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| {{redirect|SUSY||Susy (disambiguation)}}
| | These are just some urticaria treatments that you can try and make at home which I hope can help you. This happens because the rash that develops is very itchy, and when you itch it, it aggravates the skin even more which causes the rash to stay even longer. Fixed frame hives were usually used, this meaning that the complete hive was sunk to get the honey. They often appear for unknown reasons, on any part of the skin and can last for just hours or perhaps even days. Creams might be a genuine positive point because the skin and it is going to commence to look far better just after utilizing three to 4 days. <br><br>Locate your trapezius muscle (found between your neck and shoulder) and apply pressure to it. The Key and Values are where you will find the actual information which modifies functions. To avoid an adverse reaction, use hypoallergenic laundry detergent. Maybe a natural treatment for angioedema is the right approach for you. Once you have a hive, you will want to gather a few extra bits of equipment, like a veil, a smoker, and a bee feeder. <br><br>2) Environmental Changes - Moving into a new house, having a new pet, new bed, new carpet, new job in a new office. Dre and Snoop Dogg, to which both gentlemen nodded and spoke a few words of wisdom:. The bright light appears when fusion of hydrogen form helium, the stuff hydrogen bombs are made off. And according to NBC News it is expensive -- $1,200 to $1,600 a dose. Insertions are done every 20 minutes over the period of a few hours. <br><br>Text File: Exporting the registry or XP Windows registry key using this option creates a text file. Use your harvested items to make products to sell for more coins and enjoy all that Country Life has to offer. If you can follow all the above procedures and take care of your skin in a proper way, you can always prevent yourself from this skin problem. For ordinary juvenile warts a paste containing salicylic acid is sometimes effective. We have searched the grocery shelves for flavored water packets that do not have anything in it that we would worry about. <br><br>Note that the period of six weeks is only a guide and should not be regarded as a complete demarcation nor has been verified by medical science. One of the best benefits that Oxy - [http://www.joygoldkind.info/ Hives Relief] has to offer is the unique combination of herbs and other homeopathic remedies that attack many symptoms at the same time. It promotes blood circulation throughout the body and enhances wound healing process. You'll be able to buy that expensive upgrade when you're done. An allergist can test if you're allergic to substances or if your skin reacts to different possible allergens by conducting a skin test. <br><br>1: It's the usual "first step" in the treating of hives. There are many different types of allergies with some of the most common being: pollen, pet dander or dust. Themes are more effective when a bulletin board reflects the learning objective. Having a product like this on hand can be useful, especially if you have family or friends that visit, or little visitors whose clothing needs extra special care. It also has anti-inflammatory properties and is excellent in treating digestive problems. |
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| {{Expert-subject|Physics|talk=Attention_from_an_expert_nomination|reason=uninformative from an encyclopedic standpoint|date=December 2013}}
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| {{Beyond the Standard Model|expanded=Supersymmetry}}
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| In [[particle physics]], '''supersymmetry''' ('''SUSY''') is a proposed extension of [[Spacetime symmetries|spacetime symmetry]] that relates two basic classes of elementary particles: [[boson]]s, which have an integer-valued [[Spin (physics)|spin]], and [[fermion]]s, which have a half-integer spin.<ref name = DarkMatter>Sean Carroll, Ph.D., Cal Tech, 2007, The Teaching Company, ''Dark Matter, Dark Energy: The Dark Side of the Universe'', Guidebook Part 2 page 60, Accessed Oct. 7, 2013, "...Supersymmetry -- A hypothetical symmetry relating bosons to fermions..."</ref> Each particle from one group is associated with a particle from the other, called its [[superpartner]], whose spin differs by a half-integer. In a theory with [[broken symmetry|unbroken]] supersymmetry each pair of superpartners shares the same mass and internal quantum numbers besides spin, but since no superpartners have been observed yet, supersymmetry must be a [[spontaneously broken symmetry]]{{citation needed|date=February 2013}}. The failure of the [[Large Hadron Collider]] to find evidence for supersymmetry has led some physicists to suggest that the theory should be abandoned.<ref>{{cite journal |last=Wolchover |first=Natalie |title=Supersymmetry Fails Test, Forcing Physics to Seek New Ideas |magazine=Scientific American |date=November 29, 2012 |url=http://www.scientificamerican.com/article.cfm?id=supersymmetry-fails-test-forcing-physics-seek-new-idea}}</ref> Experiments with the Large Hadron Collider also yielded an extremely rare [[particle decay]] event which casts doubt on supersymmetry.<ref>http://www.bbc.co.uk/news/science-environment-23431797 [[BBC]]</ref> A major weakness of SUSY is that it is not falsifiable, because its breaking mechanism and the minimum mass above which it is restored are unknown. This minimum mass can be pushed upwards to arbitrarily large values, without disproving the symmetry.
