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Light charged Higgs bosons decaying to charm and bottom quarks in models with two or more Higgs doublets

Searches for light charged Higgs bosons (H^\pm) in the decay of top quarks, t -> H^\pm b, are being carried out at the LHC and at the Tevatron. It is assumed that the dominant decay channels for such an H^\pm state are either H^\pm -> τνor H^\pm -> cs, and separate searches are performed with comparable sensitivity to the parameters m_{H^\pm} and tanbeta of the scalar potential. The branching ratio for the decay H^\pm -> cb can be as large as 80% in the Aligned Two Higgs Doublet Model and in models with three or more Higgs doublets with natural flavour conservation, while satisfying the constraint from b -> s gamma for m_{H^\pm} < m_t. Although the current search strategy for H^\pm -> cs is also sensitive to H^\pm -> cb, a considerable gain in sensitivity could be obtained by tagging the b quark from the decay H^\pm -> cb. Such an analysis, which could be readily performed at the Tevatron and in the 7 TeV and 8 TeV runs of the LHC, would probe a parameter space of the fermionic couplings of H^\pm in the above models which at present cannot be probed by experimental observables in flavour physics.