Polarization angle requirements for CMB B-mode experiments. Application
  to the LiteBIRD satellite
  A methodology to provide the polarization angle requirements for different
sets of detectors, at a given frequency of a CMB polarization experiment, is
presented. The uncertainties in the polarization angle of each detector set are
related to a given bias on the tensor-to-scalar ratio $r$ parameter. The
approach is grounded in using a linear combination of the detector sets to
obtain the CMB polarization signal. In addition, assuming that the
uncertainties on the polarization angle are in the small angle limit (lower
than a few degrees), it is possible to derive analytic expressions to establish
the requirements. The methodology also accounts for possible correlations among
detectors, that may originate from the optics, wafers, etc. The approach is
applied to the LiteBIRD space mission. We show that, for the most restrictive
case (i.e., full correlation of the polarization angle systematics among
detector sets), the requirements on the polarization angle uncertainties are of
around 1 arcmin at the most sensitive frequency bands (i.e., $\approx 150$ GHz)
and of few tens of arcmin at the lowest (i.e., $\approx 40$ GHz) and highest
(i.e., $\approx 400$ GHz) observational bands. Conversely, for the least
restrictive case (i.e., no correlation of the polarization angle systematics
among detector sets), the requirements are $\approx 5$ times less restrictive
than for the previous scenario. At the global and the telescope levels,
polarization angle knowledge of a few arcmins is sufficient for correlated
global systematic errors and can be relaxed by a factor of two for fully
uncorrelated errors in detector polarization angle. The reported uncertainty
levels are needed in order to have the bias on $r$ due to systematics below the
limit established by the LiteBIRD collaboration.
