Detection of heavy charged Higgs bosons in $e^{+}{e}^{-}\to t\bar{b}{H}^{-}$ production at future Linear Colliders

Heavy charged Higgs bosons ($H^{\pm }$) of a Type II 2-Higgs Doublet Model (2HDM) can be detected at future electron-positron Linear Colliders (LCs) even when their mass is larger than half the collider energy. The single Higgs mode $e^+e^-\to t\bar b H^- + ~{\rm{c.c.}} \to 4b +{\rm{j}}{\rm{j}} + \ell + p_T^{\rm{miss}}$(wherejrepresentsajetandwith$\ell=e,\mu$) contributes to extend the discovery reach of $H^{\pm }$ states into the mass region $M_{H^{\pm }}\text{gsim}\sqrt{s}\mathrm{/}2$, where the well studied pair production channel $e^{+}{e}^{-}\to H^{-}{H}^{+}$ is no longer available. With a technique that allows one to reconstruct the neutrino four-momentum in the decay $t\to b W^+\to b \ell^+\nu$, one can suppress the initially overwhelming main irreducible background due to $e^{+}{e}^{-}\to t\bar{t}b\bar{b}$ (via a gluon splitting into $b\bar{b}$ pairs) to a negligible level. However, for currently foreseen luminosities, one can establish a statistically significant $H^{\pm }$ signal only over a rather limited mass region, of 20 GeV or so, beyond $M_{H^\pm}\approx \sqrt s/2$,forverylargeorverysmallvaluesof$\tan\beta$ and provided high $b$-tagging efficiency can be achieved.