The Three-Point Correlation Function for Spin-2 Fields

The three-point correlation function (3PCF) of the spin-2 fields, cosmic shear and microwave background polarization, 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 and Zaldarriaga & Scoccimarro. Using rotation and parity transformations, they posed the question: how many components of the shear 3PCF are nonzero and useful? We address this question using an analytical model and measurements from ray-tracing simulations. We show that all eight 3PCFs are generally nonzero and have comparable amplitude. These eight 3PCFs can be used to improve the signal-to-noise ratio from survey data, and their configuration dependence can be used to separate the contribution from E- and B-modes. This separation provides a new and precise probe of systematic errors. We estimate the signal-to-noise ratio 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 of the order of 10 deg² would allow for the detection of the shear 3PCFs; a survey with area exceeding 100 deg² is needed for accurate measurements.