Same-sign Charged Higgs Pair Production in bosonic decay channels at the HL-LHC and HE-LHC

Same-sign charged Higgs pair production via vector-boson scattering is a useful probe of the mass spectrum among the heavier scalar, pseudoscalar, and charged Higgs bosons in two-Higgs-doublet models. It has been shown that the production cross section scales as the square of the mass difference $\Delta m = (m_{H^0} - m_{A^0})$ in the alignment limit $(\cos(\beta - \alpha)=0)$. We study the potential measurement of this same-sign charged Higgs pair production at the high-luminosity LHC (HL-LHC) and the proposed 27 TeV $pp$ collider, with emphasis in the decay channel $H^\pm H^\pm \to (W^\pm A^0 ) (W^\pm A^0)$, which is in general the dominant mode when the charged Higgs mass is above the $W^\pm A^0$ threshold. We also examine the current allowed parameter space taking into account the theoretical constraints on the model, the electroweak precision measurements, $B$ decays, and direct searches in the $H^\pm \to \tau^\pm \nu_\tau$ and $H^\pm \to W ^\pm A^0 \to (\ell^\pm\nu_{\ell} ) (\mu \mu)$.