  We consider the production of two Higgs bosons in association with a gauge
boson or another Higgs boson at the hadron colliders. We compute the cross
sections and distributions for the processes $ p p \to H H H $ and $H H Z$
within the standard model. In particular, we compute the gluon-gluon fusion
one-loop contributions mediated via heavy quarks in the loop. It is the leading
order contribution to $ p p \to H H H $ process. To the process $ p p \to H H Z
$, it is next-to-next-to-leading-order (NNLO) contribution in QCD coupling. We
also compare this contribution to the next-to-leading-order (NLO) QCD
contribution to this process. The NNLO contribution can be similar to NLO
contribution at the Large Hadron Collider (LHC), and significantly more at
higher center-of-mass energy machines. We also study new physics effects in
these processes by considering $ttH, HHH, HHHH, HZZ$, and $HHZZ$ interactions
as anomalous. The anomalous couplings can enhance the cross sections
significantly. The $gg \to HHH$ process is specially sensitive to anomalous
trilinear Higgs boson self-coupling. For the $gg \to HHZ$ process, there is
some modest dependence on anomalous $HZZ$ couplings.

High Energy Physics - Phenomenology