Statistical imprints of CMB B-type polarization leakage in an incomplete
  sky survey analysis
  One of the main goals of modern cosmology is to search for primordial
gravitational waves by looking on their imprints in the B-type polarization in
the cosmic microwave background radiation. However, this signal is contaminated
by various sources, including cosmic weak lensing, foreground radiations,
instrumental noises, as well as the E-to-B leakage caused by the partial sky
surveys, which should be well understood to avoid the misinterpretation of the
observed data. In this paper, we adopt the E/B decomposition method suggested
by Smith in 2006, and study the imprints of E-to-B leakage residuals in the
constructed B-type polarization maps, $\mathcal{B}(\hat{n})$, by employing
various statistical tools. We find that the effects of E-to-B leakage are
negligible for the $\mathcal{B}$-mode power spectrum, as well as the skewness
and kurtosis analyses of $\mathcal{B}$-maps. However, if employing the
morphological statistical tools, including Minkowski functionals and/or Betti
numbers, we find the effect of leakage can be detected at very high confidence
level, which shows that in the morphological analysis, the leakage can play a
significant role as a contaminant for measuring the primordial B-mode signal
and must be taken into account for a correct explanation of the data.
