A new third-order cosmic shear statistics: Separating E/B-mode correlations on a finite interval

Decomposing the shear signal into E and B-modes properly, i.e. without leakage of B-modes into the E-mode signal and vice versa, has been a long-standing problem in weak gravitational lensing. At the two-point level this problem was resolved by developing the so-called ring statistics, and later the COSEBIs; however, extending these concepts to the three-point level is far from trivial. Currently used methods to decompose three-point shear correlation functions (3PCFs) into E- and B-modes require knowledge of the 3PCF down to arbitrary small scales. This implies that the 3PCF needs to be modeled on scales smaller than the minimum separation of 2 galaxies and subsequently will be biased towards the model, or, in the absence of a model, the statistics is affected by E/B-mode leakage (or mixing). In this paper we derive a new third-order E/B-mode statistic that performs the decomposition using the 3PCF only on a finite interval, and thereby is free of any E/B-mode leakage while at the same time relying solely on information from the data. In addition, we relate this third-order ring statistics to the convergence field, thereby enabling a fast and convenient calculation of this statistic from numerical simulations. We note that our new statistics should be applicable to corresponding E/B-mode separation problems in the CMB polarization field.