At the Large Hadron Collider (LHC), both the ATLAS and CMS Collaborations have been searching for light charged Higgs bosons via top (anti)quark production and decays channels, like $ppto t bar{t}$ with one top (anti)quark decaying into a charged Higgs boson and a $b$ (anti)quark, when the decay is kinematically open (i.e., when $m_{H^pm}lesssim m_t$). In this paper, we propose new searches at the LHC involving light charged Higgs bosons via their pair production channels like $ppto H^pm h/A$ and $ppto H^+ H^-$ in the 2-Higgs Doublet Model (2HDM) Type-I and -X scenarios. By focusing on the case where the heavy $H$ state plays the role of the Standard Model (SM)-like Higgs boson with a mass near 125 GeV, we study the aforementioned Higgs boson pair production channels and investigate their bosonic decays, such as $H^pm to W^{pm } h$ and/or $H^pm to W^{pm } A$. We demonstrate that for a light charged Higgs boson state, with $m_{H^pm}lesssim m_t$, at the LHC, such di-Higgs production and decay channels can give rise to signatures with event rates much larger than those emerging from $ppto tbar{t}to tbar{b} H^-$ + c.c. We specifically study $h/Ato bbar b$ and $tau^+tau^-$ decays. We, therefore, claim that the discussed combination of new production and decay modes can result in an alternative discovery channel for charged Higgs bosons lighter than the top (anti)quark at the LHC within the above two 2HDM Types. Finally, in order to motivate experimentalists in ATLAS and CMS to search for such signatures, we propose 16 Benchmark Points (BPs) which are compatible with both theoretical and experimental constraints.
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