Di-Higgs Boson Fake Lepton Study with a Signature of TwoSame Electric Charge Light Leptons Associated with a Tau

The search for di-Higgs boson production $HH$ probes the tri-linear coupling $HHH$ predicted by the Higgs mechanism. In this search with two same-sign electrically charged light leptons and one hadronically decaying tau ($2\ell$SS1$\tau$ channel), the $t\bar t$ process is the dominant source of fake (non-prompt) leptons. These fake leptons result predominantly from heavy flavour (HF) reactions, and the normalisation factors for fake electrons and fake muons are determined by a data-driven method. This study updates and extends the 2022 summer student study with the addition of an optimized computing method and full systematics. For the data-driven background determination, the Template Fit method is used. The resulting normalisation factors from HF decays are $0.87\pm 0.10$ for electrons and $0.75\pm 0.06$ for muons, including systematic uncertainties. The dominant uncertainty is statistical.