Planck constraints on cross-correlations between anisotropic cosmic birefringence and CMB polarization

Cosmic Birefringence (CB) is the in-vacuo rotation of the linear polarization direction of photons during propagation, caused by parity-violating extensions of Maxwell electromagnetism. We build low resolution CB angle maps using Planck Legacy and NPIPE products and provide for the first time estimates of the cross-correlation spectra CLαE and CLαB between the CB and the CMB polarization fields. We also provide updated CB auto-correlation spectra CLαα as well as the cross-correlation CLαT with the CMB temperature field. We report constraints by defining the scale-invariant amplitudes AαX ≡ L(L + 1)CLαX /2π, where X = α, T, E, B, finding no evidence of CB. In particular, we find AαE = (-7.8 ± 5.6) nK deg and AαB = (0.3 ± 4.0) nK deg at 68% C.L..