Bounds on Supersymmetric Particles and on E_6 Fermions from Searches of Cosmological Relics and from LEP

The problem faced in this thesis is that oflooking for ways to test (and constrain) some of the most accepted extensions of the Standard Model (SM) of elementary particles. It is divided in two parts: the first two chapters deal with the supersymmetric extension of the SM while the last two with phenomenological aspects of the exotic fermions that are present in the E6 grand unified models. I have considered some implications that the new results of the LEP collider have for these theories and analysed in detail the bounds that can be obtained from searches of cosmological relics, either of the stable lightest supersymmetric particle or of stable exotic quarks, that can in principle contribute to the missing mass that is known to exist in our universe. In the first chapter, a brief sketch of how the supersymmetric SM can be obtained as the low energy limit of supergravity theories (possibly arising from superstrings) is presented, stressing why the naturalness problem associated to the fundamental Higgs scalars requires that supersymmetry should manifest at the weak scale. The bounds on the supersymmetric parameters resulting from accelerator searches and cosmological requirements is discussed. The nature of the lightest supersymmetric particle is analyzed and it is found that the most likely candidate is the neutralino, a neutral fermion combination of the superpartners of the neutral gauge bosons I and Z and of the neutral Higgs bosons. In the second chapter it is shown that for a very wide range of the parameter space the neutralinos make a significant contribution to the mass density of the universe. This makes them one of the most attractive dark matter candidates. I discuss the strategies for detecting dark matter neutralinos and concentrate on their indirect search through the observation of the neutrino flux induced by the annihilation of neutralinos trapped in the interior of the sun and of the earth underground proton decay experiments. It is shown that present experimental results already impose further constraints beyond those imposed by accelerators and that feasible improvements could allow to test a very interesting range not accessible to present colliders. Also the direct searches with Ge spectrometers is addressed. I turn then to consider the phenomenology of the new fermions that appear m models based on E6, the predilect unification group of superstrings. In these theories, each generation is assigned to a 27 representation that besides the standard fermions contains new ones: two neutral singlets, a new lepton doublet with its charge conjugate and a color triplet isosinglet quark of charge -1/3 together with its conjugate. The avoidance of terms inducing proton decay is usually obtained forbidding some dangerous couplings. This in turn can imply that the exotic quarks have no channels to decay. In the third chapter I consider the possibility of having a stable exotic quark and reject it on the light of the unsuccessful searches of anomalously heavy isotopes and on the astrophysical implications they could have. A natural way to make the exotic fermions unstable is to allow for their mixing with the ordinary ones. However, since ordinary and exotic fermions of the same colour and charge can be in different SU(2) representations, this mixing can induce deviations from the standard couplings of the ordinary fermions to the Z boson that are being measured at present at LEP. Using the results of the first run of LEP it is possible then to obtain important constrains on these mixings, as is shown in chapter 4.