The T-E correlation coefficient of Planck legacy data

Testing deviations from the $Lambda$CDM model using the Cosmic Microwave Background (CMB) power spectra requires a pristine understanding of instrumental systematics. In this work we discuss the properties of a new observable ${cal R}^{TE}_{ell}$, the correlation coefficient of temperature and E modes. We find that this observable is mostly unaffected by systematics introducing multiplicative biases such as errors in calibration, polarisation efficiency, beam and transfer function measurements. We discuss the dependency of this observable on the cosmological model and derive its statistical properties. We then compute the T-E correlation coefficients of Planck legacy data and compare them with expectations from the Planck best-fit $Lambda$CDM and foreground model.