CMB lensing reconstruction using cut sky polarization maps and pure B modes

Detailed measurements of the CMB lensing signal are an important scientific goal of ongoing groundbased CMB polarization experiments, which are mapping the CMB at high resolution over small patches of the sky. In this work we simulate CMB polarization lensing reconstruction for the EE and EB quadratic estimators with current-generation noise levels and resolution, and show that without boundary effects the known and expected zeroth and first order Nð0Þ and Nð1Þ biases provide an adequate model for nonsignal contributions to the lensing power spectrum estimators. Small sky areas present a number of additional challenges for polarization lensing reconstruction, including leakage of E modes into B modes. We show how simple windowed estimators using filtered pure B modes can greatly reduce the mask-induced meanfield lensing signal and reduce variance in the estimators. This provides a simple method (used with recent observations) that gives an alternative to more optimal but expensive inverse-variance filtering.