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| {{Beyond the Standard Model|expanded=[[Supersymmetry]]}}
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| The '''Minimal Supersymmetric Standard Model''' ('''MSSM''') is a minimal extension to the [[Standard Model]] that realizes [[supersymmetry]], although non-minimal extensions do exist. Supersymmetry pairs [[boson]]s with [[fermion]]s; therefore every Standard Model particle has a partner that has yet to be discovered. If the superparticles are found, it may be analogous to discovering [[dark matter]] <ref name="HitoshiMurayama">
| |
| {{cite arXiv
| |
| |author = Murayama, Hitoshi
| |
| |title = Supersymmetry phenomenology
| |
| |year = 2000
| |
| |arxiv = hep-ph/0002232
| |
| }}</ref> and depending on the details of what might be found, it could provide evidence for [[Grand Unified Theory|grand unification]] and might even, in principle, provide hints as to whether [[string theory]] describes nature. 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>
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| | |
| The MSSM was originally proposed in 1981 to stabilize the weak scale, solving the [[hierarchy problem]].<ref name="DimopoulosGeorgi">
| |
| {{cite journal
| |
| |author=S. Dimopoulos, H. Georgi
| |
| |year=1981
| |
| |title=Softly Broken Supersymmetry and SU(5)
| |
| |journal=[[Nuclear Physics B]]
| |
| |volume=193 |pages=150
| |
| |doi= 10.1016/0550-3213(81)90522-8
| |
| |bibcode = 1981NuPhB.193..150D }}</ref> The [[Higgs boson]] mass of the Standard Model is unstable to quantum corrections and the theory predicts that weak scale should be much weaker than what is observed to be. In the MSSM, the [[Higgs boson]] has a fermionic superpartner, the [[Higgsino]], that has the same mass as it would if supersymmetry were an exact symmetry. Because fermion masses are radiatively stable, the Higgs mass inherits this stability. However, in MSSM there is a need for more than one Higgs field, as described [[Minimal Supersymmetric Standard Model#MSSM Fields|below]].
| |
| | |
| The only unambiguous way to claim discovery of supersymmetry is to produce superparticles in the laboratory. Because superparticles are expected to be 100 to 1000 times heavier than the proton, it requires a huge amount of energy to make these particles that can only be achieved at particle accelerators. The [[Tevatron]] was actively looking for evidence of the production of supersymmetric particles before it was shut down on 30 September 2011. Most physicists believe that supersymmetry must be discovered at the [[Large Hadron Collider|LHC]] if it is responsible for stabilizing the weak scale. There are five classes of particle that superpartners of the Standard Model fall into: [[squark]]s, [[gluino]]s, [[chargino]]s, [[neutralino]]s, and [[slepton]]s. These superparticles have their interactions and subsequent decays described by the MSSM and each has characteristic signatures.
| |
| | |
| [[Image:MSSM Flavor Changing.svg|thumb|right|200px|An example of a flavor changing neutral current process in MSSM. A strange quark emits a bino, turning into a sdown-type quark, which then emits a Z boson and reabsorbs the bino, turning into a down quark. If the MSSM squark masses are flavor violating, such a process can occur.]]
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| | |
| The MSSM imposes [[R-parity]] to explain the [[proton decay|stability of the proton]]. It adds supersymmetry breaking by introducing explicit [[soft supersymmetry breaking]] operators into the Lagrangian that is communicated to it by some unknown (and unspecified) dynamics. This means that there are 120 new parameters in the MSSM. Most of these parameters lead to unnacceptable phenomenology such as large [[flavor changing neutral current]]s or large [[electric dipole moment]]s for the neutron and electron. To avoid these problems, the MSSM takes all of the soft supersymmetry breaking to be diagonal in flavor space and for all of the new [[CP-violation|CP violating]] phases to vanish.
| |
| | |
| ==Theoretical Motivations==
| |
| There are three principal motivations for the MSSM over other theoretical extensions of the Standard Model, namely:
| |
| * [[Naturalness (physics)|Naturalness]]
| |
| * [[Gauge theory|Gauge]] coupling unification
| |
| * [[Dark matter|Dark Matter]]
| |
| These motivations come out without much effort and they are the primary reasons why the MSSM is the leading candidate for a new theory to be discovered at collider experiments such as the [[Tevatron]] or the [[Large Hadron Collider|LHC]].