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| Supersymmetry differs notably from currently known symmetries in that it establishes a symmetry between classical and quantum physics, which up to now has not been observed in any other domain. While any number of bosons can occupy the same [[quantum state]], for fermions this is not possible because of the [[exclusion principle]], which allows only one fermion in a given state. But when the occupation numbers become large, quantum physics approaches the [[classical limit]]. This means that while bosons also exist in classical physics, fermions do not. That makes it difficult to expect that bosons, if at all, possess the same [[quantum number]]s as fermions.<ref>[[Richard M. Weiner]], [[Spin-statistics-quantum number connection]] and supersymmetry, Phys. Rev. D 87 (2013) 055003-05, arXiv:1302.0969</ref>
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| There is only indirect evidence for the existence of supersymmetry, primarily in the form of evidence for [[Minimal Supersymmetric Standard Model#Gauge Coupling Unification|gauge coupling unification]].<ref name="GKane">[[Gordon L. Kane]], ''The Dawn of Physics Beyond the Standard Model'', [[Scientific American]], June 2003, page 60 and ''The frontiers of physics'', special edition, Vol 15, #3, page 8 "Indirect evidence for supersymmetry comes from the extrapolation of interactions to high energies."</ref> However this refers only to [[electroweak]] and [[strong interactions]] and does not provide the ultimate unification of all interactions, since it leaves gravitation untouched.
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| Supersymmetry is also motivated by solutions to several theoretical problems, for generally providing many desirable mathematical properties, and for ensuring sensible behavior at high energies. Supersymmetric [[quantum field theory]] is often much easier to analyze, as many more problems become exactly solvable. When supersymmetry is imposed as a ''local'' symmetry, Einstein's theory of [[general relativity]] is included automatically, and the result is said to be a theory of [[supergravity]]. It is also a feature of a candidate of a [[theory of everything]], [[superstring theory]].
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| A central motivation for supersymmetry close to the [[Electronvolt|TeV]] energy scale is the resolution of the [[hierarchy problem]] of the [[Standard Model]]. Without the extra supersymmetric particles, the [[Higgs boson]] mass is subject to quantum corrections which are so large as to naturally drive it close to the [[Planck mass]] barring its [[fine tuning]] to an extraordinarily tiny value. In the [[Minimal Supersymmetric Standard Model|supersymmetric theory]], on the other hand, these quantum corrections are canceled by those from the corresponding superpartners above the supersymmetry breaking scale, which becomes the new characteristic [[naturalness (physics)|natural]] scale for the Higgs mass. Other attractive features of TeV-scale supersymmetry are the fact that it often provides a candidate [[dark matter]] particle at a mass scale consistent with thermal relic abundance calculations,<ref>Jonathan Feng: [http://theory.fnal.gov/jetp/talks/feng.pdf Supersymmetric Dark Matter ''(pdf)''], University of California, Irvine, 11 May 2007</ref><ref>Torsten Bringmann: [http://www.desy.de/~troms/teaching/SoSe11/DM_slides_05.pdf The WIMP "Miracle" ''(pdf)''] University of Hamburg</ref> provides a natural mechanism for [[electroweak symmetry breaking]] and allows for the precise high-energy [[Grand unification theory|unification]] of the [[weak interactions|weak]], the [[strong interactions|strong]] and [[electromagnetism|electromagnetic]] interactions. Therefore, scenarios where supersymmetric partners appear with masses not much greater than 1 TeV are considered the most well-motivated by theorists.<ref>http://profmattstrassler.com/articles-and-posts/lhcposts/what-do-current-mid-august-2011-lhc-results-imply-about-supersymmetry/</ref> These scenarios would imply that experimental traces of the superpartners should begin to emerge in high-energy collisions at the [[LHC]] relatively soon. As of September 2011, no meaningful signs of the superpartners have been observed,<ref name="ATLAS SUSY search documents">[https://twiki.cern.ch/twiki/bin/view/AtlasPublic/SupersymmetryPublicResults#Early_2011_Data_5_CONF_Notes ATLAS SUSY search documents]</ref><ref name="CMS SUSY search documents">[https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsSUS CMS SUSY search documents]</ref> which is beginning to significantly constrain the most popular incarnations of supersymmetry. However, the total parameter space of consistent supersymmetric extensions of the Standard Model is extremely diverse and can not be definitively ruled out at the LHC.
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| Another theoretically appealing property of supersymmetry is that it offers the only "loophole" to the [[Coleman–Mandula theorem]], which prohibits spacetime and internal [[Symmetry (physics)|symmetries]] from being combined in any nontrivial way, for [[quantum field theory|quantum field theories]] like the Standard Model under very general assumptions. The [[Haag-Lopuszanski-Sohnius theorem]] demonstrates that supersymmetry is the only way spacetime and internal symmetries can be consistently combined.<ref>R. Haag, J. T. Lopuszanski and M. Sohnius, "[http://www.sciencedirect.com/science/article/B6TVC-4718W97-YF/1/bc160d55fb6a0faddac181fcff6871ce All Possible Generators Of Supersymmetries Of The S Matrix]", Nucl. Phys. B 88 (1975) 257</ref>
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| The [[Minimal Supersymmetric Standard Model]] is one of the best studied candidates for [[physics beyond the Standard Model]].
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| == History ==
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| A supersymmetry relating [[mesons]] and [[baryons]] was first proposed, in the context of hadronic physics, by [[Hironari Miyazawa]] in 1966. This supersymmetry did not involve spacetime, that is it concerned internal symmetry, and was badly broken. His work was largely ignored at the time.<ref>{{Cite journal
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| |author=H. Miyazawa
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| |year=1966
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| |title=Baryon Number Changing Currents
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| |journal=Prog. Theor. Phys.
