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 to 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 (SZ) 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 3 larger than the iEB
polarization estimator, unless the detector noise for measuring polarization
anisotropies is controlled under 3 microK.