| |
| | |
| ===Naturalness===
| |
| [[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]] top [[squark]] [[Feynman diagram]]s in a [[supersymmetry|supersymmetric]] extension of the [[Standard Model]]]]
| |
| | |
| The original motivation for proposing the MSSM was to stabilize the Higgs mass to radiative corrections that are quadratically divergent in the Standard Model ([[hierarchy problem]]). In supersymmetric models, scalars are related to fermions and have the same mass. Since fermion masses are logarithmically divergent, scalar masses inherit the same radiative stability. The Higgs vacuum expectation value is related to the negative scalar mass in the Lagrangian. In order for the radiative corrections to the Higgs mass to not be dramatically larger than the actual value, the mass of the superpartners of the Standard Model should not be significantly heavier than the Higgs [[vacuum expectation value|VEV]]—roughly 100 GeV. This mass scale has been probed at the [[Tevatron]], and is now being more extensively explored at the [[Large Hadron Collider|LHC]].
| |
| | |
| === Gauge-Coupling Unification ===
| |
| If the superpartners of the Standard Model are near the TeV scale, then measured gauge couplings of the three gauge groups unify at high energies.<ref name="DimopoulosRabyWilczek">
| |
| {{cite journal
| |
| |author=S. Dimopoulos, S. Raby and F. Wilczek
| |
| |year=1981
| |
| |title=Supersymmetry and the Scale of Unification
| |
| |journal=[[Physical Review D]]
| |
| |volume=24 |pages=1681–1683
| |
| |doi=10.1103/PhysRevD.24.1681
| |
| |bibcode = 1981PhRvD..24.1681D
| |
| |issue=6 }}</ref>
| |
| <ref name="IbanezRoss">
| |
| {{cite journal
| |
| |author= L.E. Ibanez and G.G. Ross
| |
| |year= 1981
| |
| |title= Low-energy predictions in supersymmetric grand unified theories
| |
| |journal=[[Physics Letters B]]
| |
| |volume= 105 |pages= 439
| |
| |doi= 10.1016/0370-2693(81)91200-4
| |
| |bibcode = 1981PhLB..105..439I }}</ref>
| |
| <ref name="MarcianoSenjanovic">
| |
| {{cite journal
| |
| |author= W.J. Marciano and G. Senjanovic
| |
| |year= 1982
| |
| |title= Predictions of supersymmetric grand unified theories
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| |journal=[[Physical Review D]]
| |
| |volume= 25 |pages= 3092
| |
| |doi= 10.1103/PhysRevD.25.3092
| |
| |bibcode = 1982PhRvD..25.3092M }}</ref>
| |
| The [[Beta function (physics)|beta-function]]s for the MSSM gauge couplings are given by
| |
| | |
| {| class="wikitable" style="background:none"
| |
| ! Gauge Group
| |
| ! style="background:none" | <math>\alpha^{-1}(M_{Z^0})</math>
| |
| ! style="background:none" | <math>b_0^\mathrm{MSSM}</math>
| |
| |-
| |
| | SU(3) || 8.5 || <math>-3</math>
| |
| |-
| |
| | SU(2) || 29.6 || <math>+1</math>
| |
| |-
| |
| | U(1) || 59.2 || <math>+6\frac{3}{5}</math>
| |
| |}
| |
| | |
| where <math>\alpha^{-1}_{1}</math> is measured in SU(5) normalization—a factor of <math>\frac{3}{5}</math> different
| |
| than the Standard Model's normalization and predicted by [[Georgi-Glashow]] SU(5) .
| |
| | |
| The condition for gauge coupling unification at one loop is whether the following expression is satisfied | |
| <math>\frac{\alpha^{-1}_3 - \alpha^{-1}_2}{\alpha^{-1}_2-\alpha^{-1}_1} = \frac{b_{0\,3} - b_{0\,2}}{b_{0\,2} -b_{0\,1}}</math>.
| |
| | |
| Remarkably, this is precisely satisfied to experimental errors in the values of <math>\alpha^{-1}(M_{Z^0})</math>. There are two loop corrections and both TeV-scale and GUT-scale [[Renormalization group#Threshold effect|threshold corrections]] that alter this condition on gauge coupling unification, and the results of more extensive calculations reveal that gauge coupling unification occurs to an accuracy of 1%, though this is about 3 standard deviations from the theoretical expectations.
