In supergravity theories combining general relativity and supersymmetry , the gravitino ( G͂ ) is the gauge fermion supersymmetric partner of the hypothesized graviton . It has been suggested as a candidate for dark matter .
86-486: If it exists, it is a fermion of spin 3 / 2 and therefore obeys the Rarita–Schwinger equation . The gravitino field is conventionally written as ψ μα with μ = 0, 1, 2, 3 a four-vector index and α = 1, 2 a spinor index. For μ = 0 one would get negative norm modes, as with every massless particle of spin 1 or higher. These modes are unphysical, and for consistency there must be
172-448: A gauge symmetry which cancels these modes: δψ μα = ∂ μ ε α , where ε α ( x ) is a spinor function of spacetime. This gauge symmetry is a local supersymmetry transformation, and the resulting theory is supergravity . Thus the gravitino is the fermion mediating supergravity interactions, just as the photon is mediating electromagnetism , and the graviton is presumably mediating gravitation . Whenever supersymmetry
258-407: A graviton . For four dimensions there are the following theories, with the corresponding multiplets (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. In d dimensions, the size of spinors
344-488: A supersymmetric extension of the Standard Model is a possible candidate for undiscovered particle physics , and seen by some physicists as an elegant solution to many current problems in particle physics if confirmed correct, which could resolve various areas where current theories are believed to be incomplete and where limitations of current theories are well established. In particular, one supersymmetric extension of
430-443: 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. In 2021, supersymmetric quantum mechanics was applied to option pricing and the analysis of markets in finance , and to financial networks . In quantum field theory, supersymmetry
516-541: A baryon containing 3 valence quarks, of which two tend to cluster together as a diquark, behaves likes a meson. SUSY concepts have provided useful extensions to the WKB approximation . 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
602-862: A consistent Lie-algebraic graded structure on which the Gervais−Sakita rediscovery was based directly first arose in 1971 in the context of an early version of string theory by Pierre Ramond , John H. Schwarz and André Neveu . In 1974, Julius Wess and Bruno Zumino identified the characteristic renormalization features of four-dimensional supersymmetric field theories, which identified them as remarkable QFTs, and they and Abdus Salam and their fellow researchers introduced early particle physics applications. The mathematical structure of supersymmetry ( graded Lie superalgebras ) has subsequently been applied successfully to other topics of physics, ranging from nuclear physics , critical phenomena , quantum mechanics to statistical physics , and supersymmetry remains
688-486: A group of researchers showed that, in theory, N = ( 0 , 1 ) {\displaystyle N=(0,1)} SUSY could be realised at the edge of a Moore–Read quantum Hall state. However, to date, no experiments have been done yet to realise it at an edge of a Moore–Read state. In 2022, a different group of researchers created a computer simulation of atoms in 1 dimensions that had supersymmetric topological quasiparticles . In 2013, integrated optics
774-444: A half-integer-valued spin and follow Fermi–Dirac statistics . The names of bosonic partners of fermions are prefixed with s- , because they are scalar particles . For example, if the electron exists in a supersymmetric theory, then there would be a particle called a selectron (superpartner electron), a bosonic partner of the electron. In supersymmetry, each particle from the class of fermions would have an associated particle in
860-496: A minus sign associated with fermionic loops). The hierarchy between the electroweak scale and the Planck scale would be achieved in a natural manner, without extraordinary fine-tuning. If supersymmetry were restored at the weak scale, then the Higgs mass would be related to supersymmetry breaking which can be induced from small non-perturbative effects explaining the vastly different scales in
946-516: A natural mechanism for radiative electroweak symmetry breaking . In many supersymmetric extensions of the Standard Model, such as the Minimal Supersymmetric Standard Model, there is a heavy stable particle (such as the neutralino ) which could serve as a weakly interacting massive particle (WIMP) dark matter candidate. The existence of a supersymmetric dark matter candidate is related closely to R-parity . Supersymmetry at
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#17328767945151032-469: A new class of functional optical structures with possible applications in phase matching , mode conversion 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 . All stochastic (partial) differential equations, the models for all types of continuous time dynamical systems, possess topological supersymmetry. In
1118-462: A power law statistical pull on soft SUSY breaking terms to large values (depending on the number of hidden sector SUSY breaking fields contributing to the soft terms). If this is coupled with an anthropic requirement that contributions to the weak scale not exceed a factor between 2 and 5 from its measured value (as argued by Agrawal et al.), then the Higgs mass is pulled up to the vicinity of 125 GeV while most sparticles are pulled to values beyond
