  The large-scale matter distribution in the late-time Universe exhibits
gravity-induced non-Gaussianity, and the bispectrum, three-point cumulant is
expected to contain significant cosmological information. In particular, the
measurement of the bispectrum helps to tighten the constraints on dark energy
and modified gravity through the redshift-space distortions (RSD). In this
paper, extending the work by Taruya, Nishimichi & Saito (2010, Phys.Rev.D 82,
063522), we present a perturbation theory (PT) based model of redshift-space
matter bispectrum that can keep the non-perturbative damping effect under
control. Characterizing this non-perturbative damping by a univariate function
with single free parameter, the PT model of the redshift-space bispectrum is
tested against a large set of cosmological $N$-body simulations, finding that
the predicted monopole and quadrupole moments are in a good agreement with
simulations at the scales of baryon acoustic oscillations (well beyond the
range of agreement of standard PT). The validity of the univariate ansatz of
the damping effect is also examined, and with the PT calculation at
next-to-leading order, the fitted values of the free parameter is shown to
consistently match those obtained from the PT model of power spectrum by
Taruya, Nishimichi & Saito (2010).
