Discovery Prospects for the $Y=0$ Scalar Triplet at Future $e^+e^-$ Colliders

The Real Higgs Triplet model, known as the $\Delta$SM, is a minimal extension of the Standard Model (SM) obtained by adding a hypercharge 0 triplet ($\Delta$). This simple model is motivated by the multi-lepton anomalies and excesses in di-photon, $Z\gamma$, and $WW$ spectra at $\approx152\,\text{GeV}$. The model contains, in addition to the SM particle content, a $CP$-even neutral Higgs ($\Delta^0$) and a charged state ($\Delta^\pm$), which are quasi-degenerate in mass. Observing the charged scalar at the LHC and measuring its mass is very challenging, since it dominantly decays to $WZ$, $tb$, and $\tau\nu$. In this article, we consider the discovery prospects at future electron-positron colliders. Taking into account $e^+e^- \to \gamma^*,Z^* \to \Delta^\pm \Delta^\mp$ as the production mechanism and the dominant decay modes, we define three signal regions (SR) to study the charged Higgs properties: SR1: $\ge 3j + 1\ell$, SR2: $\ge 3\ell + \tau_{\text{had}}$, SR3: $\ge 4j + \tau_{\text{had}}$. For $m_{\Delta^\pm}\approx150\,\text{GeV}$, a $5\sigma$ significance can be achieved in SR1 with an integrated luminosity of less than $1\text{ fb}^{-1}$. SR2 is very clean with leptonic final states having low background and small systematic uncertainties. Furthermore, SR3 is crucial for reconstructing the charged scalar invariant mass, which can be measured with $\mathcal{O}(1)\,\text{GeV}$ accuracy with an integrated luminosity of $500\text{ fb}^{-1}$.