Relieving tensions related to the lensing of CMB temperature power
  spectra
  The angular power spectra of the cosmic microwave background (CMB)
temperature anisotropies reconstructed from Planck data seem to present too
much gravitational lensing distortion. This is quantified by the control
parameter $A_L$ that should be compatible with unity for a standard cosmology.
With the Class Boltzmann solver and the profile-likelihood method, for this
parameter we measure a 2.6$\sigma$ shift from 1 using the Planck public
likelihoods. We show that, owing to strong correlations with the reionization
optical depth $\tau$ and the primordial perturbation amplitude $A_s$, a
$\sim2\sigma$ tension on $\tau$ also appears between the results obtained with
the low ($\ell\leq 30$) and high ($30<\ell\lesssim 2500$) multipoles
likelihoods. With Hillipop, another high-$\ell$ likelihood built from Planck
data, this difference is lowered to $1.3\sigma$. In this case, the $A_L$ value
is still in disagreement with unity by $2.2\sigma$, suggesting a non-trivial
effect of the correlations between cosmological and nuisance parameters. To
better constrain the nuisance foregrounds parameters, we include the very high
$\ell$ measurements of the Atacama Cosmology Telescope (ACT) and South Pole
Telescope (SPT) experiments and obtain $A_L = 1.03 \pm 0.08$. The
Hillipop+ACT+SPT likelihood estimate of the optical depth is
$\tau=0.052\pm{0.035,}$ which is now fully compatible with the low $\ell$
likelihood determination. After showing the robustness of our results with
various combinations, we investigate the reasons for this improvement that
results from a better determination of the whole set of foregrounds parameters.
We finally provide estimates of the $\Lambda$CDM parameters with our combined
CMB data likelihood.
