In this study we consider an effective model by introducing two hypothetical real scalars, $H$ and $chi$ - a dark matter candidate, where the masses of these scalars are $2 m_h < m_H < 2 m_t$ and $m_chi approx m_h/2$ with $m_h$ and $m_t$ being the Standard Model Higgs boson and top quark masses respectively. A distortion in the transverse momentum distributions of $h$ in the intermediate region of the spectrum through the processes $p p to H to hchichi$ could be observed in this model. An additional scalar, $S$, has been postulated to explain large $H to hchichi$ branching ratios, assuming $m_h lesssim m_S lesssim m_H-m_h$ and $m_S > 2 m_chi$. Furthermore, a scenario of a two Higgs doublet model (2HDM) is introduced and a detailed proposal at the present energies of the Large Hadron Collider to study the extra CP-even ($h, H$), CP-odd ($A$) and charged ($H^pm$) scalars has been pursued. With possible phenomenological implications, all possible spectra and decay modes for these scalars are discussed. Based on the mass spectrum of $H, A$ and $H^pm$, the production of multi-leptons and $Z$+jets+missing-energy events are predicted. A specific, Type-II 2HDM model is discussed in detail.
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