On Weak Lensing Response Functions

We introduce the response function (RFs) approach to model the weak lensing statistics in the context of separate universe formalism. Numerical results for the RFs are presented for various semi-analytical models that include perturbative modelling and variants of halo models. These results extend the recent studies of the Integrated Bispectrum (IB) and Trispectrum to arbitrary order. We find that due to the line-of-sight (los) projection effects, the expressions for RFs are not identical to the squeezed correlation functions of the same order. We compute the RFs in three-dimensions (3D) using the spherical Fourier-Bessel (sFB) formalism which provides a natural framework for incorporating photometric redshifts, and relate these expressions to tomographic and projected statistics. We generalise the concept of $k$-cut power spectrum to $k$-cut response functions. In addition to the response function for high-order spectra, we also define their counterparts in real space, since they are easier to estimate from surveys with low sky-coverage and non-trivial survey boundaries.