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

## TL;DR

This paper introduces a new realization-dependent estimator for internal delensing of CMB B modes, effectively reducing biases from correlations and improving sensitivity to primordial signals.

## Contribution

It develops a general optimal estimator for higher-order correlations that corrects biases in CMB internal delensing without significantly reducing delensing efficiency.

## Key findings

- The RD estimator effectively corrects biases in CMB internal delensing.
- The method reduces sensitivity to simulation uncertainties.
- Delensing efficiency is maintained with bias correction.

## Abstract

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.