Paper

{
  "raw_xml": "<entry>\n    <id>http://arxiv.org/abs/2603.02177v1</id>\n    <title>Interpreting map-based $E$/$B$ spectral properties of CMB foregrounds</title>\n    <updated>2026-03-02T18:47:46Z</updated>\n    <link href='https://arxiv.org/abs/2603.02177v1' rel='alternate' type='text/html'/>\n    <link href='https://arxiv.org/pdf/2603.02177v1' rel='related' title='pdf' type='application/pdf'/>\n    <summary>Map-space $E$/$B$ decompositions of linear polarization are attractive for foreground and CMB analyses because they isolate the $B$-family patterns that contaminate primordial tensor searches from $E$-family patterns that trace coherent Galactic structures. However, the $E$/$B$ transform is non-fully-local and induces apparent spectral complexity in projected fields even when the underlying sky is spectrally simple in $\\underline{P}=Q+iU$. We quantify this effect for synchrotron emission. We introduce a complex-parameter description of the frequency dependence of $\\underline{P}$, its spin-preserving projections $\\underline{P}_E$ and $\\underline{P}_B$, and the scalar $\\underline{S}=E+iB$, using complex log--Taylor and moment expansions (with simple transformation rules under $E$/$B$ projection) and linking their coefficients to spectral-index variations, line-of-sight mixing, synchrotron ageing, and Faraday effects. Using a toy model and a PySM template, we find that scalar combinations, especially $|E|$ and $|B|$, acquire the largest induced complexity, while $\\underline{S}$ is less affected but lacks a directly interpretable amplitude and angle. By contrast, $\\underline{P}_E$ and $\\underline{P}_B$ retain a clear geometric meaning and exhibit only moderate spectral distortions, while satisfying the closure relation $\\underline{P}=\\underline{P}_E+\\underline{P}_B$ (which extends to all spectral orders in the moment formalism). Finally, with three frequency channels, we compare low-order spectral truncations and propose diagnostics to test whether the data favour a single power law in $P$ or independent power laws in $(P_E,P_B)$. This work is intended to be of practical relevance for both Galactic science and CMB $B$-mode analyses and lays the conceptual foundation for a series of papers applying the framework to observational data.</summary>\n    <category scheme='http://arxiv.org/schemas/atom' term='astro-ph.CO'/>\n    <category scheme='http://arxiv.org/schemas/atom' term='astro-ph.GA'/>\n    <published>2026-03-02T18:47:46Z</published>\n    <arxiv:comment>22 pages, 16 figures. Submitted to MNRAS</arxiv:comment>\n    <arxiv:primary_category term='astro-ph.CO'/>\n    <author>\n      <name>Gilles Weymann-Despres</name>\n    </author>\n    <author>\n      <name>Léo Vacher</name>\n    </author>\n    <author>\n      <name>Michael E. Jones</name>\n    </author>\n    <author>\n      <name>Angela C. Taylor</name>\n    </author>\n    <author>\n      <name>Carlo Baccigalupi</name>\n    </author>\n    <author>\n      <name>A. J. Banday</name>\n    </author>\n    <author>\n      <name>Richard D. P. Grumitt</name>\n    </author>\n    <author>\n      <name>Nicoletta Krachmalnicoff</name>\n    </author>\n  </entry>"
}