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| |volume=36
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| |pages=1266–1276
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| |doi=10.1143/PTP.36.1266
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| |issue=6
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| |bibcode = 1966PThPh..36.1266M }}</ref><ref>{{Cite journal
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| |author=H. Miyazawa
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| |year=1968
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| |title=Spinor Currents and Symmetries of Baryons and Mesons
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| |journal=Phys. Rev.
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| |volume=170
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| |issue=5
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| |pages=1586–1590
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| |doi=10.1103/PhysRev.170.1586
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| |bibcode = 1968PhRv..170.1586M }}</ref><ref>[[Michio Kaku]], ''Quantum Field Theory'', ISBN 0-19-509158-2, pg 663.</ref><ref>[[Peter Freund]], ''Introduction to Supersymmetry'', ISBN 0-521-35675-X, pages 26-27, 138.</ref>
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| J. L. Gervais and [[Bunji Sakita|B. Sakita]] (in 1971),<ref>{{cite doi|10.1016/0550-3213(71)90351-8|noedit}}</ref> [[Yuri Golfand|Yu. A. Golfand]] and [[Evgeny Likhtman|E. P. Likhtman]] (also in 1971), and D.V. Volkov and V.P. Akulov (in 1972),<ref>D.V. Volkov, V.P. Akulov, Pisma Zh.Eksp.Teor.Fiz. 16 (1972) 621; Phys.Lett. B46 (1973) 109; V.P. Akulov, D.V. Volkov, Teor.Mat.Fiz. 18 (1974) 39</ref> independently rediscovered supersymmetry in the context of quantum field theory, a radically new type of symmetry of spacetime and fundamental fields, which establishes a relationship between elementary particles of different quantum nature, bosons and fermions, and unifies spacetime and internal symmetries of the microscopic world. Supersymmetry with a consistent Lie-algebraic graded structure on which the Gervais−Sakita rediscovery was based directly first arose in 1971<ref>{{cite doi|10.1103/PhysRevD.3.2415|noedit}}</ref> in the context of an early version of [[string theory]] by [[Pierre Ramond]], [[John H. Schwarz]] and [[André Neveu]].
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| Finally, [[Julius Wess|J. Wess]] and [[Bruno Zumino|B. Zumino]] (in 1974)<ref>{{cite doi|10.1016/0550-3213(74)90355-1|noedit}}</ref> identified the characteristic renormalization features of four dimensional supersymmetric field theories, which singled them out as remarkable QFTs, and they and [[Abdus Salam]] and their fellow researchers introduced early particle physics applications. The mathematical structure of supersymmetry ([[Graded Lie superalgebra]]s) has subsequently been applied successfully to other areas of physics, in a variety of fields, ranging from [[nuclear physics]],<ref>{{cite doi|10.1103/PhysRevLett.44.772|noedit}}</ref> [[critical phenomena]],<ref>{{cite doi|10.1103/PhysRevLett.52.1575|noedit}}</ref> [[quantum mechanics]] to [[statistical mechanics|statistical physics]]. It remains a vital part of many proposed theories of physics.
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| The first realistic supersymmetric version of the Standard Model was proposed in 1981 by [[Howard Georgi]] and [[Savas Dimopoulos]] and is called the [[Minimal Supersymmetric Standard Model]] or MSSM for short. It was proposed to solve the [[hierarchy problem]] and predicts superpartners with masses between 100 GeV and 1 TeV.
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| As of September 2011, no meaningful signs of the superpartners have been observed.<ref name="ATLAS SUSY search documents"/><ref name="CMS SUSY search documents"/> The [[Large Hadron Collider]] at [[CERN]] is producing the world's highest energy collisions and offers the best chance at discovering superparticles for the foreseeable future.
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| After the discovery of the [[Higgs particle]] in 2012, it was expected that supersymmetric particles would be found at CERN, but there has been still no evidence of them. The LHCb and CMS experiments at the LHC made the first definitive observation of a [[Strange B meson]] decaying into two muons, confirming a standard model prediction, but a blow for those hoping for signs of supersymmetry.<ref>[http://phys.org/news/2013-07-cern-latest-supersymmetry.html CERN latest data shows no sign of supersymmetry – yet] Phys.Org, 25 July 2013</ref> [[Neil Turok]] at [[Perimeter Institute]] concedes that theorists are disheartened at that situation, and that they are at a crossroad in theoretical (and particle) physics, calling it a deep crisis. He described the LHC results as "simple, yet extremely puzzling" and said "we have to get people to try to find the new principles that will explain the simplicity".<ref>[http://www2.macleans.ca/2013/09/05/perimeter-institute-and-the-crisis-in-modern-physics/ Perimeter Institute and the crisis in modern physics] Paul Wells, 5 Sep 2013</ref>
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| == Applications ==
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| === Extension of possible symmetry groups ===
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| One reason that physicists explored supersymmetry is because it offers an extension to the more familiar symmetries of quantum field theory. These symmetries are grouped into the [[Poincaré group]] and internal symmetries and the [[Coleman–Mandula theorem]] showed that under certain assumptions, the symmetries of the [[S-matrix]] must be a direct product of the Poincaré group with a [[Compact space|compact]] internal symmetry group or if there is no [[mass gap]], the [[conformal group]] with a compact internal symmetry group.
