Development of Large-Area GEM Detectors for the Forward Muon Endcap Upgrade of the CMS Experiment and Search for SM Higgs Boson Decay in the $H\to\tau^{+}\tau^{-}\to\mu^{+}\mu^{-}\bar{\nu}_{\mu}\nu_{\mu}\bar{\nu}_{\tau}\nu_{\tau}$ Channel at $\sqrt{s}$ = 13 TeV

Gas Electron Multiplier (GEM) technology is being considered for the forward muon upgrade of the Compact Muon Solenoid (CMS) experiment in \mbox{Phase II} of the CERN LHC. The first GEM Endcap (GE1/1) is going to be installed in the $1.5 < \mid\eta\mid < 2.2$ region of the muon endcapˆ’ mainly to control muon level-1 trigger rates after the second long LHC shutdown. A GE1/1 triple-GEM detector is read out by 3,072 radial strips with 453 $\mu$rad pitch arranged in eight $\eta$-sectors. A meter-long GE1/1 prototype-III was assembled at Florida Tech and tested in 20-120 GeV hadron beams at Fermilab using Ar/CO$_{2}$ 70:30 and the RD51 Scalable Readout System (SRS). Four GEM detectors with 2-D readout and an average measured azimuthal resolution of 36$\mu$rad provided precise reference tracks. Construction of this GE1/1 prototype-III detector and its performance in the test beam are described. Strip cluster parameters, detection efficiency, and spatial resolution are studied with position and high voltage scans. The plateau detection efficiency is \mbox{[97.80 $\pm$ 0.2 (stat)]\%.} The azimuthal resolution is found to be \mbox{[123.5 $\pm$ 1.6 (stat)] $\mu$rad} when operating in the center of the efficiency plateau and using full pulse height information. The CMS upgrade design calls for readout electronics with binary hit output. When strip clusters are formed correspondingly without charge-weighting and with fixed hit thresholds, a position resolution of [136.8 $\pm$ 2.5 stat] $\mu$rad is measured, consistent with the expected resolution from strip-pitch/$\sqrt{12}$ = 131.3 $\mu$rad. The eight $\eta$-sectors of the detector show a similar response and performance. VFAT3 electronics are being considered for the readout system of GE1/1 detectors. The charge that is induced on the GE1/1 readout strips by minimum-ionizing particles is an important parameter that informs the design of the amplifier-shaper input stage of the VFAT3 chip. To estimate the input charge range for these electronics, the most probable value, mean value, and 99th percentile value of the Landau distribution of the charge induced on a single strip are measured and found to be 4 fC, 11 fC, and 115 fC, respectively. The $\textrm{Z}/\gamma^{*} \to \tau\tau$ cross section in proton-proton collisions at $\sqrt{s} = 13~\mathrm{TeV}$ is measured, using data recorded by the CMS experiment at the LHC during 2015 and corresponding to an integrated luminosity of $2.3~\mathrm{fb}^{-1}$. The product of the cross section and branching fraction is measured in the dimuon final state to be $1967 \pm 121\text{~(stat.)} \pm 92\text{~(syst.)} \pm 37\text{~(lumi.)}~\text{pb}$, in agreement with the standard model expectation, computed at next-to-next-to-leading order accuracy in perturbative quantum chromodynamics. A search for Standard Model (SM) Higgs bosons decaying into pairs of tau leptons and then to two muons plus (anti)-neutrinos is performed using the data collected by the CMS detector in 2016 with 35.9 fb$^{-1}$ of integrated luminosity. The upper limits on the cross section relative to SM prediction are calculated in three event categories with different jet multiplicities focusing on Higgs boson signal events produced via gluon-gluon fusion and vector boson fusion. A multivariate analysis with Boosted Decision Trees (BDT) is used to suppress the large Drell-Yan background. The di-tau mass is reconstructed using a Secondary-Vertex fit (SVFit) algorithm using a maximum likelihood approach. Experimental limits are presented in all three categories extracted from the maximum likelihood fit of reconstructed di-tau mass and the visible mass of the dimuon system. The signal strength for the combination of all three categories is estimated as -1.0 $\pm$ 1.7. The expected and observed upper limits with 95$\%$ CL is at 3.2 and 2.7, respectively, with respect to the SM cross section times branching fraction.