Search for low-mass resonances in four-muon final state and generic heavy Higgs bosons in same-sign two-lepton final state with the ATLAS detector

LHCb announced the discovery of new di-$J/\psi$ resonances around $6.9$ GeV in 2020, which can be seen as a $cc\bar{c}\bar{c}$ tetraquark. The final state of di-charmonium to four muons can significantly suppress backgrounds, which is also of great benefit to the search of new resonances and can also be used to search for rare decays of bottomonium $\eta_b$ and $\chi_{b0}$. A search for low mass resonances in the four-muon final state, using $139$ fb$^{-1}$ of $pp$ collision data at $\sqrt{s}=13~\text{TeV}$ collected by the ATLAS detector, is also performed in both di-$J/\psi$ and $J/\psi$+$\psi(2S)$ channels. Backgrounds are estimated using a data-driven method and method of control regions, and checked before opening the signal regions window by window. A peak with mass of $6.9$ GeV is observed in the first signal region in the di-$J/\psi$ channel, which is consistent with the $X(6900)$ observed by LHCb. An excess of data is also seen in the $J/\psi$+$\psi(2S)$ channel. A $95\%$ confidence level upper limit on $\sigma(pp\rightarrow\eta_b/\chi_{b0}+X)\times\text{BR}(\eta_b/\chi_{b0}\rightarrow 2J/\psi)$ is set in the second signal region. ATLAS and CMS experiment groups in LHC announced the discovery of the Higgs boson in 2012, which completes the last piece of the Standard Model (SM). The SM theoretical prediction is in good agreement with experimental results, but it's still incomplete. Thus, theorists build up various Beyond Standard Models (BSM), most of which contain at least one Higgs boson. Experimentalists have been searching for BSM heavy Higgs bosons in different final states. A search for model-independent heavy Higgs boson decaying into $W$/$Z$ bosons is performed, including both phenomenological and experimental searches. The heavy Higgs boson has both dimension-four and dimension-six interactions with SM particles. The dimension-six operators can significantly enhance the Higgs boson momentum, and therefore suppress the SM background. In the associated VH (V = $W$, $Z$) production, the effect of dimension-six operators is largest and the signal sensitivity is highest. In the phenomenological search, three signal regions with at least two leptons in final states are studied. At the $95\%$ confidence level (CL), the expected exclusion regions at three heavy Higgs boson mass points ($300$ GeV, $600$ GeV and $900$ GeV) are shown. The experimental search focuses on the final state containing two same-sign leptons ($W^\pm H\rightarrow \ell^\pm\nu\ell^\pm\nu jj$) in association with one large-R jet or two small-R jets with an invariant mass consistent with a hadronically decaying $W$ boson, using $139$ fb$^{-1}$ of $pp$ collision data at $\sqrt{s}=13~\text{TeV}$ collected by the ATLAS detector. The upper limits of $\sigma(pp\rightarrow VH) \times \text{BR}(H \rightarrow VV)$ at the $95\%$ CL are calculated as a function of the resonance mass and the upper limits on BSM $HVV$ coupling modifiers are derived.