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111-675: The MSSM was originally proposed in 1981 to stabilize the weak scale, solving the hierarchy problem . 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,

222-703: A C 2 ⊕ C 3 {\displaystyle \mathbb {C} ^{2}\oplus \mathbb {C} ^{3}} splitting restricts SU(5) to S(U(2)×U(3)) , yielding matrices of the form with kernel { ( α , α − 3 I d 2 , α 2 I d 3 ) | α ∈ C , α 6 = 1 } ≅ Z 6 {\displaystyle \{(\alpha ,\alpha ^{-3}\mathrm {Id} _{2},\alpha ^{2}\mathrm {Id} _{3})|\alpha \in \mathbb {C} ,\alpha ^{6}=1\}\cong \mathbb {Z} _{6}} , hence isomorphic to

333-514: A Z 2 {\displaystyle \mathbb {Z} _{2}} matter parity to the chiral superfields with the matter fields having odd parity and the Higgs having even parity to protect the electroweak Higgs from quadratic radiative mass corrections (the hierarchy problem ). In the non-supersymmetric version the action is invariant under a similar Z 2 {\displaystyle \mathbb {Z} _{2}} symmetry because

444-897: A Φ + 3 b Φ 2 = λ 1   , {\displaystyle \ 2a\Phi +3b\Phi ^{2}=\lambda \mathbf {1} \ ,} where λ is a Lagrange multiplier. Up to an SU(5) (unitary) transformation, The three cases are called case I, II, and III and they break the gauge symmetry into   S U ( 5 ) ,   [ S U ( 4 ) × U ( 1 ) ] / Z 4   {\displaystyle \ SU(5),\ \left[SU(4)\times U(1)\right]/\mathbb {Z} _{4}\ } and   [ S U ( 3 ) × S U ( 2 ) × U ( 1 ) ] / Z 6 {\displaystyle \ \left[SU(3)\times SU(2)\times U(1)\right]/\mathbb {Z} _{6}} respectively (the stabilizer of

555-402: 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 couplings between the Higgs and both down-type quarks and up-type quarks ; these are

666-477: 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 superfields associated with the Standard Model gauge groups which contain the vector bosons and associated gauginos. It also contains chiral superfields for

777-409: A charginos and neutralinos if they are light enough to be a decay product. Fermions have bosonic 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

888-578: A gauge shift, which also absorbs the would-be "mass" term of the Goldstino. There are several problems with the MSSM—most of them falling into understanding the parameters. 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: Gravity-mediated supersymmetry breaking

999-415: A left-handed neutrino , C 0 ⊗ C ⊗ C {\displaystyle \mathbb {C} _{0}\otimes \mathbb {C} \otimes \mathbb {C} } . For the first exterior power ⋀ 1 C 5 ≅ C 5 {\displaystyle {\textstyle \bigwedge }^{1}\mathbb {C} ^{5}\cong \mathbb {C} ^{5}} ,

1110-616: A model with fewer parameters. In particle physics , the most important hierarchy problem is the question that asks why the weak force is 10 times as strong as gravity . Both of these forces involve constants of nature, the Fermi constant for the weak force and the Newtonian constant of gravitation for gravity. Furthermore, if the Standard Model is used to calculate the quantum corrections to Fermi's constant, it appears that Fermi's constant

1221-456: A number of articles where he showed that if the Universe is considered as a thin shell (a mathematical synonym for "brane") expanding in 5-dimensional space then it is possible to obtain one scale for particle theory corresponding to the 5-dimensional cosmological constant and Universe thickness, and thus to solve the hierarchy problem. It was also shown that four-dimensionality of the Universe

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1332-580: A prediction of the Georgi–Glashow model. The SM gauge fields can be embedded explicitly as well. For that we recall a gauge field transforms as an adjoint, and thus can be written as A μ a T a {\displaystyle A_{\mu }^{a}T^{a}} with T a {\displaystyle T^{a}} the S U ( 5 ) {\displaystyle SU(5)} generators. Now, if we restrict ourselves to generators with non-zero entries only in

1443-604: A quadratic term in the Higgs field, one must find a way to recover the breaking of electroweak symmetry through a non-null vacuum expectation value. This can be obtained using the Weinberg–Coleman mechanism with terms in the Higgs potential arising from quantum corrections. Mass obtained in this way is far too small with respect to what is seen in accelerator facilities and so a conformal Standard Model needs more than one Higgs particle. This proposal has been put forward in 2006 by Krzysztof Antoni Meissner and Hermann Nicolai and

1554-621: A supersymmetric grand unified theory is a promising candidate for high scale physics. If R-parity is preserved, then the lightest superparticle ( 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). The Tevatron and LHC have active experimental programs searching for supersymmetric particles. Since both of these machines are hadron colliders – proton antiproton for