| |
| | |
| This prediction is generally considered as indirect evidence for both the MSSM and SUSY [[Grand unification theory|GUT]]s.<ref name="GKane">Gordon 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> It should be noted that gauge coupling unification does not necessarily imply grand unification and there exist other mechanisms to reproduce gauge coupling unification. However, if superpartners are found in the near future, the apparent success of gauge coupling unification would suggest that a supersymmetric grand unified theory is a promising candidate for high scale physics.
| |
| | |
| === Dark Matter ===
| |
| If [[R-parity]] is preserved, then the lightest superparticle ([[Lightest Supersymmetric Particle|LSP]]) of the MSSM is stable and is a [[Weakly interacting massive particle]] (WIMP) — i.e. it does not have electromagnetic or strong interactions. This makes the LSP a good [[dark matter]] candidate and falls into the category of [[cold dark matter]] (CDM) particle.
| |
| | |
| == Predictions of the MSSM Regarding Hadron Colliders ==
| |
| The [[Tevatron]] and [[Large Hadron Collider|LHC]] have active experimental programs searching for supersymmetric particles. Since both of these machines are [[hadron]] colliders — proton antiproton for the Tevatron and proton proton for the LHC — they search best for strongly interacting particles. Therefore most experimental signature involve production of [[squark]]s or [[gluino]]s. Since the MSSM has [[R-parity]], the lightest supersymmetric particle is stable and after the squarks and gluinos decay each decay chain will contain one LSP that will leave the detector unseen. This leads to the generic prediction that the MSSM will produce a '[[missing energy]]' signal from these particles leaving the detector.
| |
| | |
| === Neutralinos ===
| |
| There are four [[Neutralino]]s that are fermions and are electrically neutral, the lightest of which is typically stable. They are typically labeled {{SubatomicParticle|Neutralino 1}}, {{SubatomicParticle|Neutralino 2}}, {{SubatomicParticle|Neutralino 3}}, {{SubatomicParticle|Neutralino 4}} (although sometimes <math> \tilde{\chi}_1^0, \ldots, \tilde{\chi}_4^0</math> is used instead). These four states are mixtures of the [[Gaugino|Bino]] and the neutral [[Wino (particle)|Wino]] (which are the neutral electroweak [[Gaugino]]s), and the neutral [[Higgsinos]]. As the neutralinos are [[Majorana fermion]]s, each of them is identical with its [[antiparticle]]. Because these particles only interact with the weak vector bosons, they are not directly produced at hadron colliders in copious numbers. They primarily appear as particles in cascade decays of heavier particles usually originating from colored supersymmetric particles such as squarks or gluinos.
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| | |
| In [[R-parity]] conserving models, the lightest neutralino is stable and all supersymmetric cascades decays end up decaying into this particle which leaves the detector unseen and its existence can only be inferred by looking for unbalanced momentum in a detector.
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| | |
| The heavier neutralinos typically decay through a {{SubatomicParticle|Z boson0}} to a lighter neutralino or through a {{SubatomicParticle|W boson+-}} to chargino. Thus a typical decay is
| |
| {|
| |
| | {{SubatomicParticle|Neutralino 2}}
| |
| | →
| |
| | {{SubatomicParticle|Neutralino 1}}
| |
| | +
| |
| | {{SubatomicParticle|Z boson0}}
| |
| | colspan=6|
| |
| | →
| |
| | Missing energy
| |
| | +
| |
| |{{SubatomicParticle|Lepton+|link=yes}}
| |
| | +
| |
| | {{SubatomicParticle|Lepton-|link=yes}}
| |
| |---
| |
| | {{SubatomicParticle|Neutralino 2}}
| |
| | →
| |
| | {{SubatomicParticle|Chargino 1+-}}
| |
| | +
| |
| | {{SubatomicParticle|W boson-+}}
| |
| | →
| |
| | {{SubatomicParticle|Neutralino 1}}
| |
| | +
| |
| | {{SubatomicParticle|W boson+-}}
| |
| | +
| |
| | {{SubatomicParticle|W boson-+}}
| |
| | →
| |
| | Missing energy
| |
| | +
| |
| | {{SubatomicParticle|Lepton+}}
| |
| | +
| |
| | {{SubatomicParticle|Lepton-}}
| |
| |}
| |
| | |
| The mass splittings between the different Neutralinos will dictate which patterns of decays are allowed.
