Many theories beyond the standard model (BSM) contain new CP-odd and CP-even neutral scalars $ϕ= \{A,H\}$, and new vector-like fermions ($ψ_{VL}$). 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) $γγ$, $τ^{+} τ^{-}$ and $t \bar t$ channel data, we derive constraints on the effective couplings of the $ϕ$ to standard model gauge bosons and fermions. We present the gluon-fusion channel cross-sections of the $ϕ$ 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 $ϕ$ and $ψ_{VL}$ 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.

29 pages, 31 figures; v2: both CP-even and CP-odd scalars included, sections reorganized to improve readability, tan\beta\ convention changed, new references added