CMB internal delensing with general optimal estimator for higher-order correlations

We present a new method for delensing $B$ modes of the cosmic microwave background (CMB) using a lensing potential reconstructed from the same realization of the CMB polarization (CMB internal delensing). The $B$-mode delensing is required to improve sensitivity to primary $B$ modes generated by, e.g., the inflationary gravitational waves, axion-like particles, modified gravity, primordial magnetic fields, and topological defects such as cosmic strings. However, the CMB internal delensing suffers from substantial biases due to correlations between observed CMB maps to be delensed and that used for reconstructing a lensing potential. We construct a realization-dependent (RD) estimator for correcting these biases by deriving a general optimal estimator for higher-order correlations. The RD estimator is less sensitive to simulation uncertainties. Compared to the previous methods, we find that the RD estimator corrects the biases without substantial degradation of the delensing efficiency.