| |
| | |
| === Charginos ===
| |
| There are two [[Chargino]]s that are fermions and are electrically charged. They are typically labeled {{SubatomicParticle|Chargino 1+-}} and {{SubatomicParticle|Chargino 2+-}} (although sometimes <math>\tilde{\chi}_1^\pm</math> and <math>\tilde{\chi}_2^\pm</math> is used instead). The heavier chargino can decay through {{SubatomicParticle|Z boson0}} to the lighter chargino. Both can decay through a {{SubatomicParticle|W boson+-}} to neutralino.
| |
| | |
| === Squarks ===
| |
| The [[squark]]s are the scalar superpartners of the quarks and there is one version for each Standard Model quark. Due to phenomenological constraints from flavor changing neutral currents, typically the lighter two generations of squarks have to be nearly the same in mass and therefore are not given distinct names. The superpartners of the top and bottom quark can be split from the lighter squarks and are called ''stop'' and ''sbottom''.
| |
| | |
| On the other way, there may be a remarkable left-right mixing of the stops <math>\tilde{t}</math> and of the sbottoms <math>\tilde{b}</math> because of the high masses of the partner quarks top and bottom:
| |
| <ref name="Bartl">
| |
| {{cite arXiv
| |
| |year=2003
| |
| |title=Impact of SUSY CP Phases on Stop and Sbottom Decays in the MSSM
| |
| |class=hep-ph
| |
| |eprint=hep-ph/0306281
| |
| |last1=Bartl | first1=A.
| |
| |last2=Hesselbach | first2=S.
| |
| |last3=Hidaka | first3=K.
| |
| |last4=Kernreiter | first4=T.
| |
| |last5=Porod | first5=W.
| |
| }}</ref>
| |
| | |
| * <math>\tilde{t}_1 = e^{+i\phi} \cos(\theta) \tilde{t_L} + \sin(\theta) \tilde{t_R}</math>
| |
| * <math>\tilde{t}_2 = e^{-i\phi} \cos(\theta) \tilde{t_R} - \sin(\theta) \tilde{t_L}</math>
| |
| | |
| Same holds for bottom <math>\tilde{b}</math> with its own parameters <math>\phi</math> and <math>\theta</math>.
| |
| | |
| Squarks can be produced through strong interactions and therefore are easily produced at hadron colliders. They decay to quarks and neutralinos or charginos which further decay. In R-parity conserving scenarios, squarks are pair produced and therefore a typical signal is
| |
| * <math> \tilde{q}\tilde{\bar{q}} \rightarrow q \tilde{N}^0_1 \bar{q} \tilde{N}^0_1 \rightarrow </math> 2 jets + missing energy
| |
| * <math> \tilde{q}\tilde{\bar{q}} \rightarrow q \tilde{N}^0_2 \bar{q} \tilde{N}^0_1 \rightarrow q \tilde{N}^0_1 \ell \bar{\ell} \bar{q} \tilde{N}^0_1 \rightarrow</math> 2 jets + 2 leptons + missing energy
| |
| | |
| === Gluinos ===
| |
| Gluinos are [[Majorana fermion|Majorana]] fermionic partners of the [[gluon]] which means that they are their own antiparticles. They interact strongly and therefore can be produced significantly at the LHC. They can only decay to a quark and a squark and thus a typical gluino signal is
| |
| *<math> \tilde{g}\tilde{g}\rightarrow (q \tilde{\bar{q}}) (\bar{q} \tilde{q}) \rightarrow (q \bar{q} \tilde{N}^0_1) (\bar{q} q \tilde{N}^0_1) \rightarrow</math> 4 jets + Missing energy
| |
| | |
| Because gluinos are Majorana, gluinos can decay to either a quark+anti-squark or an anti-quark+squark with equal probability. Therefore pairs of gluinos can decay to
| |
| *<math> \tilde{g}\tilde{g}\rightarrow (\bar{q} \tilde{q}) (\bar{q} \tilde{q}) \rightarrow (q \bar{q} \tilde{C}^+_1) (q \bar{q} \tilde{C}^+_1) \rightarrow (q \bar{q} W^+) (q \bar{q} W^+) \rightarrow </math> 4 jets+ <math> \ell^+ \ell^+</math>+ Missing energy
| |
| | |
| This is a distinctive signature because it has same-sign di-leptons and has very little background in the Standard Model.
