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 alpha E L and C alpha B L between the CB and the CMB polarization fields. We also provide updated CB auto-correlation spectra C alpha alpha L as well as the cross-correlation CL alpha T with the CMB temperature field. We report constraints by defining the scale-invariant amplitudes A alpha X -L(L + 1)C alpha X L /27r, where X = alpha, T, E, B, finding no evidence of CB. In particular, we find A alpha E = (-7.8 +/- 5.6) nK deg and A alpha B = (0.3 +/- 4.0) nK deg at 68% C.L..