1204-453: A simplification of the term super-gauge symmetry used by Wess and Zumino, although Zumino also used the same term at around the same time. The term supergauge was in turn coined by Neveu and Schwarz in 1971 when they devised supersymmetry in the context of string theory. 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
1290-491: A spin statistics-quantum number relation. As a consequence of the Pauli exclusion principle, only one fermion can occupy a particular quantum state at a given time. Suppose multiple fermions have the same spatial probability distribution , then, at least one property of each fermion, such as its spin, must be different. Fermions are usually associated with matter , whereas bosons are generally force carrier particles. However, in
1376-497: A supersymmetric extension of the Standard Model is a possible candidate for physics beyond the Standard Model . However, no supersymmetric extensions of the Standard Model have been experimentally verified. 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
1462-494: A supersymmetric extension of the Standard Model is correct, superpartners of the existing elementary particles would be new and undiscovered particles and supersymmetry is expected to be spontaneously broken. There is no experimental evidence that a supersymmetric extension to the Standard Model is correct, or whether or not other extensions to current models might be more accurate. It is only since around 2010 that particle accelerators specifically designed to study physics beyond
1548-403: A tachyon and therefore the spacetime vacuum itself would be unstable and would decay into some tachyon-free string theory usually in a lower spacetime dimension. There is no experimental evidence that either supersymmetry or misaligned supersymmetry holds in our universe, and many physicists have moved on from supersymmetry and string theory entirely due to the non-detection of supersymmetry at
1634-446: 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 (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. The maximal number of supersymmetry generators possible
1720-499: A vital part of many proposed theories in many branches of physics. In particle physics , the first realistic supersymmetric version of the Standard Model was proposed in 1977 by Pierre Fayet and is known as the Minimal Supersymmetric Standard Model or MSSM for short. It was proposed to solve, amongst other things, the hierarchy problem . Supersymmetry was coined by Abdus Salam and John Strathdee in 1974 as
1806-509: 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
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#17328767945151892-487: 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 is due to the Weinberg–Witten theorem . This corresponds to an N = 8 supersymmetry theory. Theories with 32 supersymmetries automatically have
1978-424: Is approximately 2 or 2 . Since the maximum number of supersymmetries is 32, the greatest number of dimensions in which a supersymmetric theory can exist is eleven. Fractional supersymmetry is a generalization of the notion of supersymmetry in which the minimal positive amount of spin does not have to be 1 / 2 but can be an arbitrary 1 / N for integer value of N . Such
2064-461: Is broken in supergravity theories, it acquires a mass which is determined by the scale at which supersymmetry is broken . This varies greatly between different models of supersymmetry breaking, but if supersymmetry is to solve the hierarchy problem of the Standard Model , the gravitino cannot be more massive than about 1 TeV /c. Murray Gell-Mann and Peter van Nieuwenhuizen intended the spin-3/2 particle associated with supergravity to be called
2150-434: Is known as the hierarchy problem. Supersymmetry close to the electroweak scale , such as in the Minimal Supersymmetric Standard Model, would solve the hierarchy problem that afflicts the Standard Model. It would reduce the size of the quantum corrections by having automatic cancellations between fermionic and bosonic Higgs interactions, and Planck-scale quantum corrections cancel between partners and superpartners (owing to
2236-425: Is 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 mathematically tractable. When supersymmetry is imposed as a local symmetry, Einstein's theory of general relativity is included automatically, and
2322-416: Is no longer able to fully resolve the hierarchy problem. 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 superpartners 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
2408-420: Is only seen at large (compared to size of the system) distances. At proximity, where spatial structure begins to be important, a composite particle (or system) behaves according to its constituent makeup. Fermions can exhibit bosonic behavior when they become loosely bound in pairs. This is the origin of superconductivity and the superfluidity of helium-3: in superconducting materials, electrons interact through
2494-623: Is required in superstring theory at some level. However, even in non-supersymmetric string theory, a type of supersymmetry called misaligned supersymmetry is still required in the theory in order to ensure no physical tachyons appear. Any string theories without some kind of supersymmetry, such as bosonic string theory and the E 7 × E 7 {\displaystyle E_{7}\times E_{7}} , S U ( 16 ) {\displaystyle SU(16)} , and E 8 {\displaystyle E_{8}} heterotic string theories , will have
