The CMB Cold Spot under the lens II: Lensing signatures in polarization and cosmic texture footprints

We forecast the detectability of the lensing footprint of a collapsing cosmic texture, a topological defect proposed as an explanation of the CMB Cold Spot. Our pipeline is a quadratic, template-amplitude estimator for localized, azimuthally symmetric lensing profiles: it projects the standard off-diagonal covariance response of lensed CMB fields onto a physically motivated template. Rather than reconstructing an arbitrary lensing field, the method targets weak but coherent localized footprints from sources such as voids, clusters and topological defects. Using the temperature/polarization pairs TT, TE+ET, EE, TB+BT and EB+BE for forthcoming Simons Observatory data, we estimate a $2.3\sigma$ detection if the texture amplitude reaches the current Planck 2018 $2\sigma$ upper limit, and a $1.5\sigma$ measurement for the best-fit texture parameters. This sensitivity is notable given the expected typical deflection angle below $6''$. The inclusion of polarization substantially increases the cumulative signal-to-noise ratio, by $\sim67\%$ relative to temperature alone, making sub-$10''$ localized lensing footprints accessible to SO-like surveys.