During the last decades, particle physicists have studied the tiniest building blocks of matter--the quarks and the leptons--and the forces between them in great detail. From these experiments, a theoretical framework has been built that describes the observed results with high precision. The achievement of this theory, which is referred to as the Standard Model of elementary particle physics, was the elaboration of a unified description of the strong, weak and electromagnetic forces in the framework of quantum gauge-field theories. Moreover, the Standard Model combines the weak and electromagnetic forces in a single electroweak gauge theory. The fourth force which is realized in nature, gravity, is too weak to be observable in laboratory experiments carried out in high-energy particle physics and is not part of the Standard Model. Although the Standard Model has proven highly successful in correlating a huge amount of experimental results, a key ingredient is as yet untested: the origin of electroweak symmetry breaking. Currently, the only viable ansatz that is compatible with observation is the Higgs mechanism. It predicts the existence of a scalar particle, called the Higgs boson, and the couplings to the fundamental Standard Model particles, however not its mass. An upper limit on the mass of the Higgs boson of {approx} 1 TeV can be inferred from unitarity arguments. One of the key tasks of particle physics in the next years will be to verify the existence of this particle. The introduction of an elementary scalar particle in a quantum field theory is highly problematic. The Higgs boson mass is subject to large quantum corrections, which makes it difficult to understand how its mass can be less than a TeV as required by theory. In addition, the Standard Model does not provide an answer to fundamental questions like the values of free parameters of the model, the pending integration of gravity or the evolution of the coupling constants of the fundamental forces at large energy regimes. Hence there are strong reasons to believe that the Standard Model is only a low-energy approximation to a more fundamental theory. One of the best studied candidates for an extension of the Standard Model is supersymmetry, which predicts the existence of a supersymmetric partner for each fundamental particle that differs only in spin. To allow different masses for Standard Model particles and their corresponding supersymmetric partners, supersymmetry must be broken. The mechanism behind supersymmetry breaking is currently unknown, however, various hypotheses exist. Supersymmetric models do not only solve the problem of the large quantum corrections to the Higgs boson mass, but they also allow the unification of the coupling constants at a common scale. In addition, certain supersymmetric models provide a suitable candidate for cold dark matter, which represents a large fraction of mass in our universe. Searches for supersymmetric particles have been performed by the four LEP experiments (ALEPH, DELPHI, L3, OPAL) up to the kinematic limit. Since no evidence for supersymmetric particles has been found, lower limits on their masses have been derived. The search for supersymmetry is now continuing at the Tevatron collider, located at the Fermi National Accelerator Laboratory in Batavia, Illinois. Two dedicated detector systems, CDF and D0, are installed at the Tevatron to analyze proton-antiproton collisions at a center-of-mass energy of 1.96 TeV. A particular promising discovery channel for supersymmetry within the Tevatron energy range is the trilepton channel. In this channel, the lighter supersymmetric partners of the Higgs and gauge bosons, the charginos and neutralinos, decay into final states with leptons or hadrons and missing energy. Using the leptonic final states, the signal can be separated from the large Standard Model background. Supersymmetry requires an extension of the Standard Model Higgs sector, leading to more than one neutral Higgs boson. Enhanced couplings result in sizable cross sections for Higgs boson production, and the decay into a tau pair becomes an important Higgs boson discovery channel. Within the present thesis, a search for new physics predicted by constrained supersymmetric models is performed in final states consisting of an electron and a tau using data collected with the D0 detector from April 2002 to July 2004. The first analysis searches for the associated production of the lightest chargino and the second lightest neutralino in final states with an electron, a hadronically decaying tau, an additional lepton and missing transverse energy: e + {tau}{sub h} + {ell} + E{sub T}. The second analysis searches for neutral supersymmetric Higgs bosons in the decay mode {phi} {yields} {tau}{tau} {yields} e + {tau}{sub h} + E{sub T}. To improve the sensitivity, the results are interpreted in combination with other channels.

