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.