1665-638: A triplet in SU(3), a singlet in SU(2), and under the Y = − ⁠ 1 / 3 ⁠ representation of U(1) (as α = α ); this matches a right-handed down quark , C − 1 3 ⊗ C ⊗ C 3 {\displaystyle \mathbb {C} _{-{\frac {1}{3}}}\otimes \mathbb {C} \otimes \mathbb {C} ^{3}} . The second power ⋀ 2 C 5 {\displaystyle {\textstyle \bigwedge }^{2}\mathbb {C} ^{5}}

1776-511: A typical signal is Gluinos are 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 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 This

1887-502: Is a distinctive signature because it has same-sign di-leptons and has very little background in the Standard Model. Sleptons are the scalar partners of the leptons 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). Sleptons will typically be found in decays of

1998-411: Is a hierarchy problem very similar to that of the Higgs boson mass problem, since the cosmological constant is also very sensitive to quantum corrections, but it is complicated by the necessary involvement of general relativity in the problem. Proposed solutions to the cosmological constant problem include modifying and/or extending gravity, adding matter with unvanishing pressure, and UV/IR mixing in

2109-394: Is a linear combination of the following terms: The first column is an Abbreviation of the second column (neglecting proper normalization factors), where capital indices are SU(5) indices, and i and j are the generation indices. The last two rows presupposes the multiplicity of   N c   {\displaystyle \ \mathrm {N} ^{\mathsf {c}}\ }

2220-413: 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

2331-435: Is about 3 standard deviations from the theoretical expectations. This prediction is generally considered as indirect evidence for both the MSSM and SUSY GUTs . 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

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2442-512: Is achieved in the Georgi–Glashow model via a fundamental 5 {\displaystyle \mathbf {5} } which contains the SM Higgs, with H + {\displaystyle H^{+}} and H 0 {\displaystyle H^{0}} the charged and neutral components of the SM Higgs, respectively. Note that the T i {\displaystyle T_{i}} are not SM particles and are thus

2553-403: Is allowed by the new vector bosons introduced from the adjoint representation of SU(5) which also contains the gauge bosons of the Standard Model forces. Since these new gauge bosons are in (3,2) −5/6 bifundamental representations , they violated baryon and lepton number. As a result, the new operators should cause protons to decay at a rate inversely proportional to their masses. This process

2664-453: Is an extension of this that creates 'superpartners' for all Standard Model particles. Without supersymmetry, a solution to the hierarchy problem has been proposed using just the Standard Model . The idea can be traced back to the fact that the term in the Higgs field that produces the uncontrolled quadratic correction upon renormalization is the quadratic one. If the Higgs field had no mass term, then no hierarchy problem arises. But by missing

2775-500: Is called dimension 6 proton decay and is an issue for the model, since the proton is experimentally determined to have a lifetime greater than the age of the universe. This means that an SU(5) model is severely constrained by this process. As well as these new gauge bosons, in SU(5) models, the Higgs field is usually embedded in a 5 representation of the GUT group. The caveat of this is that since

2886-465: Is communicated through the supergravity interactions was carried out by Ali Chamseddine , Richard Arnowitt , and Pran Nath in 1982. 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: Hierarchy problem In theoretical physics ,

2997-479: Is currently under scrutiny. But if no further excitation is observed beyond the one seen so far at LHC , this model would have to be abandoned. No experimental or observational evidence of extra dimensions has been officially reported. Analyses of results from the Large Hadron Collider severely constrain theories with large extra dimensions . However, extra dimensions could explain why the gravity force

3108-844: Is indeed equal to S U ( 3 ) × S U ( 2 ) × U ( 1 ) {\displaystyle SU(3)\times SU(2)\times U(1)} by noting that [ ⟨ 24 H ⟩ , G μ ] = [ ⟨ 24 H ⟩ , W μ ] = [ ⟨ 24 H ⟩ , B μ ] = 0 {\displaystyle [\langle \mathbf {24} _{H}\rangle ,G_{\mu }]=[\langle \mathbf {24} _{H}\rangle ,W_{\mu }]=[\langle \mathbf {24} _{H}\rangle ,B_{\mu }]=0} . Computation of similar commutators further shows that all other S U ( 5 ) {\displaystyle SU(5)} gauge fields acquire masses. To be precise,

3219-840: Is measured in SU(5) normalization—a factor of ⁠ 3 / 5 ⁠ 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 α 3 − 1 − α 2 − 1 α 2 − 1 − α 1 − 1 = b 0 3 − b 0 2 b 0 2 − b 0 1 {\displaystyle {\frac {\alpha _{3}^{-1}-\alpha _{2}^{-1}}{\alpha _{2}^{-1}-\alpha _{1}^{-1}}}={\frac {b_{0\,3}-b_{0\,2}}{b_{0\,2}-b_{0\,1}}}} . Remarkably, this

