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results.tex
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results.tex
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\chapter{Results}
\label{ch:results}
\section{Background Only Fit}
In the background only fit, only the CRs are used to constrain the fit parameters by maximizing the likelihood function assuming there are no signal events in the CRs. In this way, the SM background predictions are independent of the signal regions. The factors $\mu_{top}$ and $\mu_{\tau\tau}$, used to normalize of the combined $t$, $tW$, and $t\bar{t}$ samples and the $Z(\rightarrow\tau\tau)$+jets samples, are obtained in a simultaneous fit to data in CR-top and CR-tau. For exclusion, two simultaneous shape fits are performed across $ee$ and $\mu\mu$ channels, one in the $m_{\ell\ell}$ variable, and the other in the $m_{T2}^{100}$ variable. The normalization parameters $\mu_{top}$ and $\mu_{\tau\tau}$ for the background only fit are $\mu_{top} = 0.72\pm0.13$ and $\mu_{\tau\tau} = 1.02\pm0.09$, where the uncertainty is the combination of the statistical and systematic contributions.
Data and background prediction are shown for the diboson, same-sign, and different-flavor validation regions are shown in Figure~\ref{fig:pull_plot_summary_yields}. The accuracy of the background prediction is tested in each of the validation regions and is consistently within 1.5 standard deviations of the observed data yields. Figure~\ref{fig:postfitplots} shows distributions of the data and expected backgrounds for a selection of VRs and kinematic variables, including the $m_{\ell\ell}$ distribution in VR-VV and the $m_{T2}$ distribution in VR-SS. Similar levels of agreement are observed in other kinematic distributions for VR-SS and VR-VV. Data and background predictions are compatible within uncertainties. Figure~\ref{fig:SRpostfitplots} shows kinematic distributions of data and expected backgrounds in the inclusive Higgsino and slepton signal regions. No significant excesses above expected backgrounds are observed.
\begin{figure}
\centering
\includegraphics[width=0.9\columnwidth]{/Users/sheenaschier/Documents/LaFiles/figures/thesis/results/histpull_HiggsinoFit_doCRonly_VRs.pdf}
\caption{Summary of Monte Carlo yields in control, validation and signal regions in a background-only fit using data only in the two CRs to constrain the fit.}
\label{fig:pull_plot_summary_yields}
\end{figure}
\begin{figure}%[h!]
\begin{center}
\includegraphics[width=0.49\textwidth]{/Users/sheenaschier/Documents/LaFiles/figures/thesis/results/Higgsino_bkg_VRDF_iMT2f_VRDF_iMT2f_lep2Pt.pdf}
\includegraphics[width=0.49\textwidth]{/Users/sheenaschier/Documents/LaFiles/figures/thesis/results/Higgsino_bkg_VR_VV_VR_VV_mt2leplsp_100.pdf}
\includegraphics[width=0.49\textwidth]{/Users/sheenaschier/Documents/LaFiles/figures/thesis/results/Higgsino_bkg_VR_SS_AF_VR_SS_AF_lep2Pt.pdf}
\includegraphics[width=0.49\textwidth]{/Users/sheenaschier/Documents/LaFiles/figures/thesis/results/Higgsino_bkg_VR_SS_AF_VR_SS_AF_mll.pdf}
\end{center}
\caption{Kinematic distributions of data and expected backgrounds after the background-only fit. Top left plot shows the sub-leading lepton \pt distribution in the different-flavor validation region VRDF-$m_\text{T2}^{100}$; the top right plot shows the $m_\text{T2}^{100}$ distribution in the diboson validation region VR-VV (top right); the sub-leading lepton \pt distribution in the bottom right plot and the $m_{\ell\ell}$ distribution in the bottom left are shown in the same-sign validation region VR-SS inclusive of lepton flavor. Background processes containing fewer than two prompt leptons are categorized as `Fake/nonprompt'. The category `Others' contains rare backgrounds from triboson, Higgs boson, and multi-top processes. The last bin includes overflow.}
\label{fig:postfitplots}
\end{figure}
\begin{figure}%[tp]
\begin{center}
\includegraphics[width=0.49\textwidth]{/Users/sheenaschier/Documents/LaFiles/figures/thesis/results/Higgsino_bkg_SRSF_iMLLg_SRSF_iMLLg_METOverHTLep_METOverHTLep.pdf}
\includegraphics[width=0.49\textwidth]{/Users/sheenaschier/Documents/LaFiles/figures/thesis/results/Higgsino_bkg_SRSF_iMLLg_SRSF_iMLLg_mll.pdf}
\includegraphics[width=0.49\textwidth]{/Users/sheenaschier/Documents/LaFiles/figures/thesis/results/Higgsino_bkg_SRSF_iMT2f_SRSF_iMT2f_METOverHTLep_METOverHTLep.pdf}
\includegraphics[width=0.49\textwidth]{/Users/sheenaschier/Documents/LaFiles/figures/thesis/results/Higgsino_bkg_SRSF_iMT2f_SRSF_iMT2f_mt2leplsp_100.pdf}
\end{center}
% \caption{Kinematic distributions after the background-only fit}