| |
| | |
| === Sleptons ===
| |
| Sleptons are the scalar partners of the [[lepton]]s of the Standard Model. They are not strongly interacting and therefore are not produced very often at hadron colliders unless they are very light.
| |
| | |
| Because of the high mass of the tau lepton there will be left-right mixing of the stau similar to that of stop and sbottom (see above).
| |
| | |
| Sfermions will typically be found in decays of a charginos and neutralinos if they are light enough to be a decay product
| |
| | |
| * <math>\tilde{C}^+\rightarrow \tilde{\ell}^+ \nu</math>
| |
| * <math> \tilde{N}^0 \rightarrow \tilde{\ell}^+ \ell^-</math>
| |
| | |
| == MSSM Fields ==
| |
| [[Fermion]]s have [[boson]]ic superpartners (called sfermions), and bosons have fermionic superpartners (called bosinos). For most of the Standard Model particles, doubling is very straightforward. However, for the Higgs boson, it is more complicated.
| |
| | |
| A single Higgsino (the fermionic superpartner of the Higgs boson) would lead to a [[gauge anomaly]] and would cause the theory to be inconsistent. However if two Higgsinos are added, there is no gauge anomaly. The simplest theory is one with two Higgsinos and therefore two scalar Higgs doublets.
| |
| Another reason for having two scalar Higgs doublets rather than one is in order to have [[Yukawa interaction|Yukawa couplings]] between the Higgs and both [[Quark#Flavour|down-type quark]]s and [[Quark#Flavour|up-type quark]]s; these are the terms responsible for the quarks' masses. In the Standard Model the [[Quark#Flavour|down-type quark]]s couple to the Higgs field (which has Y=-1/2) and the [[Quark#Flavour|up-type quark]]s to its [[complex conjugate]] (which has Y=+1/2). However in a supersymmetric theory this is not allowed, so two types of Higgs fields are needed.
| |
| | |
| {| class="wikitable" style="background:none"
| |
| !SM Particle type
| |
| !Particle
| |
| !Symbol
| |
| ![[spin (physics)|Spin]]
| |
| !R-Parity
| |
| !Superpartner
| |
| !Symbol
| |
| !Spin
| |
| !R-parity
| |
| |-
| |
| | rowspan="2" | Fermions
| |
| |[[Quark]]
| |
| |<math>q</math>
| |
| |<math> \begin{matrix} \frac{1}{2} \end{matrix} </math>
| |
| | +1
| |
| |[[Squark]]
| |
| |<math> \tilde{q} </math>
| |
| |0
| |
| | -1
| |
| |-
| |
| |[[Lepton]]
| |
| |<math>\ell</math>
| |
| |<math> \begin{matrix} \frac{1}{2} \end{matrix} </math>
| |
| | +1
| |
| |[[Slepton]]
| |
| |<math> \tilde{\ell} </math>
| |
| |0
| |
| | -1
| |
| |-
| |
| |-
| |
| | rowspan="3" | Bosons
| |
| |[[W and Z bosons|W]]
| |
| |<math>W</math>
| |
| |1
| |
| | +1
| |
| |[[Wino (particle)|Wino]]
| |
| |<math> \tilde{W} </math>
| |
| |<math> \begin{matrix} \frac{1}{2} \end{matrix} </math>
| |
| | -1
| |
| |-
| |
| |[[W and Z bosons|B]]
| |
| |<math>B</math>
| |
| |1
| |
| | +1
| |
| |[[Gaugino|Bino]]
| |
| |<math> \tilde{B} </math>
| |
| |<math> \begin{matrix} \frac{1}{2} \end{matrix} </math>
| |
| | -1
| |
| |-
| |
| |[[Gluon]]
| |
| |<math>g</math>
| |
| |1
| |
| | +1
| |
| |[[Gluino]]
| |
| |<math> \tilde{g} </math>
| |
| |<math> \begin{matrix} \frac{1}{2} \end{matrix} </math>
| |
| | -1
| |
| |-
| |
| |Higgs bosons
| |
| |[[Higgs Boson|Higgs]]
| |
| |<math>h_u, h_d</math>
| |
| |0
| |
| | +1
| |
| |[[Higgsinos]]
| |
| |<math> \tilde{h}_u, \tilde{h}_d </math>
| |
| |<math> \begin{matrix} \frac{1}{2} \end{matrix} </math>
| |
| | -1
| |
| |-
| |
| |}
| |
| | |
| ===MSSM Superfields===
| |
| In supersymmetric theories, every field and its superpartner can be written together as a [[superfield]]. The superfield formulation of supersymmetry is very convenient to write down manifestly supersymmetric theories (i.e. one does not have to tediously check that the theory is supersymmetric term by term in the Lagrangian). The MSSM contains [[vector superfield]]s associated with the Standard Model gauge groups which contain the vector bosons and associated gauginos. It also contains [[chiral superfield]]s for the Standard Model fermions and Higgs bosons (and their respective superpartners).
