Lensing reconstruction of cluster-mass cross correlation with cosmic microwave background polarization

We extend our maximum likelihood method for reconstructing the cluster-mass cross correlation from cosmic microwave background (CMB) temperature anisotropies and develop new estimators that utilize six different quadratic combinations of CMB temperature and polarization fields. Our maximum likelihood estimators are constructed with delensed CMB temperature and polarization fields by using an assumed model of the convergence field, and they can be iteratively applied to a set of clusters, approaching the optimal condition for the lensing reconstruction as the assumed initial model is refined. Using smoothed particle hydrodynamics simulations, we create a catalog of realistic clusters obtainable from the current Sunyaev-Zel'dovich surveys, and we demonstrate the ability of the maximum likelihood estimators to reconstruct the cluster-mass cross correlation from the massive clusters. The iTT temperature estimator provides a signal-to-noise ratio of a factor of 3 larger than the iEB polarization estimator, unless the detector noise for measuring polarization anisotropies is controlled under 3.