  The full-sky Planck polarization data at 850um revealed unexpected properties
of the E and B mode power spectra of dust emission in the interstellar medium
(ISM). The positive cross-correlation between the total dust intensity, T, with
the B modes has raised new questions about the physical mechanisms that affect
dust polarization, such as the Galactic magnetic-field structure. This is key
both to better understanding ISM dynamics and to accurately describing Galactic
foregrounds to the polarization of the Cosmic Microwave Background (CMB). In
this theoretical paper we investigate the possibility that the observed
cross-correlations in the dust polarization power spectra, and specifically
between T and B, can be related to a parity-odd quantity in the ISM such as the
magnetic helicity. We produce synthetic dust polarization data, derived from 3D
analytical toy models of density structures and helical magnetic fields, to
compare with the E and B modes of observations. Focusing on the observed T-B
correlation, we propose a new line of interpretation of the Planck observations
based on a large-scale helical component of the Galactic magnetic field in the
solar neighborhood. Our analysis shows that: I) the sign of magnetic helicity
does not affect E and B modes for isotropic magnetic-field configurations; II)
helical magnetic fields threading interstellar filaments cannot reproduce the
Planck results; III) a weak helical left-handed magnetic field structure in the
solar neighborhood may explain the T-B correlation seen in the Planck data.
This work suggests a new perspective for the interpretation of the dust
polarization power spectra, which strongly supports the imprint of a
large-scale structure of the Galactic magnetic field in the solar neighborhood.
