CMB-lensing beyond the leading order: temperature and polarization
  anisotropies
  We investigate the weak lensing corrections to the CMB temperature and
polarization anisotropies. We consider all the effects beyond the leading
order: post-Born corrections, LSS corrections and, for the polarization
anisotropies, the correction due to the rotation of the polarization direction
between the emission at the source and the detection at the observer. We show
that the full next-to-leading order correction to the B-mode polarization is
not negligible on small scales and is dominated by the contribution from the
rotation, this is a new effect not taken in account in previous works.
Considering vanishing primordial gravitational waves, the B-mode correction due
to rotation is comparable to cosmic variance for $\ell \gtrsim 3500$, in
contrast to all other spectra where the corrections are always below that
threshold for a single multipole. Moreover, the sum of all the effects is
larger than cosmic variance at high multipoles, showing that higher-order
lensing corrections to B-mode polarization are in principle detectable.