3330-681: Is not zero (i.e. that a sterile neutrino exists). The coupling   H u   10 i   10 j   {\displaystyle \ \mathrm {H} _{\mathsf {u}}\ \mathbf {10} _{i}\ \mathbf {10} _{j}\ } has coefficients which are symmetric in i and j . The coupling   N i c   N j c   {\displaystyle \ \mathrm {N} _{i}^{\mathsf {c}}\ \mathrm {N} _{j}^{\mathsf {c}}\ } has coefficients which are symmetric in i and j . The number of sterile neutrino generations need not be three, unless

3441-452: Is obtained via the formula ⋀ 2 ( V ⊕ W ) = ⋀ 2 V 2 ⊕ ( V ⊗ W ) ⊕ ⋀ 2 W 2 {\displaystyle {\textstyle \bigwedge }^{2}(V\oplus W)={\textstyle \bigwedge }^{2}V^{2}\oplus (V\otimes W)\oplus {\textstyle \bigwedge }^{2}W^{2}} . As SU(5) preserves

Minimal Supersymmetric Standard Model - Misplaced Pages Continue

3552-479: Is precisely satisfied to experimental errors in the values of α − 1 ( M Z 0 ) {\displaystyle \alpha ^{-1}(M_{Z^{0}})} . There are two loop corrections and both TeV-scale and GUT-scale 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

3663-923: Is simply Newton's law of gravitation . Note that Newton's constant G can be rewritten in terms of the Planck mass . G = ℏ c M P l 2 {\displaystyle G={\frac {\hbar c}{M_{\mathrm {Pl} }^{2}}}} If we extend this idea to δ extra dimensions, then we get: g ( r ) = − m e r M P l 3 + 1 + δ 2 + δ r 2 + δ ( 2 ) {\displaystyle \mathbf {g} (\mathbf {r} )=-m{\frac {\mathbf {e_{r}} }{M_{\mathrm {Pl} _{3+1+\delta }}^{2+\delta }r^{2+\delta }}}\qquad (2)} where M P l 3 + 1 + δ {\displaystyle M_{\mathrm {Pl} _{3+1+\delta }}}

3774-429: Is so weak, and why the expansion of the universe is faster than expected. If we live in a 3+1 dimensional world, then we calculate the gravitational force via Gauss's law for gravity : g ( r ) = − G m e r r 2 ( 1 ) {\displaystyle \mathbf {g} (\mathbf {r} )=-Gm{\frac {\mathbf {e_{r}} }{r^{2}}}\qquad (1)} which

3885-415: Is surprisingly large and is expected to be closer to Newton's constant unless there is a delicate cancellation between the bare value of Fermi's constant and the quantum corrections to it. More technically, the question is why the Higgs boson is so much lighter than the Planck mass (or the grand unification energy , or a heavy neutrino mass scale): one would expect that the large quantum contributions to

3996-414: Is the 3+1+ δ {\displaystyle \delta } dimensional Planck mass. However, we are assuming that these extra dimensions are the same size as the normal 3+1 dimensions. Let us say that the extra dimensions are of size n ≪ than normal dimensions. If we let r ≪ n , then we get (2). However, if we let r ≫ n , then we get our usual Newton's law. However, when r ≫ n ,

4107-753: Is the Higgs fields 5 H and   5 ¯ H   {\displaystyle \ {\overline {\mathbf {5} }}_{\mathrm {H} }\ } which are interesting. The two relevant superpotential terms here are   5 H   5 ¯ H   {\displaystyle \ 5_{\mathrm {H} }\ {\bar {5}}_{\mathrm {H} }\ } and   ⟨ 24 ⟩ 5 H   5 ¯ H   . {\displaystyle \ \langle 24\rangle 5_{\mathrm {H} }\ {\bar {5}}_{\mathrm {H} }~.} Unless there happens to be some fine tuning , we would expect both

4218-558: Is the leading candidate for a new theory to be discovered at collider experiments such as the Tevatron or the LHC . The original motivation for proposing the MSSM was to stabilize the Higgs mass to radiative corrections that are quadratically divergent in the Standard Model (the hierarchy problem ). In supersymmetric models, scalars are related to fermions and have the same mass. Since fermion masses are logarithmically divergent, scalar masses inherit

4329-465: Is the result of stability requirement since the extra component of the Einstein field equations giving the localized solution for matter fields coincides with one of the conditions of stability. Subsequently, there were proposed the closely related Randall–Sundrum scenarios which offered their solution to the hierarchy problem. In 2019, a pair of researchers proposed that IR/UV mixing resulting in

4440-405: Is the value that gets measured in an experiment. This happens because the effective value is related to the fundamental value by a prescription known as renormalization , which applies corrections to it. Typically the renormalized value of parameters are close to their fundamental values, but in some cases, it appears that there has been a delicate cancellation between the fundamental quantity and

