Search for a new heavy scalar particle decaying into a Higgs boson and a new scalar singlet in final states with one or two light leptons and a pair of $\tau$-leptons with the ATLAS detector

A search for a new heavy scalar particle $X$ decaying into a Standard Model (SM) Higgs boson and a new singlet scalar particle $S$ is presented. The search uses a proton-proton ($pp$) collision dataset with an integrated luminosity of 140 fb$^{-1}$recorded at a center-of-mass energy of $\sqrt{s} = 13$ TeV with the ATLAS detector at the Large Hadron Collider. The explored $X$ masses range from 500 to 1500 GeV with the corresponding $S$ mass varying from 200 to 500 GeV. The search selects events with two hadronically decaying $\tau$-lepton candidates from $H\to \tau^+\tau^-$ decays and one or two light leptons ($\ell=e,\,\mu$) from $S\to VV$ ($V = W,\,Z$) decays. A multivariate discriminant based on event kinematics is used to separate signal from background. No excess events were observed beyond the expected SM background and 95\% confidence level upper limits on the cross-section for $\sigma(pp\to X\to SH)$ assuming the SM-Higgs boson-like $S\to VV$ decay are derived between 72 fb and 542 fb. Upper limits on the visible cross-section for $\sigma(pp\to X\to SH \to WW\tau\tau)$ and $\sigma(pp\to X\to SH \to ZZ\tau\tau)$ are also set in the ranges 3-26 fb and 6-33 fb, respectively.