Pure-mode correlation functions for cosmic shear and application to KiDS-1000

One probe for systematic effects in gravitational lensing surveys is the presence of so-called B-modes cosmic shear two-point correlation functions \xi_\pm(\vt), since expected to produce only E-mode shear. Furthermore, there exist ambiguous modes which can not uniquely be assigned either E- or B-mode We derive explicit equations pure-mode \xi_\pm^E/B(\vt) and their components \xi_\pm^amb(\vt), that derived from measured \xi_\pm(\vt) on a finite angular interval \tmin\le\vt\le\tmax, such latter decomposed into as \xi_+=\xi_+^E+\xi_+^B+\xi_+^amb \xi_-=\xi_-^E-\xi_-^B+\xi_-^amb. The derivation obtained by defining new set COSEBIs, relations are obtained, yields smaller covariance between COSEBI modes. relation \xi_\pm^E/B/amb underlying E-/B-mode power spectra. provide diagnostics systematics configuration space. then apply our results SLICS simulations KiDS-1000 data, calculate COSEBIs functions, well corresponding covariances, show statistics fit equally best-fitting cosmological model previous analysis recovers same level (insignificant) B-modes. also consider some detail at first- second-order level, finding surprising results; example, field point mass, when cut along line through center, ascribed an thus ambiguous, resulting random ensemble masses, over range, correspond mode.