  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 bpg and the squeezed 3PCF coefficient Qeff. 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 bpg and Qeff at pair separation of ~
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 bpg and
Qeff 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.
