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.