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| In 1971 Golfand and Likhtman were the first to show that the Poincaré algebra can be extended through introduction of four
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| anticommuting spinor generators (in four dimensions), which later became known as supercharges.
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| In 1975 the [[Haag-Lopuszanski-Sohnius theorem]]
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| analyzed all possible superalgebras in the general form, including those with an extended number of the supergenerators and [[central charge]]s.
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| This extended super-Poincaré algebra paved the way for obtaining a very large and important class of supersymmetric field theories.
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| ==== The supersymmetry algebra ====
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| {{Main|Supersymmetry algebra}}
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| Traditional symmetries in physics are generated by objects that transform under the [[tensor]] [[representations of Lie groups|representations]] of the [[Poincaré group]] and internal symmetries. Supersymmetries, on the other hand, are generated by objects that transform under the [[spinor]] representations. According to the [[spin-statistics theorem]], [[boson]]ic fields [[commutative operation|commute]] while [[fermion]]ic fields [[anticommutativity|anticommute]]. Combining the two kinds of fields into a single [[Lie algebra|algebra]] requires the introduction of a [[graded algebra|'''Z'''<sub>2</sub>-grading]] under which the bosons are the even elements and the fermions are the odd elements. Such an algebra is called a [[Lie superalgebra]].
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| The simplest supersymmetric extension of the [[Poincaré algebra]] is the [[Super-Poincaré algebra]]. Expressed in terms of two [[Weyl spinor]]s, has the following [[commutator|anti-commutation]] relation:
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| :<math>\{ Q_{ \alpha }, \bar{Q_{ \dot{ \beta }}} \} = 2( \sigma{}^{\mu} )_{ \alpha \dot{ \beta }} P_{\mu} </math>
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| and all other anti-commutation relations between the ''Q''s and commutation relations between the ''Q''s and ''P''s vanish. In the above expression <math> P_{\mu} = -i \partial{}_{\mu}</math> are the generators of translation and <math>\sigma{}^{\mu}</math> are the [[Pauli matrices]].
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| There are [[representation of a Lie superalgebra|representations of a Lie superalgebra]] that are analogous to representations of a Lie algebra. Each Lie algebra has an associated Lie group and a Lie superalgebra can sometimes be extended into representations of a [[Lie supergroup]].
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| === The Supersymmetric Standard Model ===
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| {{Main|Minimal Supersymmetric Standard Model}}
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| Incorporating supersymmetry into the [[Standard Model]] requires doubling the number of particles since there is no way that any of the particles in the Standard Model can be [[superpartner]]s of each other. With the addition of new particles, there are many possible new interactions. The simplest possible supersymmetric model consistent with the Standard Model is the [[Minimal Supersymmetric Standard Model]] (MSSM) which can include the necessary additional new particles that are able to be [[superpartner]]s of those in the [[Standard Model]].
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| [[Image:Hqmc-vector.svg|thumb|300px|right|Cancellation of the [[Higgs boson]] quadratic [[mass renormalization]] between [[fermion]]ic [[top quark]] loop and [[scalar field|scalar]] stop [[squark]] [[tadpole (physics)|tadpole]] [[Feynman diagram]]s in a supersymmetric extension of the [[Standard Model]]]]
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| One of the main motivations for SUSY comes from the quadratically divergent contributions to the Higgs mass squared. The quantum mechanical interactions of the Higgs boson causes a large renormalization of the Higgs mass and unless there is an accidental cancellation, the natural size of the Higgs mass is the highest scale possible. This problem is known as the [[hierarchy problem]]. Supersymmetry reduces the size of the quantum corrections by having automatic cancellations between fermionic and bosonic Higgs interactions. If supersymmetry is restored at the weak scale, then the Higgs mass is related to supersymmetry breaking which can be induced from small non-perturbative effects explaining the vastly different scales in the weak interactions and gravitational interactions.
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| In many supersymmetric Standard Models there is a heavy stable particle (such as [[neutralino]]) which could serve as a [[Weakly interacting massive particle]] (WIMP) [[dark matter]] candidate. The existence of a supersymmetric dark matter candidate is closely tied to [[R-parity]].
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| 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 [[spontaneous symmetry breaking|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.
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| ==== Gauge Coupling Unification ====
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| {{Main|Minimal_Supersymmetric_Standard_Model#Gauge_Coupling_Unification}}
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| One piece of evidence for supersymmetry existing is gauge coupling unification.
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| The [[renormalization group]] evolution of the three gauge [[coupling constant]]s 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]].<ref name="GKane">Gordon L. Kane, ''The Dawn of Physics Beyond the Standard Model'', [[Scientific American]], June 2003, page 60 and ''The frontiers of physics'', special edition, Vol 15, #3, page 8</ref> With the addition of minimal SUSY joint convergence of the coupling constants is projected at approximately 10<sup>16</sup> [[GeV]].<ref name="GKane"/>
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| === Supersymmetric quantum mechanics ===
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| {{Main|Supersymmetric quantum mechanics}}
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| ''Supersymmetric quantum mechanics'' adds the SUSY superalgebra to [[quantum mechanics]] as opposed to [[quantum field theory]]. Supersymmetric quantum mechanics often comes up when studying the dynamics of supersymmetric [[solitons]] and due to the simplified nature of having fields only functions of time (rather than space-time), a great deal of progress has been made in this subject and is now studied in its own right.