2580-408: Is that R-parity is slightly violated and the gravitino is the lightest supersymmetric particle. This causes almost all supersymmetric particles in the early Universe to decay into Standard Model particles via R-parity violating interactions well before the synthesis of primordial nuclei; a small fraction however decay into gravitinos, whose half-life is orders of magnitude greater than the age of
2666-426: Is the Minimal Supersymmetric Standard Model (MSSM) which can include the necessary additional new particles that are able to be superpartners of those in the Standard Model. One of the original motivations for the Minimal Supersymmetric Standard Model came from the hierarchy problem . Due to the quadratically divergent contributions to the Higgs mass squared in the Standard Model, the quantum mechanical interactions of
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2752-399: Is the only way spacetime and internal symmetries can be combined consistently. While supersymmetry has not been discovered at high energy , see Section Supersymmetry in particle physics , supersymmetry was found to be effectively realized at the intermediate energy of hadronic physics where baryons and mesons are superpartners. An exception is the pion that appears as a zero mode in
2838-467: The CPT theorem . Such EDM experiments are also much more scalable than conventional particle accelerators and offer a practical alternative to detecting physics beyond the standard model as accelerator experiments become increasingly costly and complicated to maintain. The current best limit for the electron's EDM has already reached a sensitivity to rule out so called 'naive' versions of supersymmetric extensions of
2924-492: The Haag–Łopuszański–Sohnius theorem analyzed all possible superalgebras in the general form, including those with an extended number of the supergenerators and central charges . This extended super-Poincaré algebra paved the way for obtaining a very large and important class of supersymmetric field theories. Traditional symmetries of physics are generated by objects that transform by the tensor representations of
3010-769: 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 internal symmetry group or if there is not any mass gap , the conformal group with a compact internal symmetry group. In 1971 Golfand and Likhtman were the first to show that the Poincaré algebra can be extended through introduction of four anticommuting spinor generators (in four dimensions), which later became known as supercharges. In 1975,
3096-406: The Poincaré group and internal symmetries. Supersymmetries, however, are generated by objects that transform by the spin representations . According to the spin-statistics theorem , bosonic fields commute while fermionic fields anticommute . Combining the two kinds of fields into a single algebra requires the introduction of a Z 2 -grading under which the bosons are the even elements and
3182-406: The Standard Model , the Minimal Supersymmetric Standard Model (MSSM), became popular in theoretical particle physics, as the Minimal Supersymmetric Standard Model is the simplest supersymmetric extension of the Standard Model that could resolve major hierarchy problems within the Standard Model, by guaranteeing that quadratic divergences of all orders will cancel out in perturbation theory . If
3268-465: 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
3354-405: The spin-statistics theorem in relativistic quantum field theory , particles with integer spin are bosons . In contrast, particles with half-integer spin are fermions. In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers . Therefore, what is usually referred to as the spin-statistics relation is, in fact,
3440-426: The 'hemitrion', meaning 'half-3', however the editors of Physical Review were not keen on the name and instead suggested 'massless Rarita–Schwinger particle' for their 1977 publication. The current name of gravitino was instead suggested by Sidney Coleman and Heinz Pagels , although this term was originally coined in 1954 by Felix Pirani to describe a class of negative energy excitations with zero rest mass. If
3526-535: The 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 and 150 GeV. The first runs of the LHC surpassed existing experimental limits from the Large Electron–Positron Collider and Tevatron and partially excluded
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3612-455: 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. 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
3698-406: 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 greatest scale possible. Furthermore, the electroweak scale receives enormous Planck-scale quantum corrections. The observed hierarchy between the electroweak scale and the Planck scale must be achieved with extraordinary fine tuning . This problem
3784-403: The LHC. Despite the null results for supersymmetry at the LHC so far, some particle physicists have nevertheless moved to string theory in order to resolve the naturalness crisis for certain supersymmetric extensions of the Standard Model. According to the particle physicists, there exists a concept of "stringy naturalness" in string theory , where the string theory landscape could have
