Enhancing Primordial B-mode Detection: Comprehensive Delensing Pipelines for Improved Sensitivity to $r$

Recognizing the impact of contamination from weak gravitational lensing B-modes induced by Large Scale Structure, we examine delensing methods to enhance sensitivity to the tensor-to-scalar ratio $r$ in primordial B-mode detection experiments. This study presents a realistic pipeline to improve $r$ constraints using foreground-cleaned maps with negligible residuals. The pipeline, based on simulations, is adaptable for future experiments. We focus on two delensing approaches: (1) subtracting the gradient-order lensing B-mode template, computed by convolving the E-mode with the lensing potential, from the observed B-mode signal; and (2) remapping observations using the estimated inverse deflection angle. For parameter constraints, we employ three models to reduce $r$ uncertainty and bias, finding consistent uncertainties across models, though biases vary due to the multipole-dependence of the delensing fraction. %We demonstrate the pipeline using simulated maps from future CMB polarization experiments, including a small-aperture (sub-1m) telescope, a large-aperture (6m) telescope, and a future space mission (3m). We demonstrated this pipeline using simulated observation maps from future CMB polarization experiments, which included current representative ground-based small aperture telescopes (sub-1m), next-generation ground-based large aperture telescopes (6m), and highly competitive future space-based medium aperture missions (3m). Results show a delensing efficiency of 40\% with the small-aperture telescope alone, increasing to 65\% when combined with the large-aperture telescope, and 80\% with the satellite mission. These lead to reductions in $r$ uncertainty by 46\% for ground-based and 63\% for space missions. The most promising method adds the lensing template B-mode as an additional frequency channel, minimizing bias on $r$.