  We study bounds from perturbative unitarity in a Composite 2-Higgs Doublet
Model (C2HDM) based on the spontaneous breakdown of a global symmetry $SO(6)\to
SO(4)\times SO(2)$ at the compositeness scale $f$. The eight pseudo
Nambu-Goldstone Bosons (pNGBs) emerging from such a dynamics are identified as
two isospin doublet Higgs fields. We calculate the $S$-wave amplitude for all
possible 2-to-2-body elastic (pseudo)scalar boson scatterings at energy scales
$\sqrt{s}$ reachable at the Large Hadron Collider (LHC) and beyond it,
including the longitudinal components of weak gauge boson states as the
corresponding pNGB states. In our calculation, the Higgs potential is assumed
to have the same form as that in the Elementary 2-Higgs Doublet Model (E2HDM)
with a discrete $Z_2$ symmetry, which is expected to be generated at the
one-loop level via the Coleman-Weinberg (CW) mechanism. We find that the
$S$-wave amplitude matrix can be block-diagonalized with maximally $2\times 2$
submatrices in a way similar to the E2HDM case as long as we only keep the
contributions from ${\cal O }(\xi s)$ and ${\cal O }(\xi^0 s^0)$ in the
amplitudes, where $\xi=v_{\text{SM}}^2/f^2$ and $v_{\text{SM}}^{}\simeq 246$
GeV, which is an appropriate approximation for our analysis. By requiring the
C2HDM to satisfy perturbative unitarity at energies reachable by the LHC, we
derive bounds on its parameters such as $\xi$ and the masses of extra Higgs
bosons present in the scenario alongside the Standard Model (SM)-like Higgs
state discovered in 2012.