3870-614: The Standard Model "is correct, supersymmetric particles should appear in collisions at the LHC." 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, which in 2006 were extended by the D0 experiment at
3956-471: The Standard Model have become operational (i.e. the Large Hadron Collider (LHC)), and it is not known where exactly to look, nor the energies required for a successful search. However, the negative results from the LHC since 2010 have already ruled out some supersymmetric extensions to the Standard Model, and many physicists believe that the Minimal Supersymmetric Standard Model , while not ruled out,
4042-481: 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. After incorporating minimal SUSY at the electroweak scale, the running of the gauge couplings are modified, and joint convergence of the gauge coupling constants is projected to occur at approximately 10 GeV . The modified running also provides
4128-483: The Standard Model particle interacts with the supersymmetric particles. The current best constraint on the electron electric dipole moment put it to be smaller than 10 e·cm, equivalent to a sensitivity to new physics at the TeV scale and matching that of the current best particle colliders. A permanent EDM in any fundamental particle points towards time-reversal violating physics, and therefore also CP-symmetry violation via
4214-488: The Standard Model. Research in the late 2010s and early 2020s from experimental data on the cosmological constant , LIGO noise , and pulsar timing , suggests it's very unlikely that there are any new particles with masses much higher than those which can be found in the standard model or the LHC. However, this research has also indicated that quantum gravity or perturbative quantum field theory will become strongly coupled before 1 PeV, leading to other new physics in
4300-486: The TeVs. The negative findings in the experiments disappointed many physicists, who believed that supersymmetric extensions of the Standard Model (and other theories relying upon it) were by far the most promising theories for "new" physics beyond the Standard Model, and had hoped for signs of unexpected results from the experiments. In particular, the LHC result seems problematic for the Minimal Supersymmetric Standard Model, as
4386-508: The Tevatron. From 2003 to 2015, WMAP's and Planck 's dark matter density measurements have strongly constrained supersymmetric extensions of the Standard Model, which, if they explain dark matter, have to be tuned to invoke a particular mechanism to sufficiently reduce the neutralino density. Prior to the beginning 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
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#17328767945154472-936: The Universe due to the suppression of the decay rate by the Planck scale and the small R-parity violating couplings. Fermion In particle physics , a fermion is a subatomic particle that follows Fermi–Dirac statistics . Fermions have a half-odd-integer spin ( spin 1 / 2 , spin 3 / 2 , etc.) and obey the Pauli exclusion principle . These particles include all quarks and leptons and all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei . Fermions differ from bosons , which obey Bose–Einstein statistics . Some fermions are elementary particles (such as electrons ), and some are composite particles (such as protons ). For example, according to
4558-403: The aforementioned expected ranges. In 2011–12, 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
4644-787: The class of bosons, and vice versa, known as a superpartner . The spin of a particle's superpartner is different by a half-integer. In the simplest supersymmetry theories, with perfectly " unbroken " supersymmetry, each pair of superpartners would share the same mass and internal quantum numbers besides spin. More complex supersymmetry theories have a spontaneously broken symmetry , allowing superpartners to differ in mass. Supersymmetry has various applications to different areas of physics, such as quantum mechanics , statistical mechanics , quantum field theory , condensed matter physics , nuclear physics , optics , stochastic dynamics , astrophysics , quantum gravity , and cosmology . Supersymmetry has also been applied to high energy physics , where
4730-662: The corresponding antiparticle of each of these. Mathematically, there are many varieties of fermions, with the three most common types being: Most Standard Model fermions are believed to be Dirac fermions, although it is unknown at this time whether the neutrinos are Dirac or Majorana fermions (or both). Dirac fermions can be treated as a combination of two Weyl fermions. In July 2015, Weyl fermions have been experimentally realized in Weyl semimetals . Composite particles (such as hadrons , nuclei, and atoms) can be bosons or fermions depending on their constituents. More precisely, because of
4816-478: The current reach of LHC. (The Higgs was determined to have a mass of 125 GeV ±0.15 GeV in 2022.) An exception occurs for higgsinos which gain mass not from SUSY breaking but rather from whatever mechanism solves the SUSY mu problem. Light higgsino pair production in association with hard initial state jet radiation leads to a soft opposite-sign dilepton plus jet plus missing transverse energy signal. In particle physics,