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| SUSY quantum mechanics involves pairs of [[Hamiltonian (quantum mechanics)|Hamiltonians]] which share a particular mathematical relationship, which are called ''partner Hamiltonians''. (The [[potential energy]] terms which occur in the Hamiltonians are then called ''partner potentials''.) An introductory theorem shows that for every [[eigenstate]] of one Hamiltonian, its partner Hamiltonian has a corresponding eigenstate with the same energy. 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.
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| === Supersymmetry: Applications to condensed matter physics ===
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| SUSY concepts have provided useful extensions to the [[WKB approximation]]. In addition, 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<ref>''Supersymmetry in Disorder and Chaos'', Konstantin Efetov, Cambridge university press, 1997.</ref>
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| === Mathematics ===
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| 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 model]]s of more realistic theories. A prime example of this has been the demonstration of S-duality in four-dimensional gauge theories<ref name="krasnitz02">
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| {{cite book
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| | last =Krasnitz
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| | first =Michael
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| | title =Correlation functions in supersymmetric gauge theories from supergravity fluctuations
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| | publisher = Princeton University Department of Physics
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| | year = 2002
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| | location = Princeton University Department of Physics
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| | pages =91
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| | url =http://www.princeton.edu/physics/graduate-program/theses/theses-from-2002/MKrasnitzthesis.pdf
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| }}
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| </ref> that interchanges particles and [[Magnetic monopole|monopoles]].
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| The proof of the [[Atiyah-Singer index theorem]] is much simplified by the use of supersymmetric quantum mechanics.
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| == General supersymmetry ==
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| Supersymmetry appears in many different contexts in theoretical physics that are closely related. It is possible to have multiple supersymmetries and also have supersymmetric extra dimensions.
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| === Extended supersymmetry ===
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| {{Main|Extended supersymmetry}}
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| It is possible to have more than one kind of supersymmetry transformation. Theories with more than one supersymmetry transformation are known as [[extended supersymmetry|extended supersymmetric]] theories. The more supersymmetry a theory has, the more constrained the field content and interactions are. Typically the number of copies of a supersymmetry is a power of 2, i.e. 1, 2, 4, 8. 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.
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| The maximal number of supersymmetry generators possible is 32. 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 32. This corresponds to an ''N'' = 8 supersymmetry theory. Theories with 32 supersymmetries automatically have a [[graviton]].
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| In four dimensions there are the following theories, with the corresponding multiplets<ref>Polchinski,J. ''String theory. Vol. 2: Superstring theory and beyond'', Appendix B
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| </ref>(CPT adds a copy, whenever they are not invariant under such symmetry)
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| * ''N'' = 1
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| Chiral multiplet:
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| (0,{{frac|1|2}})
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| Vector multiplet:
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| ({{frac|1|2}},1)
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| Gravitino multiplet:
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| (1,{{frac|3|2}})
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| Graviton multiplet:
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| ({{frac|3|2}},2)
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| * ''N'' = 2
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| hypermultiplet:
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| (-{{frac|1|2}},0<sup>2</sup>,{{frac|1|2}})
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| vector multiplet:
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| (0,{{frac|1|2}}<sup>2</sup>,1)
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| supergravity multiplet:
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| (1,{{frac|3|2}}<sup>2</sup>,2)
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| * ''N'' = 4
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| Vector multiplet:
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| (-1,-{{frac|1|2}}<sup>4</sup>,0<sup>6</sup>,{{frac|1|2}}<sup>4</sup>,1)
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| Supergravity multiplet:
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| (0,{{frac|1|2}}<sup>4</sup>,1<sup>6</sup>,{{frac|3|2}}<sup>4</sup>,2)
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| * ''N'' = 8
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| Supergravity multiplet:
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| (-2,-{{frac|3|2}}<sup>8</sup>,-1<sup>28</sup>,-{{frac|1|2}}<sup>56</sup>,0<sup>70</sup>,{{frac|1|2}}<sup>56</sup>,1<sup>28</sup>,{{frac|3|2}}<sup>8</sup>,2)
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| === Supersymmetry in alternate numbers of dimensions ===
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| 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. In ''d'' dimensions, the size of spinors is roughly 2<sup>''d''/2</sup> or 2<sup>(''d'' − 1)/2</sup>. Since the maximum number of supersymmetries is 32, the greatest number of dimensions in which a supersymmetric theory can exist is eleven. | |
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| == Supersymmetry as a quantum group ==
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| {{Main|Supersymmetry as a quantum group}}
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| Supersymmetry can be reinterpreted in the language of [[noncommutative geometry]] and [[quantum group]]s. In particular, it involves a mild form of noncommutativity, namely [[supercommutativity]]. See the main article for more details.
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| == Supersymmetry in quantum gravity ==
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| Supersymmetry is part of a larger enterprise of theoretical physics to unify everything we know about the physical world into a single fundamental framework of physical laws, known as the quest for a [[Theory of Everything]] (TOE). A significant part of this larger enterprise is the quest for a theory of [[quantum gravity]], which would unify the classical theory of [[general relativity]] and the [[Standard Model]], which explains the other [[fundamental interaction|three basic forces]] in physics ([[electromagnetism]], the [[strong interaction]], and the [[weak interaction]]), and provides a palette of [[fundamental particle]]s upon which all four forces act. Two of the most active approaches to forming a theory of quantum gravity are [[string theory]] and [[loop quantum gravity]] (LQG), although in theory, supersymmetry could be a component of other theoretical approaches as well.
