Searching for Charged Higgs Bosons via $e^+ e^- \to H^+ H^- \to c\bar{b} \bar{c}b $ at Linear Colliders

We study a search for the charged Higgs boson via $e^+e^- \to H^+H^- \to c\bar{b}\bar{c}b$ at the 500 GeV ILC. In a general two Higgs doublet model without $Z_2$ symmetry, extra Yukawa couplings $\rho_{tt}$ and $\rho_{tc}$ can drive baryogenesis, but searches at the HL-LHC may still go empty-handed if the couplings are relatively weak. Taking $m_{H^+ } \simeq m_H \simeq m_A \simeq 200$\;GeV, with $\rho_{tt}$, $\rho_{tc}\sim 0.1$ and no $h(125)$-$H$ mixing, $H^+ \to c\bar b$ decay is dominant, and the $c\bar{b}\bar{c}b$ final state is likely overwhelmed by QCD background at the LHC. We show that the electroweak production of $H^+ H^-$ at the ILC is discoverable with integrated luminosity of 1 ab$^{-1}$. Furthermore, we show that $m_{H^+}$ can be extracted by requiring the two pairs of $b$ and light jets be roughly equal in mass, without assuming the mass value. Thus, ILC can probe low mass Higgs bosons in multijet final states to complement HL-LHC in the future.