Breaking the degeneracy between polarization efficiency and cosmological
  parameters in CMB experiments
  Accurate cosmological parameter estimates using polarization data of the
cosmic microwave background (CMB) put stringent requirements on map
calibration, as highlighted in the recent results from the Planck satellite. In
this paper, we point out that a model-dependent determination of polarization
calibration can be achieved by the joint fit of the TE and EE CMB power
spectra. This provides a valuable cross-check to band-averaged polarization
efficiency measurements determined using other approaches. We demonstrate that,
in $\Lambda$CDM, the combination of the TE and EE constrain polarization
calibration with sub-percent uncertainty with Planck data and 2% uncertainty
with SPTpol data. We arrive at similar conclusions when extending $\Lambda$CDM
to include the amplitude of lensing $A_{\rm L}$, the number of relativistic
species $N_{\rm eff}$, or the sum of the neutrino masses $\sum m_{\nu}$. The
uncertainties on cosmological parameters are minimally impacted when
marginalizing over polarization calibration, except, as can be expected, for
the uncertainty on the amplitude of the primordial scalar power spectrum
$\ln(10^{10} A_{\rm s})$, which increases by $20-50$%. However, this
information can be fully recovered by adding TT data. For current and future
ground-based experiments, SPT-3G and CMB-S4, we forecast the cosmological
parameter uncertainties to be minimally degraded when marginalizing over
polarization calibration parameters. In addition, CMB-S4 could constrain its
polarization calibration at the level of $\sim$0.2% by combining TE and EE, and
reach $\sim$0.06% by also including TT. We therefore conclude that relying on
calibrating against Planck polarization maps, whose statistical uncertainty is
limited to $\sim$0.5%, would be insufficient for upcoming experiments.
