Search for di-Higgs production to the $b\overline{b}\tau^{+}\tau^{-}$ final state using Support Vector Machines with the ATLAS detector at the Large Hadron Collider in $pp$ collisions at $\sqrt{s}=13\textrm{TeV}$

This thesis presents a search for resonant and standard model non-resonant di-Higgs production in the $b\overline{b}\tau^{+}\tau^{-}$ decay channel, with the semi-leptonic di-tau state. The search uses data collected by the ATLAS experiment at the LHC of $pp$-collisions at $\sqrt{s}=13\textrm{TeV}$ during 2015 and 2016, corresponding to an instantaneous luminosity of $36.1\,\mathrm{fb^{-1}}$. No deviation from the Standard Model prediction is observed. For the non-resonant standard model di-Higgs production an upper limit is set on the cross-section compared to the Standard Model prediction, $\frac{\sigma}{\sigma_{\textrm{SM}}}<24.44\;@\;95\% \textrm{CL}$. Upper limits are set on the cross-section times branching ratio for the resonant searches, where the results are interpreted in terms of constraints on a 2HDM heavy scalar Higgs model and a Randall-Sundrum Kaluza-Klein graviton model. The use of Support Vector Machines is investigated and benchmarked against the nominal results of the Boosted Decision Tree multivariate analysis, in pursuit of potential future improvements.