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 $C_L^{\alpha E}$ and $C_L^{\alpha B}$ between the CB and the CMB polarization fields. We also provide updated CB auto-correlation spectra $C_L^{\alpha\alpha}$ as well as the cross-correlation $C_L^{\alpha T}$ with the CMB temperature field. We report constraints by defining the scale-invariant amplitudes $A^{\alpha X} \equiv L(L + 1)C_L^{\alpha X}/2\pi$, where $X = \alpha, T, E, B$, finding no evidence of CB. In particular, we find $A^{\alpha E} = (-7.8 \pm 5.6)$ nK deg and $A^{\alpha B} = (0.3 \pm 4.0)$ nK deg at 68% C.L..