This Thesis consists of three parts. In the first part a theory of integration is constructed for supermanifolds and supergroups. With this theory expressions for the invariant integral on several Lie supergroups are obtained including the super Poincaré group and supers pace. The unitary irreducible representations of the super Poincaré group are examined by considering the unitary irreducible representations of a certain set of Lie groups equivalent to the super Poincaré group. These irreducible representations contain, at most, particles of a single spin. In the second part a detailed examination of the massive representations of the super Poincaré algebra is undertaken. Supermultiplets of second quantized fields are constructed for each of the. massive representations, which allows an understanding of the auxiliary fields of supersymmetry theories. In the third part super Poincaré invariant superfields on superspace are constructed from the supermultiplets of the second part. This enables a connection between the representations of part one and those of part two to be established. An examination of action integrals on superspace is made enabling the relationship between the integration theory constructed in part one and the Berezin integral to be established.

On open access repositories Creative Commons Attribution License CC-BY 4.0 Published source must be acknowledged Publisher's version/PDF may be used / 京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19498号 / 理博第4158号 / 新制||理||1597(附属図書館) / 32534 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 國友 浩, 教授 田中 貴浩, 教授 杉本 茂樹 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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<p>There is very strong evidence that ordinary matter in the Universe is outweighed by almost ten times as much so-called dark matter. Dark matter does neither emit nor absorb light and we do not know what it is. One of the theoretically favoured candidates is a so-called neutralino from the supersymmetric extension of the Standard Model of particle physics.</p><p>A theoretical calculation of the expected cosmic neutralino density must include the so-called coannihilations. Coannihilations are particle processes in the early Universe with any two supersymmetric particles in the initial state and any two Standard Model particles in the final state. In this thesis we discuss the importance of these processes for the calculation of the relic density. We will go through some details in the calculation of coannihilations with one or two so-called sfermions in the initial state. This includes a discussion of Feynman diagrams with clashing arrows, a calculation of colour factors and a discussion of ghosts in non-Abelian field theory. </p><p>Supersymmetric models contain a large number of free parameters on which the masses and couplings depend. The requirement, that the predicted density of cosmic neutralinos must agree with the density observed for the unknown dark matter, will constrain the parameters. Other constraints come from experiments which are not related to cosmology. For instance, the supersymmetric loop contribution to the rare <i>b</i> -><i> sγ</i> decay should agree with the measured branching fraction. The principles of the calculation of the rare decay are discussed in this thesis. Also on-going and planned searches for cosmic neutralinos can constrain the parameters. In one of the accompanying papers in the thesis we compare the detection prospects for several current and future searches for neutralino dark matter. </p>

The switching on of the Large Hadron Collider (LHC) in March 2010 and its successful operation thereafter has opened doors in the search for new physics beyond the Standard Model. Supersymmetry (SUSY) is one of the leading theories that extends the Standard Model of particle physics. A search for new SUSY particles is presented requiring large numbers of hadronic jets and missing transverse momentum. Novel background estimation techniques were developed specifically for this final state, allowing the control of the backgrounds where the missing transverse momentum is dominated by jet miss-measurement. Other backgrounds are estimated from Monte-Carlo simulations validated and normalised in dedicated control regions. No significant excess was observed in the search. Model independent upper limits on the number of signal events passing the selection are given and the results are also interpreted in two planes of the parameter space. This is the most recent and sensitive incarnation of several searches developed by the author in this channel.

Low scale supersymmetry (SUSY) is a compelling solution to the electroweak hierarchy problem. However, increasingly strong limits on the masses of superpartners, first from LEP and now the LHC, mean that the simplest models require significant fine tuning. This thesis is dedicated to the study of a possible alternative low energy superpartner spectrum, natural SUSY, in which only superparticles directly involved in stabilising the electroweak scale are light, alleviating collider limits and potentially reducing tuning. After reviewing how low scale SUSY is motivated by the hierarchy problem, we build a model of SUSY breaking and mediation that successfully generates a natural SUSY spectrum. This also suppresses the first two generation fermion Yukawas, and leads to small parameters in the hidden sector, which are required for successful SUSY breaking. A challenge in models of natural SUSY is raising the physical Higgs mass to 125 GeV, and we study the possibility that this could occur through the addition of a singlet to the theory. If stops are very light, the coupling of the singlet to the Higgs needs to be so large that it becomes nonperturbative before the scale of grand unification, raising the concern that precision gauge coupling unification may be upset. However, we find that this is not necessarily the case. Rather it is possible this could correct for the present &bsim; 3&percnt; discrepancy in the two-loop minimal supersymmetric model's unification prediction. We then turn to the fine tuning in models of natural SUSY, emphasising that this should be measured with respect to the theory's ultraviolet (UV) parameters. We show that the first two generation sfermions can be made relatively heavy, beyond LHC reach, without introducing tuning. However, the gluino generates a significant tuning through the stops during the renormalisation group flow. As a result, there is no fine tuning benefit in reducing the stop masses below (50 - 75)&percnt; of the weak scale gluino mass, and we obtain strong lower bounds on the tuning of theories compatible with collider limits. We also study theories with Dirac gauginos, which have relatively low fine tuning even if the scale of mediation is high. Finally, we consider the effect of relaxing a common assumption and allowing the hidden SUSY breaking sector to modify the running of the visible sector soft masses. This may plausibly occur in realistic models and could dramatically reduce the fine tuning of SUSY theories.

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Supersymmetric extensions to the Standard Model (SM) have many interesting experimental consequences which can provide important hints to the physics beyond the SM. In this thesis, we first study the anomalous magnetic moment of the muon and show that a significant constraint on the parameter space can be obtained from its current experimental value. In the next topic, we study the CP violations in B -> phi K decays and show that the SM and the minimal supergravity model (mSUGRA) cannot account for the current experimental observation. We then show that all the data can be accommodated for a wide range of parameters in models with non-universal soft breaking left-right A terms. In our last topic, which is based on a Horava-Witten inspired model proposed by R. Arnowitt and B. Dutta, we extend their analysis to the full fermion sector of the SM and propose a new mechanism different from the usual see saw mechanism to generate small neutrino masses which are in good agreement with the current neutrino oscillation data.

There is very strong evidence that ordinary matter in the Universe is outweighed by almost ten times as much so-called dark matter. Dark matter does neither emit nor absorb light and we do not know what it is. One of the theoretically favoured candidates is a so-called neutralino from the supersymmetric extension of the Standard Model of particle physics. A theoretical calculation of the expected cosmic neutralino density must include the so-called coannihilations. Coannihilations are particle processes in the early Universe with any two supersymmetric particles in the initial state and any two Standard Model particles in the final state. In this thesis we discuss the importance of these processes for the calculation of the relic density. We will go through some details in the calculation of coannihilations with one or two so-called sfermions in the initial state. This includes a discussion of Feynman diagrams with clashing arrows, a calculation of colour factors and a discussion of ghosts in non-Abelian field theory. Supersymmetric models contain a large number of free parameters on which the masses and couplings depend. The requirement, that the predicted density of cosmic neutralinos must agree with the density observed for the unknown dark matter, will constrain the parameters. Other constraints come from experiments which are not related to cosmology. For instance, the supersymmetric loop contribution to the rare b -&gt; sγ decay should agree with the measured branching fraction. The principles of the calculation of the rare decay are discussed in this thesis. Also on-going and planned searches for cosmic neutralinos can constrain the parameters. In one of the accompanying papers in the thesis we compare the detection prospects for several current and future searches for neutralino dark matter.