| |
| | |
| {| class="wikitable" style="background:none"
| |
| ! field
| |
| ! multiplicity
| |
| ! representation
| |
| ! '''Z'''<sub>2</sub>-parity
| |
| ! Standard Model particle
| |
| |-
| |
| | Q || 3 || <math>(3,2)_{\frac{1}{6}}</math> || − || [[Chirality (physics)|left-handed]] quark doublet
| |
| |-
| |
| | U<sup>c</sup> || 3 || <math>(\bar{3},1)_{-\frac{2}{3}}</math> || − || [[Chirality (physics)|right-handed]] [[Quark#Flavour|up-type anti-quark]]
| |
| |-
| |
| | D<sup>c</sup> || 3 || <math>(\bar{3},1)_{\frac{1}{3}}</math> || − || [[Chirality (physics)|right-handed]] [[Quark#Flavour|down-type anti-quark]]
| |
| |-
| |
| | L || 3 || <math>(1,2)_{-\frac{1}{2}}</math> || − || [[Chirality (physics)|left-handed]] lepton doublet
| |
| |-
| |
| | E<sup>c</sup> || 3 || <math>(1,1)_{1\frac{}{}}</math> || − || [[Chirality (physics)|right-handed]] anti-lepton
| |
| |-
| |
| | H<sub>u</sub> || 1 || <math>(1,2)_{\frac{1}{2}}</math> || + || Higgs
| |
| |-
| |
| | H<sub>d</sub> || 1 || <math>(1,2)_{-\frac{1}{2}}</math> || + || Higgs
| |
| |}
| |
| | |
| ==The MSSM Lagrangian==
| |
| The Lagrangian for the MSSM contains several pieces.
| |
| | |
| *The first is the Kähler potential for the matter and Higgs fields which produces the kinetic terms for the fields.
| |
| | |
| *The second piece is the gauge field superpotential that produces the kinetic terms for the gauge bosons and gauginos.
| |
| | |
| *The next term is the [[superpotential]] for the matter and Higgs fields. These produce the Yukawa couplings for the Standard Model fermions and also the mass term for the [[Higgsinos]]. After imposing [[R-parity]], the [[renormalizable]], [[gauge invariant]] operators in the superpotential are
| |
| | |
| <math>W_{}^{} = \mu H_u H_d+ y_u H_u Q U^c+ y_d H_d Q D^c + y_l H_d L E^c</math>
| |
| | |
| The constant term is unphysical in global supersymmetry (as opposed to [[supergravity]]).
| |
| | |
| ===Soft Susy Breaking===
| |
| {{main|Soft SUSY breaking}}
| |
| The last piece of the MSSM Lagrangian is the soft supersymmetry breaking Lagrangian. The vast majority of the parameters of the MSSM are in the susy breaking Lagrangian. The soft susy breaking are divided into roughly three pieces.
| |
| | |
| *The first are the gaugino masses
| |
| | |
| <math> \mathcal{L} \supset m_{\frac{1}{2}} \tilde{\lambda}\tilde{\lambda} + h.c.</math>
| |
| | |
| Where <math>\tilde{\lambda}</math> are the gauginos and <math>m_{\frac{1}{2}}</math> is different for the wino, bino and gluino.
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| *The next are the soft masses for the scalar fields
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| <math> \mathcal{L} \supset m^2_0 \phi^\dagger \phi</math>
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| where <math>\phi</math> are any of the scalars in the MSSM and <math>m_0</math> are <math>3\times 3</math> hermitean matrices for the squarks and sleptons of a given set of gauge quantum numbers. The [[eigenvalue]]s of these matrices are actually the masses squared, rather than the masses.
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| *There are the <math>A</math> and <math> B</math> terms which are given by
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| <math>\mathcal{L} \supset B_{\mu} h_u h_d + A h_u \tilde{q} \tilde{u^c}+ A h_d \tilde{q} \tilde{d^c} +A h_d \tilde{l} \tilde{e^c} + h.c.</math>
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| The <math>A</math> terms are <math>3\times 3</math> complex matrices much as the scalar masses are.
