The consequences of parity symmetry for higher-order statistics of cosmic shear and other polar fields

We consider the parity transformation and the consequences of parity invariance on the $n$-point correlation function of the cosmic shear, or any other polar (or `spin-2') field. The decomposition of the shear field into E- and B-modes then yields the result that any correlation function which contains an odd number of B-mode shear components vanishes for parity-invariant random shear fields. This result is at variance with some statements in the literature, and the reasons for this is explained. We argue that the parity invariance provides a very specific diagnostic of systematic effects in shear data.