4551-589: Is used instead). These four states are mixtures of the bino and the neutral wino (which are the neutral electroweak gauginos ), and the neutral higgsinos . As the neutralinos are Majorana fermions , 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. In R-parity conserving models,

Minimal Supersymmetric Standard Model - Misplaced Pages Continue

4662-414: Is used instead). The heavier chargino can decay through Z to the lighter chargino. Both can decay through a W to neutralino. The squarks 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

4773-409: Is within the maximal upper bound of approximately 130 GeV that loop corrections within the MSSM would raise the Higgs mass to. Proponents of the MSSM point out that a Higgs mass within the upper bound of the MSSM calculation of the Higgs mass is a successful prediction, albeit pointing to more fine tuning than expected. The only susy -preserving operator that creates a quartic coupling for the Higgs in

4884-559: The U ( 1 ) {\displaystyle U(1)} hypercharge (up to some normalization N {\displaystyle N} .) Using the embedding, we can explicitly check that the fermionic fields transform as they should. This explicit embedding can be found in Ref. or in the original paper by Georgi and Glashow. SU(5) breaking occurs when a scalar field (Which we will denote as 24 H {\displaystyle \mathbf {24} _{H}} ), analogous to

4995-532: The ADD model , also known as the model with large extra dimensions , an alternative scenario to explain the weakness of gravity relative to the other forces. This theory requires that the fields of the Standard Model are confined to a four-dimensional membrane , while gravity propagates in several additional spatial dimensions that are large compared to the Planck scale . In 1998–99 Merab Gogberashvili published on arXiv (and subsequently in peer-reviewed journals)

5106-512: The Dirac field and H {\displaystyle H} the Higgs field . Also, the mass of a fermion is proportional to its Yukawa coupling, meaning that the Higgs boson will couple most to the most massive particle. This means that the most significant corrections to the Higgs mass will originate from the heaviest particles, most prominently the top quark. By applying the Feynman rules , one gets

5217-417: The Higgs field and transforming in the adjoint of SU(5), acquires a vacuum expectation value (vev) proportional to the weak hypercharge generator When this occurs, SU(5) is spontaneously broken to the subgroup of SU(5) commuting with the group generated by Y . Using the embedding from the previous section, we can explicitly check that S U ( 5 ) {\displaystyle SU(5)}

5328-487: The Standard Model gauge groups SU(3) × SU(2) × U(1) are combined into a single simple gauge group SU(5) . The unified group SU(5) is then thought to be spontaneously broken into the Standard Model subgroup below a very high energy scale called the grand unification scale . Since the Georgi–Glashow model combines leptons and quarks into single irreducible representations , there exist interactions which do not conserve baryon number, although they still conserve

5439-444: The Standard Model 's true gauge group S U ( 3 ) × S U ( 2 ) × U ( 1 ) / Z 6 {\displaystyle SU(3)\times SU(2)\times U(1)/\mathbb {Z} _{6}} . For the zeroth power ⋀ 0 C 5 {\displaystyle {\textstyle \bigwedge }^{0}\mathbb {C} ^{5}} , this acts trivially to match

5550-693: The Y = ⁠ 1 / 2 ⁠ representation of U(1) (as weak hypercharge is conventionally normalized as α = α ); this matches a right-handed anti- lepton , C 1 2 ⊗ C 2 ∗ ⊗ C {\displaystyle \mathbb {C} _{\frac {1}{2}}\otimes \mathbb {C} ^{2*}\otimes \mathbb {C} } (as C 2 ≅ C 2 ∗ {\displaystyle \mathbb {C} ^{2}\cong \mathbb {C} ^{2*}} in SU(2)). The C 3 {\displaystyle \mathbb {C} ^{3}} transforms as

5661-427: The hierarchy problem is the problem concerning the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 10 times stronger than gravity . A hierarchy problem occurs when the fundamental value of some physical parameter, such as a coupling constant or a mass, in some Lagrangian is vastly different from its effective value, which

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5772-458: The Feynman rules, the correction (from both scalars) is: (Note that the contribution here is positive. This is because of the spin-statistics theorem, which means that fermions will have a negative contribution and bosons a positive contribution. This fact is exploited.) This gives a total contribution to the Higgs mass to be zero if we include both the fermionic and bosonic particles. Supersymmetry

5883-460: The Georgi–Glashow model. The fermion sector is then composed of an anti fundamental 5 ¯ {\displaystyle {\overline {\mathbf {5} }}} and an antisymmetric 10 {\displaystyle \mathbf {10} } . In terms of SM degrees of freedoms, this can be written as and with d i {\displaystyle d_{i}} and u i {\displaystyle u_{i}}

5994-465: The Higgs field has an associated Yukawa coupling λ f . The coupling with the Higgs field for fermions gives an interaction term L Y u k a w a = − λ f ψ ¯ H ψ {\displaystyle {\mathcal {L}}_{\mathrm {Yukawa} }=-\lambda _{f}{\bar {\psi }}H\psi } , with ψ {\displaystyle \psi } being

