Requirements for future CMB satellite missions: photometric and
  band-pass response calibration
  Current and future Cosmic Microwave Background (CMB) Radiation experiments
are targeting the polarized $B$-mode signal. The small amplitude of this signal
makes a successful measurement challenging for current technologies. Therefore,
very accurate studies to mitigate and control possible systematic effects are
vital to achieve a successful observation. An additional challenge is coming
from the presence of polarized Galactic foreground signals that contaminate the
CMB signal. When they are combined, the foreground signals dominate the
polarized CMB signal at almost every relevant frequency. Future experiments,
like the LiteBIRD space-borne mission, aim at measuring the CMB $B$-mode signal
with high accuracy to measure the tensor-to-scalar ratio $r$ at the $10^{-3}$
level. We present a method to study the photometric calibration requirement
needed to minimize the leakage of polarized Galactic foreground signals into
CMB polarization maps for a multi-frequency CMB experiment. We applied this
method to the LiteBIRD case, and we found precision requirements for the
photometric calibration in the range $\sim10^{-4}-2.5\times10^{-3}$ depending
on the frequency band. Under the assumption that the detectors are
uncorrelated, we found requirements per detector in the range
$\sim0.18\times10^{-2}-2.0\times10^{-2}$. Finally, we relate the calibration
requirements to the band-pass resolution to define constraints for a few
representative band-pass responses: $\Delta\nu\sim0.2-2$ GHz.
