Statical properties of CMB B-mode polarisation in a partial sky analysis

Measuring the imprint of primordial gravitational waves in the cosmic microwave background (CMB) polarisation field is one of the main goals in modern cosmology. However, the so called $B$-mode polarisation can be generated by different sources besides the primary one predicted by inflationary theories, known as secondary $B$-mode signal. Among them, CMB lensing and astrophysical foregrounds play an important role. Moreover, a partial sky analysis leads to a leakage between $E$-modes and $B$-modes. In this article, we use the well known Minkowski functionals (MF) statistics to study the significance of this leakage in the CMB lensing $B$-mode signal. We find that the MF can detect the $E$-to-$B$ leakage contamination, thus it should not be neglected in future CMB data analysis.