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| For [[string theory]] to be consistent, supersymmetry appears to be required at some level (although it may be a strongly broken symmetry). In particle theory, supersymmetry is recognized as a way to stabilize the [[hierarchy problem|hierarchy]] between the unification scale and the electroweak scale (or the [[Higgs boson]] mass), and can also provide a natural [[dark matter]] candidate. String theory also requires extra spatial dimensions which have to be compactified as in [[Kaluza-Klein theory]].
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| [[Loop quantum gravity]] (LQG) predicts no additional spatial dimensions, nor anything else about particle physics. These theories can be formulated in three spatial dimensions and one dimension of time, although in some LQG theories dimensionality is an [[emergent property]] of the theory, rather than a fundamental assumption of the theory. Also, LQG is a theory of quantum gravity which does not require supersymmetry. [[Lee Smolin]], one of the originators of LQG, has proposed that a loop quantum gravity theory incorporating either supersymmetry or extra dimensions, or both, be called "loop quantum gravity II".
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| If experimental evidence confirms supersymmetry in the form of [[supersymmetric particle]]s such as the [[neutralino]] that is often believed to be the lightest [[superpartner]], some people believe this would be a major boost to [[string theory]]. Since supersymmetry is a required component of string theory, any discovered supersymmetry would be consistent with string theory. If the [[Large Hadron Collider]] and other major particle physics experiments fail to detect supersymmetric partners or evidence of extra dimensions, many versions of [[string theory]] which had predicted certain low mass superpartners to existing particles may need to be significantly revised. The failure of experiments to discover either supersymmetric partners or extra spatial dimensions, {{As of|2013|lc=on}}, has encouraged [[loop quantum gravity]] researchers.
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| == Current status ==
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| 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 [[Brookhaven National Laboratory|Brookhaven]]; the [[WMAP]] dark matter density measurement and direct detection experiments, for example [[XENON]]-100; 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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| Historically, the tightest limits were from direct production at colliders. The first mass limits for squarks and gluinos were made at [[CERN]] by the [[UA1 experiment]] and the [[UA2 experiment]] at the [[Super Proton Synchrotron]]. LEP later set very strong limits.<ref>LEPSUSYWG, ALEPH, DELPHI, L3 and OPAL experiments, charginos, large m0 LEPSUSYWG/01-03.1</ref> In 2006 these limits were extended by the D0 experiment.<ref>{{cite paper |author=The D0-Collaboration |title=Search for associated production of charginos and neutralinos in the trilepton final state using 2.3 fb<sup>−1</sup> of data |year=2009 |arxiv=0901.0646 }}</ref><ref>{{cite paper |author=The D0 Collaboration |title=Search for squarks and gluinos in events with jets and missing transverse energy in <math>p\bar{p}</math> collisions at <math>\sqrt{s}</math>=1.96 TeV |arxiv=0712.3805 |year=2006 }}</ref>
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| From 2003, [[WMAP]]'s [[dark matter]] density measurements have strongly constrained supersymmetry models, which have to be tuned to invoke a particular mechanism to sufficiently reduce the [[neutralino]] density.
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| Prior to the launch of the LHC, in 2009, fits of available data to CMSSM and NUHM1 indicated that squarks and gluinos were most likely to have masses in 500 to 800 GeV range, though values as high as 2.5 TeV were allowed with low probabilities. Neutralinos and sleptons were expected to be quite light, with the lightest neutralino and the lightest stau most likely to be found between 100 to 150 GeV.<ref>{{cite journal|url=http://xxx.lanl.gov/pdf/0907.5568v1.pdf|title=Likelihood Functions for Supersymmetric Observables in Frequentist Analyses of the CMSSM and NUHM1|author=O. Buchmueller et al.}}</ref>
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| As of 2012, the [[LHC]] has found no evidence for supersymmetry, and, as a result, has surpassed existing experimental limits from [[Large Electron–Positron Collider]] and [[Tevatron]] and partially excluded the aforementioned expected ranges.<ref>[http://www.math.columbia.edu/~woit/wordpress/?p=3479 Implications of Initial LHC Searches for Supersymmetry]</ref><ref>[http://arxiv.org/abs/1101.4664 Fine-tuning implications for complementary dark matter and LHC SUSY searches]</ref><ref>[http://resonaances.blogspot.com/2011/02/what-lhc-tells-about-susy.html What LHC tells about SUSY]</ref><ref>[http://www.hep.ph.ic.ac.uk/susytalks/iop-susytapper.pdf Early SUSY searches at the LHC]</ref> Based on the data sample collected by the CMS detector at the LHC through the summer of 2011, [[Minimal Supersymmetric Standard Model|CMSSM]] squarks have been excluded up to the mass of 1.1 TeV and gluinos have been excluded up to 500 GeV.<ref>{{cite journal|title=Search for Supersymmetry at the LHC in Events with Jets and Missing Transverse Energy|author=CMS Collaboration|journal=Physical Review Letters|date=November 2011|doi=10.1103/PhysRevLett.107.221804|last2=Khachatryan|first2=V.|last3=Sirunyan|first3=A.|last4=Tumasyan|first4=A.|last5=Adam|first5=W.|last6=Bergauer|first6=T.|last7=Dragicevic|first7=M.|last8=Erö|first8=J.|last9=Fabjan|first9=C.|volume=107|issue=22|last1000=Andreev|first1000=Yu|last1001=Dermenev|first1001=A|last1002=Gninenko|first1002=S|last1003=Golubev|first1003=N|last1004=Kirsanov|first1004=M|last1005=Krasnikov|first1005=N|last1006=Matveev|first1006=V|last1007=Pashenkov|first1007=A|last1008=Toropin|first1008=A|last1009=Troitsky|first1009=S|last2000=Baumgartel|first2000=D|last2001=Boeriu|first2001=O|last2002=Chasco|first2002=M|last2003=Reucroft|first2003=S|last2004=Swain|first2004=J|last2005=Trocino|first2005=D|last2006=Wood|first2006=D|last2007=Zhang|first2007=J|last2008=Anastassov|first2008=A|last2009=Kubik|first2009=A}}</ref> Searches are only applicable for a finite set of tested points because simulation using the [[Monte Carlo method]] must be made so that limits for that particular model can be calculated. This complicates matters because different experiments have looked at different sets of points. Some extrapolation between points can be made within particular models but it is difficult to set general limits even for the [[Minimal Supersymmetric Standard Model]].
