Modeling the Marked Spectrum of Matter and Biased Tracers in Real- and
  Redshift-Space
  We present the one-loop perturbation theory for the power spectrum of the
marked density field of matter and biased tracers in real- and redshift-space.
The statistic has been shown to yield impressive constraints on cosmological
parameters; to exploit this, we require an accurate and computationally
inexpensive theoretical model. Comparison with $N$-body simulations
demonstrates that linear theory fails on all scales, but inclusion of one-loop
Effective Field Theory terms gives a substantial improvement, with $\sim 5\%$
accuracy at $z = 1$. The expansion is less convergent in redshift-space
(achieving $\sim 10\%$ accuracy), but there are significant improvements for
biased tracers due to the freedom in the bias coefficients. The large-scale
theory contains non-negligible contributions from all perturbative orders; we
suggest a reorganization of the theory that contains all terms relevant on
large-scales, discussing both its explicit form at one-loop and structure at
infinite-loop. This motivates a low-$k$ correction term, leading to a model
that is sub-percent accurate on large scales, albeit with the inclusion of two
(three) free coefficients in real- (redshift-)space. We further consider the
effects of massive neutrinos, showing that beyond-EdS corrections to the
perturbative kernels are negligible in practice. It remains to see whether the
purported gains in cosmological parameters remain valid for biased tracers and
can be captured by the theoretical model.
