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We present a new method for delensing $B$ modes of the cosmic microwavebackground (CMB) using a lensing potential reconstructed from the samerealization of the CMB polarization (CMB internal delensing). The $B$-modedelensing is required to improve sensitivity to primary $B$ modes generated by,e.g., the inflationary gravitational waves, axion-like particles, modifiedgravity, primordial magnetic fields, and topological defects such as cosmicstrings. However, the CMB internal delensing suffers from substantial biasesdue to correlations between observed CMB maps to be delensed and that used forreconstructing a lensing potential. We construct a realization-dependent (RD)estimator for correcting these biases by deriving a general optimal estimatorfor higher-order correlations. The RD estimator is less sensitive to simulationuncertainties. Compared to the previous methods, we find that the RD estimatorcorrects the biases without substantial degradation of the delensingefficiency.

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