Map-based asymmetric beam treatment: application of real-space beam patterns in CMB data analysis

Real telescope beams are asymmetric, breaking the simple B factorisation in harmonic space and coupling modes across and m. We develop a map-domain treatment in which beam convolution is a local, scan-dependent operation applied directly to the time-ordered data (TOD), accommodating the full beam shape and giving a direct handle on intensity-to-polarisation (I to P) leakage. A noiseless validation against spherical-harmonic convolution reproduces the input temperature and B-mode power spectra up to 1000, well beyond the range of primordial B-mode science. We outline how the operation maps onto a sparse linear BeamOperator for modular map-making.