6105-434: The Higgs field is an SU(2) doublet, the remaining part, an SU(3) triplet, must be some new field - usually called D or T. This new scalar would be able to generate proton decay as well and, assuming the most basic Higgs vacuum alignment, would be massless so allowing the process at very high rates. While not an issue in the Georgi–Glashow model, a supersymmeterised SU(5) model would have additional proton decay operators due to

6216-456: The Higgs mass a free parameter in the MSSM (though not in non-minimal extensions). This means that Higgs mass is a prediction of the MSSM. The LEP II and the IV experiments placed a lower limit on the Higgs mass of 114.4  GeV . This lower limit is significantly above where the MSSM would typically predict it to be but does not rule out the MSSM; the discovery of the Higgs with a mass of 125 GeV

6327-410: The Higgs mass at loop level, but is not logarithmically enhanced by pushing a → 6 {\displaystyle a\rightarrow {\sqrt {6}}} (known as 'maximal mixing') it is possible to push the Higgs mass to 125 GeV without decoupling the top squark or adding new dynamics to the MSSM. As the Higgs was found at around 125 GeV (along with no other superparticles ) at

6438-448: The Higgs mass inherits this stability. However, in MSSM there is a need for more than one Higgs field, as described 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

6549-470: The Higgs mass. These dominantly arise from the 'top sector': where m t {\displaystyle m_{t}} is the top mass and m t ~ {\displaystyle m_{\tilde {t}}} is the mass of the top squark. This result can be interpreted as the RG running of the Higgs quartic coupling from the scale of supersymmetry to the top mass—however since

6660-508: The LHC, this strongly hints at new dynamics beyond the MSSM, such as the 'Next to Minimal Supersymmetric Standard Model' ( NMSSM ); and suggests some correlation to the little hierarchy problem . The Lagrangian for the MSSM contains several pieces. The constant term is unphysical in global supersymmetry (as opposed to supergravity ). The last piece of the MSSM Lagrangian is the soft supersymmetry breaking Lagrangian. The vast majority of

6771-567: The MSSM and each has characteristic signatures. The MSSM imposes R-parity to explain the 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 unacceptable phenomenology such as large flavor changing neutral currents or large electric dipole moments for

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6882-687: The MSSM arise for the D-terms of the SU(2) and U(1) gauge sector and the magnitude of the quartic coupling is set by the size of the gauge couplings. This leads to the prediction that the Standard Model-like Higgs mass (the scalar that couples approximately to the VEV) is limited to be less than the Z ;mass: Since supersymmetry is broken, there are radiative corrections to the quartic coupling that can increase

6993-604: The MSSM will produce a ' missing energy ' signal from these particles leaving the detector. There are four neutralinos that are fermions and are electrically neutral, the lightest of which is typically stable. They are typically labeled N͂ 1 , N͂ 2 , N͂ 3 , N͂ 4 (although sometimes χ ~ 1 0 , … , χ ~ 4 0 {\displaystyle {\tilde {\chi }}_{1}^{0},\ldots ,{\tilde {\chi }}_{4}^{0}}

7104-534: The SU(5) is embedded in a higher unification scheme such as SO(10) . The vacua correspond to the mutual zeros of the F and D terms. Let's first look at the case where the VEVs of all the chiral fields are zero except for Φ . The F zeros corresponds to finding the stationary points of W subject to the traceless constraint   T r [ Φ ] = 0   . {\displaystyle \ Tr[\Phi ]=0~.} So,   2

7215-457: The Standard Model and gravity. Some physicists have resorted to anthropic reasoning to solve the cosmological constant problem, but it is disputed whether anthropic reasoning is scientific. Georgi%E2%80%93Glashow In particle physics , the Georgi–Glashow model is a particular Grand Unified Theory (GUT) proposed by Howard Georgi and Sheldon Glashow in 1974. In this model,

7326-512: The Standard Model fermions and Higgs bosons (and their respective superpartners). The MSSM Higgs mass is a prediction of the Minimal Supersymmetric Standard Model. The mass of the lightest Higgs boson is set by the Higgs quartic coupling . Quartic couplings are not soft supersymmetry-breaking parameters since they lead to a quadratic divergence of the Higgs mass. Furthermore, there are no supersymmetric parameters to make

7437-448: The Standard Model's group action preserves the splitting C 5 ≅ C 2 ⊕ C 3 {\displaystyle \mathbb {C} ^{5}\cong \mathbb {C} ^{2}\oplus \mathbb {C} ^{3}} . The C 2 {\displaystyle \mathbb {C} ^{2}} transforms trivially in SU(3) , as a doublet in SU(2) , and under

