Search for a top-philic heavy resonance in association with top quarks in $pp$ collisions at $\sqrt{s}=$ 13 TeV and 13.6 TeV with the ATLAS detector

A search for a new top-philic vector boson ($Z^{\mathrm{\prime }}$) produced in association with a top-quark or a pair of top quarks, and decaying into a top quark pair is presented. The search uses $pp$ collision data collected by the ATLAS detector at the Large Hadron Collider at centre-of-mass energies of $\sqrt{s}=$ 13 TeV and 13.6 TeV, corresponding to integrated luminosities of 140 fb${}^{-1}$ and 56 fb${}^{-1}$, respectively. Events containing exactly two same-sign leptons or at least three leptons (electrons or muons) are selected. A transformer-based classifier parameterised as a function of the $Z^{\mathrm{\prime }}$ mass is used to optimise the signal-to-background discrimination. The results are interpreted in a simplified model with a colour-singlet vector boson coupled to top quarks with coupling strength $c_t$ and chirality angle $\theta$. No significant excess is observed above the expected Standard Model background. A $Z^{\mathrm{\prime }}$ boson with mass below 1150 GeV is excluded at 95% confidence level for a benchmark scenario with $c_t=1$ and $\theta =0$, with an expected limit of 1250 GeV.