Scalar-Tensor Anti-Cross-Correlation does not Help to Reconcile the
  Tension between BICEP2 and Planck
  We examine the recent proposal [1] that the anti-cross-correlation of the
scalar and tensor primordial fluctuations reconciles the tension between BICEP2
and Planck observations. We show that unfortunately the contribution from the
scalar-tensor correlation to the CMB temperature power spectrum vanishes once
summed over the angular mode $m$ so the tension between BICEP2 and Planck can
not be reconciled. The reason is that one has to use the spin-weighted
spherical harmonics when projecting fields with nonzero spins into the CMB sky.
These nonzero spin-weighted spherical harmonics are subject to orthogonality
conditions when summed over the angular direction and thus the desired
cross-correlation between the scalar and tensor perturbations in CMB map
vanishes.