7548-588: The Standard Model's representation F ⊕ F* of one generation of fermions and antifermions lies within ∧ C 5 {\displaystyle \wedge \mathbb {C} ^{5}} . Similar motivations apply to the Pati–Salam model, and to SO(10) , E6, and other supergroups of SU(5). Owing to its relatively simple gauge group S U ( 5 ) {\displaystyle SU(5)} , GUTs can be written in terms of vectors and matrices which allows for an intuitive understanding of

7659-517: The TeV scale). The gauge algebra 24 decomposes as This 24 is a real representation, so the last two terms need explanation. Both ( 3 , 2 ) − 5 6 {\displaystyle (3,2)_{-{\frac {5}{6}}}} and   ( 3 ¯ , 2 ) 5 6   {\displaystyle \ ({\bar {3}},2)_{\frac {5}{6}}\ } are complex representations. However,

7770-462: The Tevatron and proton proton for the LHC – they search best for strongly interacting particles. Therefore, most experimental signature involve production of squarks or gluinos. 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

7881-476: The VEV). In other words, there are at least three different superselection sections, which is typical for supersymmetric theories. Only case III makes any phenomenological sense and so, we will focus on this case from now onwards. It can be verified that this solution together with zero VEVs for all the other chiral multiplets is a zero of the F-terms and D-terms . The matter parity remains unbroken (right up to

7992-482: The adjoint Higgs to be absorbed. The other real half acquires a mass coming from the D-terms . And the other three components of the adjoint Higgs,   ( 8 , 1 ) 0 , ( 1 , 3 ) 0   {\displaystyle \ (8,1)_{0},(1,3)_{0}\ } and   ( 1 , 1 ) 0   {\displaystyle \ (1,1)_{0}\ } acquire GUT scale masses coming from self pairings of

8103-424: The breakdown of the effective quantum field theory could resolve the hierarchy problem. In 2021, another group of researchers showed that UV/IR mixing could resolve the hierarchy problem in string theory. In physical cosmology , current observations in favor of an accelerating universe imply the existence of a tiny, but nonzero cosmological constant . This problem, called the cosmological constant problem ,

8214-473: The canonical volume form of C 5 {\displaystyle \mathbb {C} ^{5}} , Hodge duals give the upper three powers by ⋀ p C 5 ≅ ( ⋀ 5 − p C 5 ) ∗ {\displaystyle {\textstyle \bigwedge }^{p}\mathbb {C} ^{5}\cong ({\textstyle \bigwedge }^{5-p}\mathbb {C} ^{5})^{*}} . Thus

8325-523: The different neutralinos will dictate which patterns of decays are allowed. There are two charginos that are fermions and are electrically charged. They are typically labeled C͂ 1 and C͂ 2 (although sometimes χ ~ 1 ± {\displaystyle {\tilde {\chi }}_{1}^{\pm }} and χ ~ 2 ± {\displaystyle {\tilde {\chi }}_{2}^{\pm }}

8436-675: The direct sum of both representation decomposes into two irreducible real representations and we only take half of the direct sum, i.e. one of the two real irreducible copies. The first three components are left unbroken. The adjoint Higgs also has a similar decomposition, except that it is complex. The Higgs mechanism causes one real HALF of the   ( 3 , 2 ) − 5 6   {\displaystyle \ (3,2)_{-{\frac {5}{6}}}\ } and   ( 3 ¯ , 2 ) 5 6   {\displaystyle \ ({\bar {3}},2)_{\frac {5}{6}}\ } of

8547-529: The evidence for neutrino oscillations , unless a way is found to introduce an infinitesimal Majorana coupling for the left-handed neutrinos. Since the homotopy group is this model predicts 't Hooft–Polyakov monopoles . Because the electromagnetic charge Q is a linear combination of some SU(2) generator with ⁠ Y / 2 ⁠ , these monopoles also have quantized magnetic charges Y , where by magnetic , here we mean magnetic electromagnetic charges. The minimal supersymmetric SU(5) model assigns

8658-1908: The flux in the extra dimensions becomes a constant, because there is no extra room for gravitational flux to flow through. Thus the flux will be proportional to n because this is the flux in the extra dimensions. The formula is: g ( r ) = − m e r M P l 3 + 1 + δ 2 + δ r 2 n δ − m e r M P l 2 r 2 = − m e r M P l 3 + 1 + δ 2 + δ r 2 n δ {\displaystyle {\begin{aligned}\mathbf {g} (\mathbf {r} )&=-m{\frac {\mathbf {e_{r}} }{M_{\mathrm {Pl} _{3+1+\delta }}^{2+\delta }r^{2}n^{\delta }}}\\[2pt]-m{\frac {\mathbf {e_{r}} }{M_{\mathrm {Pl} }^{2}r^{2}}}&=-m{\frac {\mathbf {e_{r}} }{M_{\mathrm {Pl} _{3+1+\delta }}^{2+\delta }r^{2}n^{\delta }}}\end{aligned}}} which gives: 1 M P l 2 r 2 = 1 M P l 3 + 1 + δ 2 + δ r 2 n δ ⟹ M P l 2 = M P l 3 + 1 + δ 2 + δ n δ {\displaystyle {\begin{aligned}{\frac {1}{M_{\mathrm {Pl} }^{2}r^{2}}}&={\frac {1}{M_{\mathrm {Pl} _{3+1+\delta }}^{2+\delta }r^{2}n^{\delta }}}\\[2pt]\implies \quad M_{\mathrm {Pl} }^{2}&=M_{\mathrm {Pl} _{3+1+\delta }}^{2+\delta }n^{\delta }\end{aligned}}} Thus

