-1}\mathrm{Mpc}$ is enforced on the 4PCF
tetrahedra (such that the statistic can be modelled more easily). The
detectability of the 4PCF in the quasi-linear regime implies that it will
become a useful tool in constraining cosmological and galaxy formation
parameters from upcoming spectroscopic surveys.
