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Fermion mixing renormalization and gauge invariance - Gambino, P. Gauge theories of the strong and electroweak interaction - Bohm, M. Teubner p. D82 arXiv: Renormalization of the quark mixing matrix - QCD and collider physics - Ellis, R. Single top production and decay at next-to-leading order - Campbell, John M. Automatized one loop calculations in four-dimensions and D-dimensions - Hahn, T.
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Structural properties of polylogarithms. Mathematical surveys and monographs. Can the mass of the lightest Higgs boson of the minimal supersymmetric model be larger than m Z? Radiative corrections to the masses of supersymmetric higgs bosons - A Program for Higgs boson decays in the standard model and its supersymmetric extension - Djouadi, A. A Program for calculating relic density and flavor physics observables in Supersymmetry - Arbey, A.
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A program for calculating relic density and flavour physics observables: A Program for calculating flavor physics observables in Supersymmetry - Mahmoudi, F. D86 arXiv: Decays of supersymmetric particles: Dark matter, light stops and electroweak baryogenesis - Balazs, C. High energy experiments and theory - Dissertori, G. The existence of a supersymmetric dark matter candidate is related closely to R-parity. The standard paradigm for incorporating supersymmetry into a realistic theory is to have the underlying dynamics of the theory be supersymmetric, but the ground state of the theory does not respect the symmetry and supersymmetry is broken spontaneously.
The supersymmetry break can not be done permanently by the particles of the MSSM as they currently appear. This means that there is a new sector of the theory that is responsible for the breaking. The only constraint on this new sector is that it must break supersymmetry permanently and must give superparticles TeV scale masses.
There are many models that can do this and most of their details do not matter. In order to parameterize the relevant features of supersymmetry breaking, arbitrary soft SUSY breaking terms are added to the theory which temporarily break SUSY explicitly but could never arise from a complete theory of supersymmetry breaking.
One piece of evidence for supersymmetry existing is gauge coupling unification. The renormalization group evolution of the three gauge coupling constants of the Standard Model is somewhat sensitive to the present particle content of the theory. These coupling constants do not quite meet together at a common energy scale if we run the renormalization group using the Standard Model.
Supersymmetric quantum mechanics adds the SUSY superalgebra to quantum mechanics as opposed to quantum field theory. Supersymmetric quantum mechanics often becomes relevant when studying the dynamics of supersymmetric solitons , and due to the simplified nature of having fields which are only functions of time rather than space-time , a great deal of progress has been made in this subject and it is now studied in its own right.
SUSY quantum mechanics involves pairs of Hamiltonians which share a particular mathematical relationship, which are called partner Hamiltonians. The potential energy terms which occur in the Hamiltonians are then known as partner potentials. An introductory theorem shows that for every eigenstate of one Hamiltonian, its partner Hamiltonian has a corresponding eigenstate with the same energy.
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This fact can be exploited to deduce many properties of the eigenstate spectrum. It is analogous to the original description of SUSY, which referred to bosons and fermions. We can imagine a "bosonic Hamiltonian", whose eigenstates are the various bosons of our theory. The SUSY partner of this Hamiltonian would be "fermionic", and its eigenstates would be the theory's fermions. Each boson would have a fermionic partner of equal energy. Additionally, SUSY has been applied to disorder averaged systems both quantum and non-quantum through statistical mechanics , the Fokker-Planck equation being an example of a non-quantum theory.
The 'supersymmetry' in all these systems arises from the fact that one is modelling one particle and as such the 'statistics' don't matter. The use of the supersymmetry method provides a mathematical rigorous alternative to the replica trick , but only in non-interacting systems, which attempts to address the so-called 'problem of the denominator' under disorder averaging. For more on the applications of supersymmetry in condensed matter physics see the book [26].
