  We investigate the effect of equilateral-type primordial trispectrum on the
halo/galaxy bispectrum. We consider three types of equilateral primordial
trispectra which are generated by quartic operators naturally appeared in the
effective field theory of inflation and can be characterized by three
non-linearity parameters, $g_{\rm NL} ^{\dot{\sigma}^4}$, $g_{\rm NL}
^{\dot{\sigma}^2 (\partial \sigma)^2}$, and $g_{\rm NL} ^{(\partial
\sigma)^4}$. Recently, constraints on these parameters have been investigated
from CMB observations by using WMAP9 data. In order to consider the halo/galaxy
bispectrum with the equilateral-type primordial trispectra, we adopt the
integrated Perturbation Theory (iPT) in which the effects of primordial
non-Gaussianity are wholly encapsulated in the linear primordial polyspectrum
for the evaluation of the biased polyspectrum. We show the shapes of the
halo/galaxy bispectrum with the equilateral-type primordial trispectra, and
find that the primordial trispectrum characterized by $g_{\rm NL}
^{\dot{\sigma}^4}$ provides the same scale-dependence as the gravity-induced
halo/galaxy bispectrum. Hence, it would be difficult to obtain the constraint
on $g_{\rm NL} ^{\dot{\sigma}^4}$ from the observations of the halo/galaxy
bispectrum. On the other hand, the primordial trispectra characterized by
$g_{\rm NL} ^{\dot{\sigma}^2 (\partial \sigma)^2}$ and $g_{\rm NL} ^{(\partial
\sigma)^4}$ provide the common scale-dependence which is different from that of
the gravity-induced halo/galaxy bispectrum on large scales. Hence future
observations of halo/galaxy bispectrum would give constraints on the
non-linearity parameters, $g_{\rm NL} ^{\dot{\sigma}^2 (\partial \sigma)^2}$
and $g_{\rm NL} ^{(\partial \sigma)^4}$ independently from CMB observations and
it is expected that these constraints can be comparable to ones obtained by
CMB.
