  The three-point correlation function (3PCF) of the spin-2 fields, the cosmic
shear and cosmic microwave background polarization fields, is a statistical
measure of non-Gaussian signals. At each vertex of a triangle, the shear field
has two independent components. The resulting eight possible 3PCFs were
recently investigated by Schneider & Lombardi (2002) and Zaldarriaga &
Scoccimarro (2002). Using rotation and parity transformations they addressed
the question: how many non-zero components for the shear 3PCF exist? We address
this question using an analytical model and measurements from ray-tracing
simulations. We show that all the eight 3PCFs are generally non-zero and have
comparable amplitude. These eight 3PCFs can be used to improve the
signal-to-noise from survey data and their configuration dependence can be used
to separate the contribution from E and B-modes. We estimate the
signal-to-noise for measuring the shear 3PCF from weak lensing surveys using
simulated maps that include the noise due to intrinsic ellipticities. A deep
lensing survey with area exceeding 10 square degrees would allow for the
detection of the shear 3PCFs, but a survey area of order 100 square degrees is
needed for accurate measurements.