\caption{Kinematic distributions after the background-only fit showing the data as well as the expected background in the most inclusive electroweakino SR$\ell\ell$-$m_{\ell\ell}$~$[1, 60]$ (top) and slepton $m_\text{T2}^{100}$~$[100, \infty]$ (bottom) signal regions. The arrow in the $\met/H_{T}^{lep}$ variables indicates the minimum value of the requirement imposed in the final SR selection. The $m_{\ell\ell}$ and $m_\text{T2}^{100}$ distributions (right) have all the SR requirements applied. Background processes containing fewer than two prompt leptons are categorized as `Fake/nonprompt'. The category `Others' contains rare backgrounds from triboson, Higgs boson, and multi-top processes. The last bin includes overflow. The dashed lines represent benchmark signal samples corresponding to the Higgsino $\widetilde{H}$ and slepton $\tilde\ell$ simplified models. Orange arrows in the Data/SM panel indicate values that are beyond the y-axis range.}
\label{fig:SRpostfitplots}
\end{figure}
\section{Model Independent Upper Limits on New Physics}
{\renewcommand{\arraystretch}{1.3}
\input{/Users/sheenaschier/Documents/LaFiles/figures/thesis/results/Merged_SimpleDiscoveryUpperLimits_unrounded.tex}
Model independent limits are useful so that, for any signal model of interest, one can evaluate the number of events predicted in a signal region and check if the model is excluded by current measurements. For this, single-binned inclusive SRs are used, since binning in the SRs requires some model-based assumptions about the distribution of the signal over these bins. Table~\ref{table.results.exclxsec.pval.upperlimit.SRSF_iMLLa} present the observed and expected event yields, the upper limits on the number of observed and expected signal events, and the visible cross-section for new physics in each of the inclusive Higgsino SR$\ell\ell$-$m_{\ell\ell}$ and slepton $m_\text{T2}^{100}$ signal regions. An upper limit on the number of observed ($S^{95}_{obs}$) and expected ($S^{95}_{exp}$) signal events in each SR at $95\%$ CL is procured in the same way as the background only fit, but now using CRs and SRs and with the observed number of events in a signal region given as inputs to the fit. The observed ($N_{\mathrm{obs}}$) and predicted ($N_{\mathrm{exp}}$) event yields are used to set the upper limits by including one inclusive signal region at a time in a simultaneous fit with the CRs. The profile-likelihood hypothesis test performed to get the upper limits uses the background estimates obtained from the background only test in the CRs and SRs, and both the expected and observed upper limits use the same background estimates.
An upper limit on the visible cross-section for new physics in a given SR, $\langle\epsilon\mathrm{\sigma}\rangle_\text{obs}^{95}$ [fb], is equal to product of the signal region acceptance, the reconstruction efficiency, and the production cross-section. The discovery p-value, p(s=0) in the right most column of the table, represents the significance of an excess of events in a signal region by considering the probability that the backgrounds in a SR are more signal-like than observed.
\section{Model Dependent Sensitivity with Shape Fit}
{\renewcommand{\arraystretch}{1.3}
\input{/Users/sheenaschier/Documents/LaFiles/figures/thesis/results/MyYieldsTable_exclSRs.tex}
Here we assume the Higgsino and slepton signals give rise to the $m_{\ell\ell}$ and $M_{T2}$ distributions in our signal regions. This consideration provides better constraining power for these models over the model independent upper limits of the 'Discovery' fit. Like in the model independent case, the fit is performed on the CRs and SRs simultaneously, but different from the model independent case, the multi-binned exclusive SRs and considered. Background and signal samples are included in both the CR and SR fits to account for any signal contamination in the CRs.
Table~\ref{tab:results:exclusiveSRYields} summarizes the observed event yields in the exclusive electroweakinio signal regions, and Table~\ref{tab:results:exclusiveSRYields2} summarizes the observed event yields in the exclusive slepton signal regions after the fit is performed using an exclusion fit configuration where the signal strength parameter is set to zero. Extending the background only fit to include the signal regions further constrains the background contributions in the absence of any signal, therefore these predicted yields differ slightly compared to those obtained with the background only fit. Figure~\ref{fig:pull_plot_summary_yields:exclSRs} demonstrates the harmony between the fitted and observed yields in these signal regions. No significant contrast between the fitted background estimates and the observed event yields are observed in any of the exclusive signal regions.
\begin{figure}
\centering
\includegraphics[width=\textwidth]{/Users/sheenaschier/Documents/LaFiles/figures/thesis/results/histpull_HiggsinoFit_doCRplusSRMLLandMT2_exclSR.pdf}
\caption{Comparison of observed and expected event yields after the
exclusion fit.
Background processes containing fewer than two prompt leptons are categorized as `Fake/nonprompt'.
The category `Others' contains rare backgrounds from triboson, Higgs boson, and multi-top processes. Uncertainties in the background estimates include
both the statistical and systematic uncertainties, where $\sigma_\text{tot}$ denotes the total uncertainty.}
\label{fig:pull_plot_summary_yields:exclSRs}
\end{figure}
\FloatBarrier