CMB EB and TB cross-spectrum estimation via pseudo-spectrum techniques
  We discuss methods for estimating EB and TB spectra of the Cosmic Microwave
Background anisotropy maps covering limited sky area. Such odd-parity
correlations are expected to vanish whenever parity is not broken. As this is
indeed the case in the standard cosmologies, any evidence to the contrary would
have a profound impact on our theories of the early Universe. Such correlations
could also become a sensitive diagnostic of some particularly insidious
instrumental systematics. In this work we introduce three different unbiased
estimators based on the so-called standard and pure pseudo-spectrum techniques
and later assess their performance by means of extensive Monte Carlo
simulations performed for different experimental configurations. We find that a
hybrid approach combining a pure estimate of B-mode multipoles with a standard
one for E-mode (or T) multipoles, leads to the smallest error bars for both EB
(or TB respectively) spectra as well as for the three other
polarization-related angular power spectra i.e. EE, BB and TE$. However, if
both E and B multipoles are estimated using the pure technique the loss of
precision for the EB spectrum is not larger than ~30%. Moreover, for the
experimental configurations considered here, the statistical uncertainties --
due to sampling variance and instrumental noise -- of the pseudo-spectrum
estimates is at most a factor ~1.4 for TT, EE and TE spectra and a factor ~2
for BB, TB and EB spectra, higher than the most optimistic Fisher estimate of
the variance.