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| In 2011 and 2012, the [[LHC]] discovered a [[Higgs boson]] with a mass of about 125 GeV, and with couplings to fermions and bosons which are consistent with the [[Standard Model]]. The MSSM predicts that the mass of the lightest [[Higgs boson]] should not be much higher than the mass of the [[Z boson]], and, in the absence of [[fine tuning]] (with the supersymmetry breaking scale on the order of 1 TeV), should not exceed 130 GeV. Furthermore, for values of the MSSM parameter ''tan'' β ≤ 3, it predicts Higgs mass below 114 GeV over most of the parameter space.<ref>{{cite journal|title=Higgs Boson Theory and Phenomenology|author=Marcela Carena and Howard E. Haber|arxiv=hep-ph/0208209v3.pdf|year=1970|bibcode=2003PrPNP..50...63C|last2=Haber|volume=50|pages=63|journal=Progress in Particle and Nuclear Physics|doi=10.1016/S0146-6410(02)00177-1}}</ref> This region of Higgs mass was excluded by [[LEP]] by 2000. The [[LHC]] result is somewhat problematic for the minimal supersymmetric model, as the value of 125 GeV is relatively large for the model and can only be achieved with large radiative loop corrections from top [[squarks]], which many theorists consider to be "unnatural" (see [[naturalness]] and [[fine tuning]]).<ref>{{cite journal|title=Implications of a 125 GeV Higgs for the MSSM and Low-Scale SUSY Breaking|author=Patrick Draper et al|date=December 2011|arxiv=1112.3068}}</ref> Furthermore, in 2012, the [[LHC]] measured deviations from [[Standard Model]] predicted [[Higgs boson|Higgs]] couplings, particularly in their gamma-gamma final state, which, if they persist, could severely constrain the MSSM.
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| A summary listed eight arguments against supersymmetry.<ref>"Eight Arguments Against Supersymmetry" http://www.physicsforums.com/showthread.php?t=727664</ref> (1) The LUX experiment for cold dark matter has not observed neutralinos. (2) The large size of the WMAP cold spot is larger than predicted by Lambda cold dark matter models. (3) The large-scale flow of galaxies is larger than predicted by Lambda CDM models. (4) The number of faint dwarf galaxies is smaller than predicted by Lambda CDM models. (5) Neither the ATLAS nor the CMS collaboration have observed gluinos and squarks. (6) The rest mass, interaction cross-section and decay rates of the Higgs boson are compatible with the standard theory, but not with earlier predictions by supersymmetric models. (7) Dirac fermions can be described by a gravitation theory which includes Cartan torsion (Einstein-Cartan theory), supersymmetry is not required. (8) The mass hierarchy problem of Grand Unified theories need not arise if Grand Unification does not exist. The proton decay predicted by Grand Unified theories has not been observed. The quantization of electric charge can be explained by theories which include Dirac magnetic monopoles, so Grand Unification is not necessary.
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| In spite of the null searches and the heavy Higgs, a recent analysis of the constrained minimal supersymmetric Standard Model, the [[CMSSM]], suggests that the model is still compatible with all present experimental constraints.<ref>[http://arxiv.org/abs/1212.2636]"Global Fits of the cMSSM and NUHM including the LHC Higgs discovery and new XENON100 constraints", C. Strege, G. Bertone, F. Feroz, M. Fornasa, R. Ruiz de Austri, R. Trotta, arXiv:1212.2636</ref> The preferred masses for squarks and gluinos is about 2 TeV. The resulting fine-tuning of the [[Higgs boson]] mass (see [[little hierarchy problem]]) and [[Z-boson]] mass (see [[mu problem]]), however, is considered "unnatural," and some theorists now favor extended supersymmetry models, for example, the [[NMSSM]].
