Cornering the Planck $A_{lens}$ tension with future CMB data

The precise measurements of Cosmic Microwave Background Anisotropy angular power spectra made by the Planck satellite show an anomalous value for the lensing amplitude, defined by the parameter $A_{lens}$, at more than $2$ standard deviations. In this paper, after discussing the current status of the anomaly, we quantify the potential of future CMB measurements in confirming/falsifying the $A_{lens}$ tension. We find that a space-based experiment as LiteBIRD could falsify the current $A_{lens}$ tension at the level of $5$ standard deviations. Similar constraints can be achieved by a Stage-III experiment assuming an external prior on the reionization optical depth of $\tau=0.055\pm0.010$ as already provided by the Planck satellite. A Stage-IV experiment could further test the $A_{lens}$ tension at the level of $10$ standard deviations. A comparison between temperature and polarization measurements made at different frequencies could further identify possible systematics responsible for $A_{lens}>1$. We show that, in the case of the CMB-S4 experiment, polarization data alone will have the potential of falsifying the current $A_{lens}$ anomaly at more than five standard deviation and to strongly bound its frequency dependence. We also evaluate the future constraints on a possible scale dependence for $A_{lens}$.