Search for scalar quarks in $e^{+}e^{-}$ collisions at LEP II

This thesis is devoted to searches for the scalar top and the scalar bottom quarks within the framework of the Minimal Supersymmetric Standard Model (MSSM) with the assumption of R-parity conservation. Searches for the following decay modes of the stop quark have been performed: stop -> c neutralino_1, stop -> b l sneutrino, (where l is either electron, muon or tau-lepton with equal probabilities) and stop -> b tau sneutrino (where only the tau-lepton is considered). In addition, a three body decay stop -> b W neutralino_1 has been searched for in the allowed mass region of M_stop > M_b + M_W + M_neutralino1 >= 86 GeV. For the sbottom quark the decay sbottom -> b neutralino_1 was considered. Each of these decay modes was considered independently assuming a branching ratio of 100 %. For this search, the experimental data of electron-positron collisions at center-of-mass energies (c.m.s.) in the range of 202-208 GeV have been used. These data were collected in the year 2000 by the L3 detector at the Large Electron Positron Collider (LEP) at CERN. The results of the year 2000 data analysis were also combined with results of the squark searches performed by the L3 Collaboration in previous years at center-of-mass energies from 161 up to 202 GeV. The analyzed squark decay channels determine the topology of the events of our interest: 2 jets (or b-jets) + missing energy (+ 2 leptons for stop three body decays). The stop -> b W neutralino_1 decay topology depends significantly on the further decay of the W boson and can have up to 6 jets in the final state. The assumed conservation of R-parity implies stability of the lightest supersymmetric particle (the LSP), which is the lightest neutralino. The LSP interacts only weakly and thus escapes undetected. This leads to a large missing energy as a feature of the signal events. The visible energy is roughly proportional to the difference between the masses of the squark and the LSP, and since the Standard Model background composition depends on the visible energy fraction, the whole analysis depends also on the value of this mass difference. Depending on the magnitude of visible energy, the Standard Model background can be grouped into three categories: - the two-fermion processes are e e -> e e, e e -> mu mu, e e -> tau tau and e e -> q q; - the four-fermion category is composed of e e -> W W, e e -> W e nu, e e -> Z Z and e e -> Z e e processes; - the two-photon background processes are e e -> e e e e, e e -> e e mu mu, e e -> e e tau tau and e e -> e e q q. The last process, e e -> e e q q, constitutes the largest fraction of all SM background processes (due to very high and highly fluctuating missing energy and the highest cross section). At the very first step of the analysis, only the events of interesting topology (with 2 jets and high missing energy) were preselected. Then, taking into account the small value of the theoretically predicted production cross section of the scalar quarks, the selection of stop and sbottom events was optimized by minimization of the 95 % confidence level expected upper limit on the squark cross section using calculated Monte Carlo events. In all selections optimized for each particular squark decay channel, the number of selected data events statistically agrees with the number of events expected from the Standard Model processes: - for stop -> c neutralino_1 decay, 29 data evens were observed, while 26.5 +- 2.7 were expected from the SM processes; - for the three body decay stop -> b l sneutrino, 4 data events were selected and the expectation from the Standard Model is 4.0 +- 1.0 events; - for the decay stop -> b tau sneutrino, the data and SM event numbers are 5 and 3.9 +- 1.0, respectively; - in the selection for stop -> b W neutralino_1, 184 data events were observed and 181.6 +- 3.0 were expected from the Standard Model; - for the bottom squark decay sbottom -> b neutralino_1 the observed 6 events correspond to the SM expectation of 7.7 +- 1.3. Thus, the MSSM scalar quarks were not observed in the experimental data and the search results are negative. The model independent 95 % C.L. upper limits on the squark production cross section have been derived from the numbers of the observed data events and numbers of events expected from the Standard Model. For calculation of the upper cross section limits, the results of the squark searches performed in the L3 data of c.m.s. energy 202 - 208 GeV were combined with results of searches performed by the L3 Collaboration previously in the data of c.m.s. energy from 161 up to 202 GeV. A new method has been developed for calculating such combined limits. This method takes into account the statistical independence of each measurement and the dependency of the squark production cross section on the center-of-mass energy. In this calculation, the systematic uncertainties in the Standard Model background estimation and in the signal selection efficiency have been also accounted for. For the considered squark decays, the typical obtained 95 % C.L. upper limits on the squark production cross section are: ~ 0.05-0.2 pb (for stop) and ~ 0.05-0.1 pb (for sbottom). In the searches for the stop three body decay stop -> b W neutralino_1, the cross sections above 0.7-1.0 pb have been excluded at 95 % C.L. Within the framework of MSSM with conserved R-parity, the experimental model independent cross section limits have been used for exclusion of the MSSM model parameters, in particular, exclusion of the stop and the sbottom masses. For each considered decay channel, the squark masses have been excluded in two possible scenarios: for the maximal and for the (approximately) minimal theoretical cross section. The first case corresponds to the maximal mixing between the left and right squark eigenstates, cos(theta) = 1; the second case is defined by the cos(theta) value, where squarks decouple from the Z boson. Depending on the mass difference between squark and the LSP, the squark masses have been excluded at 95 % C.L. up to the following values: - for stop -> c neutralino_1: M_stop < 90-93 GeV for minimal cross section, M_stop < 95-96 GeV for maximal cross section; - for stop -> b l sneutrino: M_stop < 87-89 GeV for minimal cross section, M_stop < 90-91 GeV for maximal cross section; - for stop -> b tau sneutrino: M_stop < 83-88 GeV for minimal cross section, M_stop < 88-91 GeV for maximal cross section; - for sbottom -> b neutralino_1: M_stop < 76-83 GeV for minimal cross section, M_stop < 94-97 GeV for maximal cross section. For both cases, the experimentally observed 95 \% C.L. mass exclusions are compared to the expected ones, which have been obtained from the Monte-Carlo assuming no SUSY particles. The observed exclusions of the squark masses are at the same level as the expected ones. The obtained 95 % C.L. upper limits on the stop production cross section in the decay stop -> b W neutralino_1 are bigger than the corresponding theoretical predictions, so, the exclusion of masses at 95 % C.L. was not possible with the available data sample. Assuming the topology of decays of the scalar quarks of the first two generations to be similar to the two body decay of the stop, the results of the searches for the decay stop -> c neutralino_1 have been also used for calculation of the mass exclusion limits for the squarks of the first two families. Two possibilities were considered here: the mass degeneracy between four (scalar u, d, c, s) and five (scalar b in addition) squarks. The 95 % C.L. exclusion limits on the mass degenerate scalar quarks for the cases of the "right-only" or "left-and-right" eigenstates are the following: - for the mass degeneration between 4 squarks: M_squark < 95-96 GeV ("right-only"), M_squark < 99-100 GeV ("left-and-right"); - for the mass degeneration between 5 squarks: M_squark < 96-97 GeV ("right-only"), M_squark < 99-101 GeV ("left-and-right"). Using the MSSM assumption about gaugino unification at the GUT scale, the limits on the four mass degenerate squarks have been reinterpreted on the squark-gluino mass plane. Moreover, the absolute limit on the MSSM parameter M_2, obtained for tan(beta) = 4 from other L3 SUSY searches (for chargino, neutralino and scalar leptons), has been translated into a gluino mass limit. The obtained 95 % C.L. exclusions in the squark-gluino mass plane are - M_gluino > 267-314 GeV, - M_squark > 99-100 GeV.