Light Non-prompt (Fake) Lepton Background Estimation with the Matrix Method for $HH$ Production with a Signature of Two Same 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 electrically charged light leptons and one hadronically decaying tau (2lSS1tau channel), the $t\bar{t}$ background is dominant and the estimation of this background by a data-driven method is studied. For the data-driven $t\bar{t}$ background determination, the Matrix Method is used with the implementation of ATLAS Isolation and Fake Forum (IFF) tools. The IFF tools are used both for the real and fake efficiency determination of light leptons, and the Matrix Method event weight determination. For the display of signal, background and data the TRexFitter package is used. The study shows that the Matrix Method is well suited for the data-driven background determination of expected $t\bar{t}$ events, and closure tests are successfully completed. They indicate the expected systematic uncertainty of the method to be below 10\%. The data-driven efficiencies are applied in the Matrix Method for a test in the control region and in the signal region.