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| *Although not often mentioned with regard to soft terms, to be consistent with observation, one must also include Gravitino and Goldstino soft masses given by
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| <math> \mathcal{L} \supset m_{3/2}\Psi_{\mu}^{\alpha}(\sigma^{\mu\nu})_{\alpha}^{\beta}\Psi_{\beta} + m_{3/2}G^{\alpha}G_{\alpha}+h.c. </math>
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| The reason these soft terms are not often mentioned are that they arise through local supersymmetry and not global supersymmetry, although they are required otherwise if the Goldstino were massless it would contradict observation. The Goldstino mode is eaten by the Gravitino to become massive, through a gauge shift, which also absorbs the would-be "mass" term of the Goldstino.
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| ==Problems with the MSSM==
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| There are several problems with the MSSM — most of them falling into understanding the parameters.
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| * The [[mu problem]]: The supersymmetric [[Peter Higgs|Higgs]] mass parameter μ appears as the following term in the [[superpotential]]: μH<sub>u</sub>H<sub>d</sub>. It should have the same order of magnitude as the [[electroweak scale]], many orders of magnitude smaller than that of the [[planck scale]], which is the natural [[cutoff (physics)|cutoff]] scale. The soft supersymmetry breaking terms should also be of the same order of magnitude as the [[electroweak scale]]. This brings about a problem of [[Naturalness (particle physics)|naturalness]]: why are these scales so much smaller than the cutoff scale yet happen to fall so close to each other?
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| * Flavor universality of soft masses and A-terms: since no [[Flavour changing processes|flavor mixing]] additional to that predicted by the [[standard model]] has been discovered so far, the coefficients of the additional terms in the MSSM Lagrangian must be, at least approximately, [[flavor]] invariant (i.e. the same for all flavors).
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| * Smallness of CP violating phases: since no [[CP violation]] additional to that predicted by the [[standard model]] has been discovered so far, the additional terms in the MSSM Lagrangian must be, at least approximately, CP invariant, so that their CP violating phases are small.
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| ==Theories of Supersymmetry breaking==
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| A large amount of theoretical effort has been spent trying to understand the mechanism for soft [[supersymmetry breaking]] that produces the desired properties in the superpartner masses and interactions. The three most extensively studied mechanisms are:
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| ===Gravity-Mediated Supersymmetry Breaking===
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| Gravity-Mediated Supersymmetry Breaking is a method of communicating supersymmetry breaking to the supersymmetric Standard Model through gravitational interactions. It was the first method proposed to communicate supersymmetry breaking. In gravity-mediated supersymmetry-breaking models, there is a part of the theory that only interacts with the MSSM through gravitational interaction. This hidden sector of the theory breaks supersymmetry. Through the supersymmetric version of the [[Higgs mechanism]], the [[gravitino]], the supersymmetric version of the graviton, acquires a mass. After the gravitino has a mass, gravitational radiative corrections to soft masses are incompletely cancelled beneath the gravitino's mass.
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| It is currently believed that it is not generic to have a sector completely decoupled from the MSSM and there should be higher dimension operators that couple different sectors together with the higher dimension operators suppressed by the Planck scale. These operators give as large of a contribution to the soft supersymmetry breaking masses as the gravitational loops; therefore, today people usually consider gravity mediation to be gravitational sized direct interactions between the hidden sector and the MSSM.