8769-461: The fundamental Planck mass (the extra-dimensional one) could actually be small, meaning that gravity is actually strong, but this must be compensated by the number of the extra dimensions and their size. Physically, this means that gravity is weak because there is a loss of flux to the extra dimensions. This section is adapted from "Quantum Field Theory in a Nutshell" by A. Zee. In 1998 Nima Arkani-Hamed , Savas Dimopoulos , and Gia Dvali proposed

8880-573: The high masses of the partner quarks top and bottom: A similar story holds for bottom b ~ {\displaystyle {\tilde {b}}} with its own parameters ϕ {\displaystyle \phi } and θ {\displaystyle \theta } . 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

8991-544: 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. mSUGRA stands for minimal supergravity. The construction of a realistic model of interactions within N = 1 supergravity framework where supersymmetry breaking

9102-423: The left and right-handed electron, respectively. In addition to the fermions, we need to break S U ( 3 ) × S U L ( 2 ) × U Y ( 1 ) → S U ( 3 ) × U E M ( 1 ) {\displaystyle SU(3)\times SU_{L}(2)\times U_{Y}(1)\rightarrow SU(3)\times U_{EM}(1)} ; this

9213-404: The left-handed up and down type quark, d i c {\displaystyle d_{i}^{c}} and u i c {\displaystyle u_{i}^{c}} their righthanded counterparts, ν {\displaystyle \nu } the neutrino, e {\displaystyle e} and e R {\displaystyle e_{R}}

9324-404: The lightest neutralino is stable and all supersymmetric cascade 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. The heavier neutralinos typically decay through a Z to a lighter neutralino or through a W to chargino. Thus a typical decay is Note that

9435-399: The matter fields are all fermionic and thus must appear in the action in pairs, while the Higgs fields are bosonic . As complex representations: A generic invariant renormalizable superpotential is a (complex) S U ( 5 ) × Z 2 {\displaystyle SU(5)\times \mathbb {Z} _{2}} invariant cubic polynomial in the superfields. It

9546-673: The model has led particle physicists to use it as the foundation for more complex models which yield longer proton lifetimes, particularly SO(10) in basic and SUSY variants. (For a more elementary introduction to how the representation theory of Lie algebras are related to particle physics, see the article Particle physics and representation theory .) Also, this model suffers from the doublet–triplet splitting problem . SU(5) acts on C 5 {\displaystyle \mathbb {C} ^{5}} and hence on its exterior algebra ∧ C 5 {\displaystyle \wedge \mathbb {C} ^{5}} . Choosing

9657-405: 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 violating phases to vanish. There are three principal motivations for the MSSM over other theoretical extensions of the Standard Model, namely: These motivations come out without much effort and they are the primary reasons why the MSSM

9768-605: The others that it needs a factor of 4 × 10 to allow it to be related to them in terms of effects, how did our universe come to be so exactly balanced when its forces emerged? In current particle physics , the differences between some parameters are much larger than this, so the question is even more noteworthy. One answer given by philosophers is the anthropic principle . If the universe came to exist by chance, and perhaps vast numbers of other universes exist or have existed, then life capable of physics experiments only arose in universes that, by chance, had very balanced forces. All of

9879-405: The parameters have values: 1.2, 1.31, 0.9 and a value near 4 × 10 . One might wonder how such figures arise. But in particular, might be especially curious about a theory where three values are close to one, and the fourth is so different; in other words, the huge disproportion we seem to find between the first three parameters and the fourth. We might also wonder if one force is so much weaker than

9990-483: The parameters of the MSSM are in the susy breaking Lagrangian. The soft susy breaking are divided into roughly three pieces. 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

10101-464: The power-law divergences of the radiative corrections to the Higgs mass and solves the hierarchy problem as long as the supersymmetric particles are light enough to satisfy the Barbieri – Giudice criterion. This still leaves open the mu problem , however. The tenets of supersymmetry are being tested at the LHC , although no evidence has been found so far for supersymmetry. Each particle that couples to

10212-470: The precise details of the quantum gravity , we cannot even address how this delicate cancellation between two large terms occurs. Therefore, researchers are led to postulate new physical phenomena that resolve hierarchy problems without fine-tuning. Suppose a physics model requires four parameters to produce a very high-quality working model capable of generating predictions regarding some aspect of our physical universe. Suppose we find through experiments that