4902-472: The current state of particle physics, the distinction between the two concepts is unclear. Weakly interacting fermions can also display bosonic behavior under extreme conditions. For example, at low temperatures, fermions show superfluidity for uncharged particles and superconductivity for charged particles. Composite fermions, such as protons and neutrons , are the key building blocks of everyday matter . English theoretical physicist Paul Dirac coined
4988-526: The decay as to destroy almost all the nuclei created in the era of nucleosynthesis , in contrast with observations. In fact, in such a case the universe would have been made of hydrogen alone, and star formation would probably be impossible. One possible solution to the cosmological gravitino problem is the split supersymmetry model, where the gravitino mass is much higher than the TeV scale, but other fermionic supersymmetric partners of standard model particles already appear at this scale. Another solution
5074-554: The demonstration of S-duality in four-dimensional gauge theories 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 an integral part of string theory , a possible theory of everything . There are two types of string theory, supersymmetric string theory or superstring theory , and non-supersymmetric string theory. By definition of superstring theory, supersymmetry
5160-442: 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
5246-413: The electroweak scale (augmented with a discrete symmetry) typically provides a candidate dark matter particle at a mass scale consistent with thermal relic abundance calculations. 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
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#17328767945155332-400: The exchange of phonons , forming Cooper pairs , while in helium-3, Cooper pairs are formed via spin fluctuations. The quasiparticles of the fractional quantum Hall effect are also known as composite fermions ; they consist of electrons with an even number of quantized vortices attached to them. Supersymmetry Supersymmetry is a theoretical framework in physics that suggests
5418-443: The existence of a symmetry between particles with integer spin ( bosons ) and particles with half-integer spin ( fermions ). It proposes that for every known particle, there exists a partner particle with different spin properties. There have been multiple experiments on supersymmetry that have failed to provide evidence that it exists in nature . If evidence is found, supersymmetry could help explain certain phenomena, such as
5504-431: The fact that one is modelling one particle and as such the 'statistics' do not 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 Efetov (1997). In 2021,
5590-500: The fermions are the odd elements. Such an algebra is called a Lie superalgebra . The simplest supersymmetric extension of the Poincaré algebra is the Super-Poincaré algebra . Expressed in terms of two Weyl spinors , has the following anti-commutation relation: 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 P μ = − i ∂ μ are
5676-503: The generators of translation and σ are the Pauli matrices . There are 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 . Supersymmetric quantum mechanics adds the SUSY superalgebra to quantum mechanics as opposed to quantum field theory. Supersymmetric quantum mechanics often becomes relevant when studying
5762-412: The gravitino indeed has a mass of the order of TeV, then it creates a problem in the standard model of cosmology , at least naïvely. One option is that the gravitino is stable. This would be the case if the gravitino is the lightest supersymmetric particle and R-parity is conserved (or nearly so). In this case the gravitino is a candidate for dark matter ; as such gravitinos will have been created in
5848-496: The hierarchy problem naturally with supersymmetry, while other researchers have moved on to other supersymmetric models such as split supersymmetry . Still others have moved to string theory as a result of the naturalness crisis. Former enthusiastic supporter Mikhail Shifman went as far as urging the theoretical community to search for new ideas and accept that supersymmetry was a failed theory in particle physics. However, some researchers suggested that this "naturalness" crisis
5934-504: The mass spectrum and thus protected by the supersymmetry: It has no baryonic partner. The realization of this effective supersymmetry is readily explained in quark–diquark models : Because two different color charges close together (e.g., blue and red) appear under coarse resolution as the corresponding anti-color (e.g. anti-green), a diquark cluster viewed with coarse resolution (i.e., at the energy-momentum scale used to study hadron structure) effectively appears as an antiquark. Therefore,
6020-504: 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. The Goldstone theorem explains the associated emergence of the long-range dynamical behavior that manifests itself as 1 / f noise , butterfly effect , and
6106-569: The muon at Fermilab ; the WMAP dark matter density measurement and direct detection experiments – for example, XENON -100 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 . In fact, CERN publicly states that if a supersymmetric model of
6192-417: The name fermion from the surname of Italian physicist Enrico Fermi . The Standard Model recognizes two types of elementary fermions: quarks and leptons . In all, the model distinguishes 24 different fermions. There are six quarks ( up , down , strange , charm , bottom and top ), and six leptons ( electron , electron neutrino , muon , muon neutrino , tauon and tauon neutrino ), along with
