We investigate the three-point correlation function ( 3PCF ) in the squeezed limit by considering galaxy pairs as discrete objects and cross-correlating them with the galaxy field .
We develop an efficient algorithm using Fast Fourier Transforms to compute such cross-correlations and their associated pair-galaxy bias b _ { p,g } and the squeezed 3PCF coefficient Q _ { eff } .
We implement our method using N-body cosmological simulations and a fiducial Halo Occupation Distribution ( HOD ) and present the results in both the real space and redshift space .
In real space , we observe a peak in b _ { p,g } and Q _ { eff } at pair separation of \sim 2 Mpc , attributed to the fact that galaxy pairs at 2 Mpc separation trace the most massive dark matter halos .
We also see strong anisotropy in the b _ { p,g } and Q _ { eff } signals that track the large-scale filamentary structure .
In redshift space , both the 2 Mpc peak and the anisotropy are significantly smeared out along the line-of-sight due to Finger-of-God effect .
In both the real space and redshift space , the squeezed 3PCF shows a factor of 2 variation , contradicting the hierarchical ansatz but offering rich information on the galaxy-halo connection .
Thus , we explore the possibility of using the squeezed 3PCF to constrain the HOD .
When we compare two simple HOD models that are closely matched in their projected two-point correlation function ( 2PCF ) , we do not yet see a strong variation in the 3PCF that is clearly disentangled from variations in the projected 2PCF .
Nevertheless , we propose that more complicated HOD models , e.g .
those incorporating assembly bias , can break degeneracies in the 2PCF and show a distinguishable squeezed 3PCF signal .