Field-level constraints on cosmic birefringence from hybrid ILC maps combining $E$- and $B$-mode channels

Cosmic birefringence, arising from a potential parity-violating interaction between cosmic microwave background (CMB) photons and evolving pseudo-scalar fields such as axion-like particles, can rotate the CMB polarization plane and induce an effective correlation between the CMB $E$- and $B$-mode polarization. In this work, we introduce a hybrid internal linear combination (ILC) method that combines both $E$- and $B$-mode frequency maps into the component separation pipeline, enabling the disentanglement of correlated and uncorrelated components of CMB polarization in the presence of cosmic birefringence and instrumental polarization angle miscalibration. We derive an analytic linear relation connecting the birefringence-induced correlated component of the CMB $E$- (or $B$-) mode field to the full CMB $B$- (or $E$-) mode field convolved with a modulating field. By performing linear regression between these fields across multiple sky patches, we directly estimate the birefringence angle at the field level. This allows us to distinguish cosmic birefringence from polarization angle miscalibration and foreground contamination, as the ILC responds differently to achromatic cosmic birefringence and chromatic systematic effects, with its weights projecting spatial or harmonic dependence only onto the latter. This non-parametric, field-level approach provides a novel way to probe cosmic birefringence directly in real space. When applied to realistic simulations of the forthcoming LiteBIRD satellite mission, our method yields constraints that are competitive with, and complementary to, existing power spectrum-based analyses. When applied to Planck Release 4 (PR4) data, we find a birefringence angle of $β= 0.32^\circ \pm 0.12^\circ$, a $2.7σ$ detection that remains robust against varying sky fractions.