Elementary particle physics tries to find an answer to no minor question: What is our universe made of? To our current knowledge, the elementary constituents of matter are quarks and leptons, which interact via four elementary forces: electromagnetism, strong force, weak force and gravity. All forces, except gravity, can be described in one framework, the Standard Model of particle physics. The model's name reflects its exceptional success in describing all available experimental high energy physics data to high precision up to energies of about 100 GeV. An exception is given by the neutrino masses but even these can be integrated into the model. The Standard Model is based on the requirement of invariance of all physics processes under certain fundamental symmetry transformations. The consideration of these symmetries leads naturally to the correct description of the electromagnetic, weak and strong forces as the exchange of interaction particles, the gauge bosons. However, this formalism has the weakness that it only allows for massless particles. In order to obey the symmetries, a way to introduce the particle masses is given by the Higgs mechanism, which predicts the existence of the only particle of the Standard Model which has yet to be observed: the Higgs boson. In spite of the success of the Standard Model, it has to be considered as a low energy approximation of a more profound theory for various reasons. For example, the underlying theory is expected to allow for an integration of gravity into the framework and to provide a valid particle candidate for the dark matter in our universe. Furthermore, a solution has to be found to the problem that the Higgs boson as a fundamental scalar is sensitive to large radiative corrections driving its mass to the Planck scale of 1019 GeV. Several models have been proposed to address the remaining open questions of the Standard Model. Currently, the most promising extension of the Standard Model is Supersymmetry, which provides elegant solutions to the named problems by introducing a supersymmetric partner to each Standard Model particle. The superpartners of the matter particles are called squarks and sleptons, while the superpartners of the interaction particles are called gauginos. The mass eigenstates of the gauginos are referred to as charginos and neutralinos, according to their electric charge. Since the predicted supersymmetric particles have not yet been observed, Supersymmetry, if it exists in nature, has to be broken in such a way that the masses of Standard Model particles and of their superpartners differ. During the last decades, the energies accessible to experiments has steadily increased. The Tevatron Accelerator at the Fermi National Accelerator Laboratory, with the two multipurpose experiments D0 and CDF, provides currently the highest center-of-mass energy ever reached in experiments using collisions of protons and antiprotons ((square root)s = 1.96 TeV). The study of the particle collisions allows probing of predictions of the Standard Model and its extensions, e.g. Supersymmetry.

The Higgs boson, with a measured mass of approximately $125~GeV$, has been studied extensively since its discovery in 2012 at the Large Hadron Collider. This discovery opens the question of whether the Higgs boson of the Standard Model (SM) is the only scalar particle of Nature or it belongs to a larger scalar sector, as predicted in many Beyond the Standard Model (BSM) theories. Therefore, observation of charged Higgs bosons would indicate new physics. This thesis presents results of a search for a charged Higgs boson in the mass range $80~GeV$ to $3~TeV$, through tau-lepton final states. The search is performed using proton-proton collisions data at $\sqrt{s}=13~\mbox{TeV}$, collected with the ATLAS experiment, during 2015 to 2018. The final results are interpreted in the context of the Minimal SuperSymmetric Standard Model (MSSM) benchmark scenarios. In these scenarios, charged Higgs bosons coupling to tau-lepton are enhanced for some parts of the search phase space, thus increasing the chance of their discovery. No significant excess of events above the expected background from the Standard Model processes is observed. Therefore, upper limits on the charged Higgs boson production cross section times its branching ratio to tau-lepton and its associated neutrino are set at a 95\% Confidence Level. The results are also interpreted in the context of the hMSSM and $m^{mod -}_{h}$ benchmark scenarios of the MSSM. Due to the enhancement of the charged Higgs boson coupling to tau-leptons at high values of the $\tan\beta$ parameter of the MSSM, it is possible to exclude the high $\tan\beta$ region in the $M_{H^{\pm}}$--$\tan\beta$ parameter space. In this work, $\tan\beta$ values around 60 are excluded up to a charged Higgs boson mass of $1400~\GeV$. Furthermore, in the low mass region, below $170~GeV$, all values of $\tan\beta$ in range 1--60 are excluded at 95\% confidence level.

A search for directly produced Supersymmetric Higgs Bosons has been performed in the di-tau decay channel in 86.3 {+-} 3.5 pb{sup -1} of data collected by CDF during Run1b at the Tevatron. They search for events where one tau decays to an electron and the other tau decays hadronically. They perform a counting experiment and set limits on the cross section for Higgs production in the high tan {beta} region of the m{sub A}-tan {beta} plane. For a benchmark parameter space point where m{sub A} = 100 and tan {beta} = 50, they set a 95% confidence level upper limit at 891 pb compared to the theoretically predicted cross section of 122 pb. For events where the tau candidates are not back-to-back, they utilize a di-tau mass reconstruction technique for the first time on hadron collider data. Limits based on a likelihood binned in di-tau mass from non-back-to-back events alone are weaker than the limits obtained from the counting experiment using the full di-tau sample.