  Many theories beyond the standard model (BSM) contain new CP-odd and CP-even
neutral scalars $\phi = \{A,H\}$, and new vector-like fermions ($\psi_{VL}$).
The couplings of the CP-odd scalar $A$ to two standard model (SM) gauge bosons
cannot occur from renormalizable operators in a CP-conserving sector, but can
be induced at the quantum loop level. We compute these effective couplings at
the 1-loop level induced by the SM fermions and vector-like fermions, present
analytical expressions for them, and plot them numerically. Using the 8~TeV
Large Hadron Collider (LHC) $\gamma\gamma$, $\tau^{+} \tau^{-}$ and $t \bar t$
channel data, we derive constraints on the effective couplings of the $\phi$ to
standard model gauge bosons and fermions. We present the gluon-fusion channel
cross-sections of the $\phi$ at the 8~and~14~TeV LHC, and its branching-ratios
into SM fermion and gauge-boson pairs. We present our results first
model-independently, and then also for some simple models containing $\phi$ and
$\psi_{VL}$ in the singlet and doublet representations of $SU(2)$. In the
doublet case, we focus on the two-Higgs-doublet (2HDM) Type-II and Type-X
models in the alignment limit.
