Local bandpower diagnostics for the hemispherical power asymmetry in CMB E-mode polarization

We present local bandpower diagnostics that test whether a candidate dipolar modulation in E-mode polarization data originates in the cosmic microwave background (CMB) itself rather than in noise or systematics. The target is the hemispherical power asymmetry (HPA), one of the most persistent large-scale anomalies in the CMB temperature field; polarization offers an independent probe of its origin, but at Planck sensitivity the polarized sky is noise-dominated. Local power is estimated in overlapping patches on the masked sky, with E-to-B leakage corrected through standard pseudo- C deconvolution, and dipole directions are fitted independently to the two Planck half-mission maps, which share the same sky but carry independent noise. Tight directional agreement indicates a CMB-level signal, although it cannot distinguish a real modulation from a chance CMB fluctuation. Applied to Planck PR3 Commander data at = 15 - 40, the half-mission directions are separated by 8.7, a closer agreement than in any of the 300 isotropic simulations (p < 0.33%), and lie near the temperature HPA axis. The coherence appears only in EE, vanishes without leakage correction, and is corroborated by a cross-spectrum check. LiteBIRD, with substantially higher polarization sensitivity, is a natural next application.