Integrated optics was recently found [27] to provide a fertile ground on which certain ramifications of SUSY can be explored in readily-accessible laboratory settings. In this manner, a new class of functional optical structures with possible applications in phase matching , mode conversion [28] and space-division multiplexing becomes possible. SUSY transformations have been also proposed as a way to address inverse scattering problems in optics and as a one-dimensional transformation optics [29].
All stochastic partial differential equations, the models for all types of continuous time dynamical systems, possess topological supersymmetry.
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The topological sector of the so-emerging supersymmetric theory of stochastic dynamics can be recognized as the Witten-type topological field theory. The meaning of the topological supersymmetry in dynamical systems is the preservation of the phase space continuity—infinitely close points will remain close during continuous time evolution even in the presence of noise. When the topological supersymmetry is broken spontaneously, this property is violated in the limit of the infinitely long temporal evolution and the model can be said to exhibit the stochastic generalization of the butterfly effect.
From a more general perspective, spontaneous breakdown of the topological supersymmetry is the theoretical essence of the ubiquitous dynamical phenomenon variously known as chaos , turbulence , self-organized criticality etc. SUSY is also sometimes studied mathematically for its intrinsic properties. This is because it describes complex fields satisfying a property known as holomorphy , which allows holomorphic quantities to be exactly computed.
This makes supersymmetric models useful " toy models " of more realistic theories. A prime example of this has been the demonstration of S-duality in four-dimensional gauge theories [32] that interchanges particles and monopoles. The proof of the Atiyah-Singer index theorem is much simplified by the use of supersymmetric quantum mechanics. Supersymmetry is part of superstring theory , a string theory of quantum gravity , although it could in theory be a component of other quantum gravity theories as well, such as loop quantum gravity.
For superstring theory to be consistent, supersymmetry seems to be required at some level although it may be a strongly broken symmetry. If experimental evidence confirms supersymmetry in the form of supersymmetric particles such as the neutralino that is often believed to be the lightest superpartner , some people believe this would be a major boost to superstring theory. Since supersymmetry is a required component of superstring theory, any discovered supersymmetry would be consistent with superstring theory.
Supersymmetry
If the Large Hadron Collider and other major particle physics experiments fail to detect supersymmetric partners, many versions of superstring theory which had predicted certain low mass superpartners to existing particles may need to be significantly revised. Supersymmetry appears in many related contexts of theoretical physics. It is possible to have multiple supersymmetries and also have supersymmetric extra dimensions.
It is possible to have more than one kind of supersymmetry transformation.
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Theories with more than one supersymmetry transformation are known as extended supersymmetric theories. The more supersymmetry a theory has, the more constrained are the field content and interactions. Typically the number of copies of a supersymmetry is a power of 2, i.
In four dimensions, a spinor has four degrees of freedom and thus the minimal number of supersymmetry generators is four in four dimensions and having eight copies of supersymmetry means that there are 32 supersymmetry generators. The maximal number of supersymmetry generators possible is Theories with more than 32 supersymmetry generators automatically have massless fields with spin greater than 2. It is not known how to make massless fields with spin greater than two interact, so the maximal number of supersymmetry generators considered is This is due to the Weinberg-Witten theorem.
Theories with 32 supersymmetries automatically have a graviton. For four dimensions there are the following theories, with the corresponding multiplets [33] CPT adds a copy, whenever they are not invariant under such symmetry. It is possible to have supersymmetry in dimensions other than four.
Because the properties of spinors change drastically between different dimensions, each dimension has its characteristic. Since the maximum number of supersymmetries is 32 [ why? Such a generalization is possible in two or less spacetime dimensions. Supersymmetric models are constrained by a variety of experiments, including measurements of low-energy observables — for example, the anomalous magnetic moment of the muon at Fermilab ; the WMAP dark matter density measurement and direct detection experiments — for example, XENON and LUX ; and by particle collider experiments, including B-physics , Higgs phenomenology and direct searches for superpartners sparticles , at the Large Electron—Positron Collider , Tevatron and the LHC.
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