The first measurement of the spin correlation strength in pairs of top quarks at √s=8 TeV is presented, using data collected using the ATLAS detector, corresponding to an integrated luminosity of 20.3 fb⁻¹. Dileptonically decaying tt^- events are selected with two high-pT leptons and at least two jets, one of which is required to be b-tagged. The azimuthal angle between the two charged leptons, Δφ, is used to measure the degree of spin correlation of top quark pairs. The extracted value of fSM, which is a measure of the spin-correlation strength, is fSM=1.20 ± 0.14. This is the most precise spin-correlation measurement to date. Using the Δφ distribution, a search for Supersymmetric top squarks is performed, with the assumption that the top squarks decay to a top quark and a neutralino. No excess of events is observed and top squarks with masses between the top quark mass and 191 GeV are excluded at 95% confidence level, extending previous limits.

This thesis presents measurements of the the spin correlation strength in top anti-top quark pair production at the LHC using the ATLAS detector. The data used corresponds to 4.6 fb−1 of integrated luminosity taken during 2011 at the LHC at a center of mass energy of 7 TeV. The spin correlation is studied utilising different observables with different sensitivities to the production mechanism, in particular to gluon-gluon fusion in the like or unlike helicity state, quark anti- quark annihilation in the unlike helicity state, or a combination of the three. In addition cuts are made on the invariant mass of the ttbar system to enhance or suppress contributions from different initial state production mechanisms. The analysis presented is a precision test of both ttbar production and decay in the SM. These measurements are compared to the most current theoretical predictions. No deviation from the SM expectation was observed. In a subset of the data, corresponding to an integrated luminosity of 2.1 fb−1, the hypothesis of zero spin correlation is excluded at 5.1 standard deviations.

The thesis comprises investigations of two topics related to the PANDA experiment. The first part is dedicated to energy resolution and light yield uniformity studies of PWO crystals for the electromagnetic calorimeter. The second part of the thesis is dedicated to simulation studies of the p̅p→Λ̅Λ and the p̅p→Λ̅Σ0 channels. Photon response measurements with one 3×3 crystals matrix of rectangular crystals and one 5×5 matrix with tapered crystals have been performed at the MAX-Lab synchrotron facility in Lund, Sweden. Photon energies in the range of 13-84 MeV were used. GEANT4 simulations were performed in order to find the most suitable method for adding the energy contributions and for calibration purposes. The widths, σ, of the resulting experimental summed energy peaks were fitted using the Novosibirsk distribution. The results show that the electromagnetic shower at 84 MeV is completely contained in the 5×5 matrix. The widths (σ) for the summed energy peaks were determined.Studies of the uniformity of the light yield were performed for crystals of three different shapes and different wrapping materials. The light yield as a function of distance between the point of energy depositions and the PM tube, was shown to be closely related to the crystal shape and the wrapping material. The p̅p→Λ̅Λ channel was studies at beam momenta of 1.64 GeV/c, 4 GeV/c and 15 GeV/c, while p̅p→Λ̅Σ0 was studied at 4 GeV/c. In the simulations, both phase space differential cross-sections and experimental differential cross-sections from PS185 were used as input. The purpose of the simulations was to show that the reaction channels can be reconstructed in the detector. Special interest was paid to the polarisation and spin correlations of the hyperons. The result is that there is acceptance of cosθ angular range over the full momentum range of the HESR for both channels. Using isotropic differential cross-sections, the polarisation for Λ̅ and Σ0 as well as spin correlations between Λ̅Λ and Λ̅Σ0 can be well reconstructed. Using the differential cross-sections from PS185, the particles are more likely to go forwards in their respective directions in the CM-system, thus making reconstruction over the full angular range more difficult at high beam momenta.

The prospects of studying multi-strange and charmed antihyperon-hyperon physics and CP violation in hyperon decays in the upcoming PANDA experiment at FAIR, Germany, have been studied in this thesis. The angular dependence on polarisation parameters in the decay of the spin 3/2 Omega hyperon was calculated using the density matrix formalism. Expressions for the angular distributions in the Ω -> ΛK and the subsequent Λ -> pπ decays were derived. Simulations were performed for the pbar p -> Ξ+ Ξ-, pbar p -> Ω+Ω- and pbar p -> Λc-Λc+ reactions. Special attention was given to the reconstruction of spin variables. It is shown that PANDA will register tens of events per second for the pbar p -> Ξ+Ξ- reaction. This should be compared to the previously existing data of a handfull of events. For the other two reactions the event rates will be lower, but still reasonably high. This will be the first measurements of these reactions. It is shown that spin variables can be reconstructed in all three reactions for all production angles of the hyperons. Simulations concerning the possibility to measure CP violation parameters in hyperon decays were also made for the reactions pbar p- > Λbar Λ and pbar p -> Ξ+Ξ-. It was found that false signals from detector asymmetries disappears if no particle identification criterium is used and the analysis is restricted to events were the hyperon decays occur close to the beam axis. The effect of the magnetic field in the PANDA detector on the measurement of hyperon spin variables was investigated for the case of pbar p -> Λbar Λ. The effect was observed to be small for polarisation and negligible for spin correlations.

We consider the finite two-dimensional Ising model on a lattice with periodic boundaryconditions. Kaufman determined the spectrum of the transfer matrix on the finite,periodic lattice, and her derivation was a simplification of Onsager's famous result onsolving the two-dimensional Ising model. We derive and rework Kaufman's resultsby applying representation theory, which give us a more direct approach to computethe spectrum of the transfer matrix. We determine formulas for the spin correlationfunction that depend on the matrix elements of the induced rotation associated withthe spin operator. The representation of the spin matrix elements is obtained byconsidering the spin operator as an intertwining map. We wrap the lattice aroundthe cylinder taking the semi-infinite volume limit. We control the scaling limit of themulti-spin Ising correlations on the cylinder as the temperature approaches the criticaltemperature from below in terms of a Bugrij-Lisovyy conjecture for the spin matrixelements on the finite, periodic lattice. Finally, we compute the matrix representationof the spin operator for temperatures below the critical temperature in the infinite-volume limit in the pure state defined by plus boundary conditions.

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