  The study of higher-order statistics, particularly three-point statistics, of
the Large Scale Structure (LSS) of the Universe provides us with unique
information on the biasing relation between luminous and dark matter and on
deviations from primordial Gaussianity. As a result, much effort has been put
into improving measurement techniques as well as theoretical modelling,
especially in Fourier space. Comparatively, little progress has been made,
instead, in configuration space analyses. This work represents a first step
towards filling this gap by proposing a new strategy for modelling 3-point
statistics at higher perturbative orders in configuration space. Starting from
the next-to-leading order model for the matter bispectrum, we use 2D- FFTLog to
generate its counterpart in configuration space. We calibrate the procedure
using the leading order predictions for which an analytic model for the
three-point correlation function (3PCF) already exists. Then we assess the
goodness of the 3PCF model by comparing its predictions with measurements
performed on the matter distribution in collisionless cosmological N-body
simulations (DEMNUni). We focus on two redshifts (z = 0.49 and z = 1.05) in the
range spanned by current and future galaxy redshift surveys. The chi-square
analysis reveals that the next-to-leading order 3PCF models significantly
improve over the leading order one for all triangle configurations in both
redshifts, increasing the number of matched configurations at redshift z = 1.05
and z = 0.49, respectively. In particular, a significant improvement is also
seen on the Baryonic Acoustic Oscillations (BAO) scale for triangle
configurations whose smallest side length is well into the nonlinear regime.
The computational cost of the model proposed here is high but not prohibitively
large and represents the first step towards a complete 3PC model for the
galaxies.
