Combining perturbation theories with halo models for the matter
  bispectrum
  We investigate how unified models should be built to be able to predict the
matter-density bispectrum (and power spectrum) from very large to small scales
and that are at the same time consistent with perturbation theory at low $k$
and with halo models at high $k$. We use a Lagrangian framework to decompose
the bispectrum into "3-halo", "2-halo", and "1-halo" contributions, related to
"perturbative" and "non-perturbative" terms. We describe a simple
implementation of this approach and present a detailed comparison with
numerical simulations. We show that the 1-halo and 2-halo contributions contain
counterterms that ensure their decay at low $k$, as required by physical
constraints, and allow a better match to simulations. Contrary to the power
spectrum, the standard 1-loop perturbation theory can be used for the
perturbative 3-halo contribution because it does not grow too fast at high $k$.
Moreover, it is much simpler and more accurate than two resummation schemes
investigated in this paper. We obtain a good agreement with numerical
simulations on both large and small scales, but the transition scales are
poorly described by the simplest implementation. This cannot be amended by
simple modifications to the halo parameters, but we show how it can be
corrected for the power spectrum and the bispectrum through a simple
interpolation scheme that is restricted to this intermediate regime. Then, we
reach an accuracy on the order of 10% on mildly and highly nonlinear scales,
while an accuracy on the order of 1% is obtained on larger weakly nonlinear
scales. This also holds for the real-space two-point correlation function.