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| == See also ==
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| <div style="-moz-column-count:2; column-count:2;">
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| * [[Supersymmetric gauge theory]]
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| * [[Wess–Zumino model]]
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| * [[Minimal Supersymmetric Standard Model]]
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| * [[Supersymmetry as a quantum group]]
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| * [[Quantum group#Quantum groups and non-commutative geometry|Quantum group]]
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| * [[Supercharge]]
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| * [[Superfield]]
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| * [[Supergeometry]]
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| * [[Supergravity]]
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| * [[Supergroup (physics)|Supergroup]]
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| * [[Superspace]]
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| </div>
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| == References ==
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| {{Reflist|30em}}
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| == Further reading ==
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| [http://www.stringwiki.org/wiki/Supersymmetry_and_Supergravity Supersymmetry and Supergravity] page in [http://www.stringwiki.org/wiki/String_Theory_Wiki String Theory Wiki] lists more books and reviews.
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| === Theoretical introductions, free and online ===
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| * {{cite arXiv|eprint=hep-ph/9709356|title= A Supersymmetry Primer|author=S. Martin|year=2011}}
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| * {{cite arXiv|eprint=hep-th/9612114|title=Introduction to Supersymmetry|author=[[Joseph Lykken|Joseph D. Lykken]]|year=1996}}
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| * {{cite arXiv|eprint=hep-ph/9611409|title=An Introduction to Supersymmetry|author=Manuel Drees|year=1996}}
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| * {{cite arXiv|eprint=hep-th/0101055|title=Introduction to Supersymmetry|author=Adel Bilal|year=2001}}
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| * [http://www.physics.uc.edu/~argyres/661/susy2001.pdf An Introduction to Global Supersymmetry] by [[Philip Arygres]], 2001
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| === Monographs ===
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| * [http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521857864 Weak Scale Supersymmetry] by Howard Baer and Xerxes Tata, 2006.
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| * Cooper, F., A. Khare and U. Sukhatme. "Supersymmetry in Quantum Mechanics." Phys. Rep. 251 (1995) 267-85 (arXiv:hep-th/9405029).
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| * Junker, G. ''Supersymmetric Methods in Quantum and Statistical Physics'', Springer-Verlag (1996).
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| * Gordon L. Kane.''Supersymmetry: Unveiling the Ultimate Laws of Nature'' Basic Books, New York (2001). ISBN 0-7382-0489-7.
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| * Gordon L. Kane and Shifman, M., eds. ''The Supersymmetric World: The Beginnings of the Theory,'' World Scientific, Singapore (2000). ISBN 981-02-4522-X.
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| * Weinberg, Steven, ''The Quantum Theory of Fields, Volume 3: Supersymmetry'', Cambridge University Press, Cambridge, (1999). ISBN 0-521-66000-9.
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| * Wess, Julius, and Jonathan Bagger, ''Supersymmetry and Supergravity'', Princeton University Press, Princeton, (1992). ISBN 0-691-02530-4.
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| *Duplij, Steven; Siegel, Warren; Bagger, Jonathan (eds.) (2005). ''Concise Encyclopedia of Supersymmetry'', Springer, Berlin/New York, (Second printing) ISBN 978-1-4020-1338-6
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| === On experiments ===
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| * {{cite journal | author=Bennett GW, ''et al.''; Muon (g−2) Collaboration | title=Measurement of the negative muon anomalous magnetic moment to 0.7 ppm | journal=Physical Review Letters | volume=92 | issue=16 | year=2004 | pages=161802 | pmid=15169217 | doi=10.1103/PhysRevLett.92.161802 | bibcode=2004PhRvL..92p1802B|arxiv = hep-ex/0401008 }}
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| * Brookhaven National Laboratory (Jan. 8, 2004). ''[http://www.bnl.gov/bnlweb/pubaf/pr/2004/bnlpr010804.htm New g−2 measurement deviates further from Standard Model].'' Press Release.
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| * Fermi National Accelerator Laboratory (Sept 25, 2006). ''[http://www.fnal.gov/pub/presspass/press_releases/CDF_meson.html Fermilab's CDF scientists have discovered the quick-change behavior of the B-sub-s meson.]'' Press Release.
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| == External links ==
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| * [http://profmattstrassler.com/articles-and-posts/lhcposts/what-do-current-mid-august-2011-lhc-results-imply-about-supersymmetry/ What do current LHC results (mid-August 2011) imply about supersymmetry?] Matt Strassler
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| * [https://twiki.cern.ch/twiki/bin/view/AtlasPublic/SupersymmetryPublicResults#Early_2011_Data_5_CONF_Notes ATLAS Experiment Supersymmetry search documents]
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| * [https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsSUS CMS Experiment Supersymmetry search documents]
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| * [http://www.cosmosmagazine.com/node/714 "Particle wobble shakes up supersymmetry"], ''Cosmos'' magazine, September 2006
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| * [http://www.bbc.co.uk/news/science-environment-14680570 LHC results put supersymmetry theory 'on the spot'] BBC news 27/8/2011
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| * [http://www.bbc.co.uk/news/science-environment-20300100 SUSY running out of hiding places] BBC news 12/11/2012
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| {{Particles}}
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| [[Category:Theoretical physics]]
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| [[Category:Concepts in physics]]
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| [[Category:Supersymmetry| ]]
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| [[Category:Physics beyond the Standard Model]]
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