6278-571: The nature of dark matter and the hierarchy problem in particle physics. A supersymmetric theory is a theory in which the equations for force and the equations for matter are identical. In theoretical and mathematical physics , any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories exist. In theory, supersymmetry is a type of spacetime symmetry between two basic classes of particles: bosons , which have an integer-valued spin and follow Bose–Einstein statistics , and fermions , which have
6364-418: The operator representation of stochastic evolution, the topological supersymmetry is the exterior derivative which is commutative with the stochastic evolution operator defined as the stochastically averaged pullback induced on differential forms by SDE-defined diffeomorphisms of the phase space . The topological sector of the so-emerging supersymmetric theory of stochastic dynamics can be recognized as
6450-492: The order of M pl / m in natural units , where M pl is the Planck mass and m is the mass of a gravitino. For a gravitino mass of the order of TeV this would be 10 s , much later than the era of nucleosynthesis . At least one possible channel of decay must include either a photon , a charged lepton or a meson , each of which would be energetic enough to destroy a nucleus if it strikes one. One can show that enough such energetic particles will be created in
6536-428: The order of 1 TeV), should not exceed 135 GeV. The LHC found no previously unknown particles other than the Higgs boson which was already suspected to exist as part of the Standard Model, and therefore no evidence for any supersymmetric extension of the Standard Model. Indirect methods include the search for a permanent electric dipole moment (EDM) in the known Standard Model particles, which can arise when
6622-399: The relation between spin and statistics, a particle containing an odd number of fermions is itself a fermion. It will have half-integer spin. Examples include the following: The number of bosons within a composite particle made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion. Fermionic or bosonic behavior of a composite particle (or system)
6708-406: 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. SUSY extensions of the standard model are constrained by a variety of experiments, including measurements of low-energy observables – for example, the anomalous magnetic moment of
6794-406: The result is said to be a theory of supergravity . Another theoretically appealing property of supersymmetry is that it offers the only "loophole" to the Coleman–Mandula theorem , which prohibits spacetime and internal symmetries from being combined in any nontrivial way, for quantum field theories with very general assumptions. The Haag–Łopuszański–Sohnius theorem demonstrates that supersymmetry
6880-605: The scale-free statistics of sudden (instantonic) processes, such as earthquakes, neuroavalanches, and solar flares, known as the Zipf's law and the Richter scale . 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
6966-405: 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). In response to the so-called "naturalness crisis" in the Minimal Supersymmetric Standard Model, some researchers have abandoned naturalness and the original motivation to solve
7052-425: The very early universe. However, one may calculate the density of gravitinos and it turns out to be much higher than the observed dark matter density. The other option is that the gravitino is unstable. Thus the gravitinos mentioned above would decay and will not contribute to the observed dark matter density. However, since they decay only through gravitational interactions, their lifetime would be very long, of
7138-438: The weak interactions and gravitational interactions. Another motivation for the Minimal Supersymmetric Standard Model comes from grand unification , the idea that the gauge symmetry groups should unify at high-energy. In the Standard Model, however, the weak , strong and electromagnetic gauge couplings fail to unify at high energy. In particular, the renormalization group evolution of the three gauge coupling constants of
7224-569: Was broken badly. Miyazawa's work was largely ignored at the time. J. L. Gervais and B. Sakita (in 1971), Yu. A. Golfand and E. P. Likhtman (also in 1971), and D. V. Volkov and V. P. Akulov (1972), 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 microscopic phenomena. Supersymmetry with
7310-473: Was found to provide a fertile ground on which certain ramifications of SUSY can be explored in readily-accessible laboratory settings. Making use of the analogous mathematical structure of the quantum-mechanical Schrödinger equation and the wave equation governing the evolution of light in one-dimensional settings, one may interpret the refractive index distribution of a structure as a potential landscape in which optical wave packets propagate. In this manner,
7396-547: Was premature because various calculations were too optimistic about the limits of masses which would allow a supersymmetric extension of the Standard Model as a solution. 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. Theories with more than one supersymmetry transformation are known as extended supersymmetric theories. The more supersymmetry
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