Increasing the sensitivity of full-shape galaxy clustering measurements in configuration-space with three-point statistics

We investigate the cosmological constraining power of a compressed line of sight dependent three point correlation function (3PCF) estimator on small scales (<80 Mpc/h) in configuration space, with a particular focus on emission line galaxies (ELGs) targeted by the Nancy Grace Roman Space Telescope's Galaxy Redshift Survey (GRS), and complementary luminous red galaxy (LRG) samples observed by the Dark Energy Spectroscopic Instrument (DESI). These scales avoid the baryon acoustic oscillation (BAO) feature and are therefore expected to provide information that is largely complementary to standard BAO measurements, while retaining partial overlap with full shape clustering analyses. Our forecasts are based on AbacusSummit simulations at z = 1.1 and z = 0.8, populated with galaxies using halo occupation distribution (HOD) models matched to Roman ELG and DESI LRG samples respectively. The three point measurements are computed with TriCo, a fast configuration space triangle counting code developed for this analysis. After marginalizing over uncertainties in the galaxy halo connection, we find that incorporating the 3PCF yields a substantial improvement over two point statistics alone, tightening the constraint on sigma 8 by a factor of 5 in our fiducial forecast. This gain arises not from a localized feature or specific scale range, but from the cumulative information content across triangle configurations. Restricting to the monopole of the 3PCF captures only part of this information, with the full line of sight dependent measurement providing an additional factor of 2 to 3 improvement over the monopole. Adding line of sight dependent three point information substantially increases the constraining power of small scale configuration space galaxy clustering.