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| [[MSUGRA#mSUGRA|mSUGRA]] stands for minimal supergravity. The construction of a realistic model of interactions within ''N'' = 1 [[supergravity]] framework where supersymmetry breaking is communicated through the supergravity interactions was carried out by [[Ali Chamseddine]], [[Richard Arnowitt]], and [[Pran Nath]] in 1982.<ref name="CAN">
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| {{cite journal
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| |author=A. Chamseddine, R. Arnowitt, P. Nath
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| |year=1982
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| |title=Locally Supersymmetric Grand Unification
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| |journal=[[Physical Review Letters]]
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| |volume=49 |pages=970–974
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| |doi=10.1103/PhysRevLett.49.970
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| |bibcode=1982PhRvL..49..970C
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| |issue=14
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| }}</ref> mSUGRA is one of the most widely investigated models of [[particle physics]] due to its predictive power requiring only 4 input parameters and a sign, to determine the low energy phenomenology from the scale of Grand Unification. The most widely used set of parameters is:
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| {| class="wikitable"
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| |-
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| ! Symbol !! Description
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| |-
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| | <math>m_0</math> || the common mass of the scalars (sleptons, squarks, Higgs bosons) at the Grand Unification scale
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| |-
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| | <math>m_{1/2}</math> || the common mass of the gauginos and higgsinos at the Grand Unification scale
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| |-
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| | <math>A_0</math> || the common trilinear coupling
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| |-
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| | <math>\tan \beta</math> || the ratio of the vacuum expectation values of the two Higgs doublets
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| |-
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| | <math>\mathrm{sign}(\mu)</math> || the sign of the higgsino mass parameter
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| |}
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| Gravity-Mediated Supersymmetry Breaking was assumed to be flavor universal because of the universality of gravity; however, in 1986 Hall, Kostelecky, and Raby <ref name="HallKosteleckyRaby">
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| {{cite journal
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| |author=L.J. Hall, V.A. Kostelecky, S. Raby
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| |year=1986
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| |title= New Flavor Violations in Supergravity Models
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| |journal=[[Nuclear Physics B]]
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| |volume=267 |pages=415
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| |doi=10.1016/0550-3213(86)90397-4
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| |bibcode = 1986NuPhB.267..415H
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| |issue=2 }}</ref> showed that Planck-scale physics that are necessary to generate the Standard-Model Yukawa couplings spoil the universality of the supersymmetry breaking.
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| ===Gauge Mediated Supersymmetry Breaking (GMSB)===
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| Gauge Mediated Supersymmetry Breaking is method of communicating supersymmetry breaking to the supersymmetric Standard Model through the Standard Model's gauge interactions. Typically a hidden sector breaks supersymmetry and communicates it to massive messenger fields that are charged under the Standard Model. These messenger fields induce a gaugino mass at one loop and then this is transmitted on to the scalar superpartners at two loops. The maximum Higg's boson mass predicted is just 121.5GeV.<ref name="arxiv.org">http://arxiv.org/pdf/1112.3028v3.pdf</ref> With the Higgs being discovered at 125GeV - this has likely been disproved.
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| ===Anomaly Mediated Supersymmetry Breaking (AMSB)===
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| Anomaly Mediated Supersymmetry Breaking is a special type of gravity mediated supersymmetry breaking that results in supersymmetry breaking being communicated to the supersymmetric Standard Model through the conformal anomaly.<ref name="RandallSundrum">
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| {{cite journal
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| |author=L. Randall, R. Sundrum
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| |year=1999
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| |title=Out of this world supersymmetry breaking
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| |journal=[[Nuclear Physics B]]
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| |volume=557 |pages=79–118
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| |doi=10.1016/S0550-3213(99)00359-4
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| |arxiv = hep-th/9810155 |bibcode = 1999NuPhB.557...79R }}</ref><ref name="GiudiceLutyMurayamaRattazzi">
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| {{cite journal
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| |author=G. Giudice, M. Luty, H. Murayama, R. Rattazzi
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| |year=1998
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| |title=Gaugino mass without singlets
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| |journal=[[Journal of High Energy Physics]]
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| |volume=9812 |pages=027
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| |doi=10.1088/1126-6708/1998/12/027
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| |arxiv = hep-ph/9810442 |bibcode = 1998JHEP...12..027G
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| |issue=12 }}</ref> The maximum Higg's boson mass predicted is just 121.0GeV.<ref name="arxiv.org"/> With the Higgs being discovered at 125GeV - this has likely been disproved.
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| ==See also==
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| *[[MSSM Higgs Mass]]
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| *[[Desert (particle physics)]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| *[http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=231444 MSSM on arxiv.org ]
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| * [http://arxiv.org/abs/hep-ph/9709356 A Supersymmetry Primer] by Stephen P. Martin
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| * [http://pdg.lbl.gov/2007/listings/s046.pdf Particle Data Group review of MSSM and search for MSSM predicted particles]
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| * [http://arxiv.org/abs/hep-ph/0505105 Supersymmetry and the MSSM: An Elementary Introduction] by Ian J R Aitchison
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| [[Category:Supersymmetry]]
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| [[Category:Particle physics]]
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| [[Category:Physics beyond the Standard Model]]
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