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 (2002) and Zaldarriaga & Scoccimarro (2002). Using rotation and parity transformations they posed the question: how many components of the shear 3PCF are non-zero and useful? 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 Eand B-modes. This separation provides a new and precise probe of systematic errors. 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 of order 10 square degrees would allow for the detection of the shear 3PCFs; a survey with area exceeding 100 square degrees is needed for accurate measurements. Subject headings: cosmology: theory – gravitational lensing – large-scale structure of universe – cosmic microwave background