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The Born and Lens-Lens Corrections to Weak Gravitational Lensing Angular Power Spectra

We revisit the estimation of higher order corrections to the angular power spectra of weak gravitational lensing. Extending a previous calculation of Cooray and Hu, we find two additional terms to the fourth order in potential perturbations of large-scale structure corresponding to corrections associated with the Born approximation and the neglect of line-of-sight coupling of two foreground lenses in the standard first order result. These terms alter the convergence ($κκ$), the lensing shear E-mode ($εε$), and their cross-correlation ($κε$) power spectra on large angular scales, but leave the power spectra of the lensing shear B-mode ($ββ$) and rotational ($ωω$) component unchanged as compared to previous estimates. The new terms complete the calculation of corrections to weak lensing angular power spectra associated with both the Born approximation and the lens-lens coupling to an order in which the contributions are most significant. Taking these features together, we find that these corrections are unimportant for any weak lensing survey, including for a full sky survey limited by cosmic variance.