An optimal estimator for resonance bispectra in the CMB
  We propose an (optimal) estimator for a CMB bispectrum containing
logarithmically spaced oscillations. There is tremendous theoretical interest
in such bispectra, and they are predicted by a plethora of models, including
axion monodromy models of inflation and initial state modifications. The number
of resolved logarithmical oscillations in the bispectrum is limited due to the
discrete resolution of the multipole bispectrum. We derive a simple relation
between the maximum number of resolved oscillations and the frequency. We
investigate several ways to factorize the primordial bispectrum, and conclude
that a one dimensional expansion in the sum of the momenta $\sum k_i = k_t$ is
the most efficient and flexible approach. We compare the expansion to the exact
result in multipole space and show for $\omega_{\rm eff}=100$ that
$\mathcal{O}(10^3)$ modes are sufficient for an accurate reconstruction. We
compute the expected $\sigma_{f_{\rm NL}}$ and find that within an effective
field theory (EFT) the overall signal to noise scales as $S/N\propto
\omega^{3/2}$. Using only the temperature data we find
$S/N\sim\mathcal{O}(1-10^2)$ for the frequency domain set by the EFT.
