  The field of cosmology is entering an epoch of unparalleled wealth of
observational data thanks to galaxy surveys such as DESI, Euclid, and Roman.
Therefore, it is essential to have a firm theoretical basis that allows the
effective analysis of the data. With this purpose, we compute the nonlinear,
gravitationally-induced connected galaxy 4-point correlation function (4PCF) at
the tree level in Standard Perturbation Theory (SPT), including redshift-space
distortions (RSD). We begin from the trispectrum and take its inverse Fourier
transform into configuration space, exploiting the isotropic basis functions of
Cahn & Slepian (2023). We ultimately reduce the configuration-space expression
to low-dimensional radial integrals of the power spectrum. This model will
enable the use of the BAO feature in the connected 4PCF to sharpen our
constraints on the expansion history of the Universe. It will also offer an
additional avenue for determining the galaxy bias parameters, and thus tighten
our cosmological constraints by breaking degeneracies. Survey geometry can be
corrected in the 4PCF, and many systematics are localized, which is an
advantage over data analysis with the trispectrum. Finally, this work is a
first step in using the parity-even 4PCF to calibrate out any possible
systematics in the parity-odd 4PCF; comparing our model to the measurement will
offer a consistency test that can serve as a "canary in the coal mine" for
systematics in the odd sector.