10323-459: The quantum corrections to the Higgs mass squared from a fermion to be: The Λ U V {\displaystyle \Lambda _{\mathrm {UV} }} is called the ultraviolet cutoff and is the scale up to which the Standard Model is valid. If we take this scale to be the Planck scale, then we have the quadratically diverging Lagrangian. However, suppose there existed two complex scalars (taken to be spin 0) such that: Then by

10434-462: The quantum corrections. Hierarchy problems are related to fine-tuning problems and problems of naturalness. Over the past decade many scientists argued that the hierarchy problem is a specific application of Bayesian statistics . Studying renormalization in hierarchy problems is difficult, because such quantum corrections are usually power-law divergent, which means that the shortest-distance physics are most important. Because we do not know

10545-409: The quantum number B – L associated with the symmetry of the common representation. This yields a mechanism for proton decay , and the rate of proton decay can be predicted from the dynamics of the model. However, proton decay has not yet been observed experimentally, and the resulting lower limit on the lifetime of the proton contradicts the predictions of this model. Nevertheless, the elegance of

10656-459: 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 . In the other direction, there may be a remarkable left-right mixing of the stops t ~ {\displaystyle {\tilde {t}}} and of the sbottoms b ~ {\displaystyle {\tilde {b}}} because of

10767-451: The same radiative stability. The Higgs vacuum expectation value (VEV) 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 VEV – roughly 100 GeV. In 2012, the Higgs particle

10878-405: The square of the Higgs boson mass would inevitably make the mass huge, comparable to the scale at which new physics appears unless there is an incredible fine-tuning cancellation between the quadratic radiative corrections and the bare mass. The problem cannot even be formulated in the strict context of the Standard Model, for the Higgs mass cannot be calculated. In a sense, the problem amounts to

10989-554: The superpotential,   a Φ 2 + b < Φ > Φ 2   . {\displaystyle \ a\Phi ^{2}+b<\Phi >\Phi ^{2}~.} The sterile neutrinos, if any exist, would also acquire a GUT scale Majorana mass coming from the superpotential coupling ν  . Because of matter parity, the matter representations   5 ¯   {\displaystyle \ {\overline {\mathbf {5} }}\ } and 10 remain chiral. It

11100-464: 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. 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

11211-451: The terms responsible for the quarks' masses. In the Standard Model the down-type quarks couple to the Higgs field (which has Y=− ⁠ 1 / 2 ⁠ ) and the up-type quarks 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. In supersymmetric theories, every field and its superpartner can be written together as

11322-461: The top squark mass should be relatively close to the top mass, this is usually a fairly modest contribution and increases the Higgs mass to roughly the LEP ;II bound of 114 GeV before the top squark becomes too heavy. Finally there is a contribution from the top squark A-terms: where a {\displaystyle a} is a dimensionless number. This contributes an additional term to

11433-412: The triplet terms and the doublet terms to pair up, leaving us with no light electroweak doublets. This is in complete disagreement with phenomenology. See doublet-triplet splitting problem for more details. Unification of the Standard Model via an SU(5) group has significant phenomenological implications. Most notable of these is proton decay which is present in SU(5) with and without supersymmetry. This

11544-586: The unbroken subgroup is actually Under this unbroken subgroup, the adjoint 24 transforms as to yield the gauge bosons of the Standard Model plus the new X and Y bosons . See restricted representation . The Standard Model's quarks and leptons fit neatly into representations of SU(5). Specifically, the left-handed fermions combine into 3 generations of   5 ¯ ⊕ 10 ⊕ 1   . {\displaystyle \ {\overline {\mathbf {5} }}\oplus \mathbf {10} \oplus \mathbf {1} ~.} Under

11655-485: The unbroken subgroup these transform as to yield precisely the left-handed fermionic content of the Standard Model where every generation d , u , e , and ν correspond to anti- down-type quark , anti- up-type quark , anti- down-type lepton , and anti- up-type lepton , respectively. Also, q and ℓ {\displaystyle \ell } correspond to quark and lepton. Fermions transforming as 1 under SU(5) are now thought to be necessary because of

11766-512: The universes where the forces were not balanced did not develop life capable of asking this question. So if lifeforms like human beings are aware and capable of asking such a question, humans must have arisen in a universe having balanced forces, however rare that might be. A second possible answer is that there is a deeper understanding of physics that we currently do not possess. There might be parameters that we can derive physical constants from that have less unbalanced values, or there might be

11877-426: The upper 3 × 3 {\displaystyle 3\times 3} block, in the lower 2 × 2 {\displaystyle 2\times 2} block, or on the diagonal, we can identify with the S U ( 3 ) {\displaystyle SU(3)} colour gauge fields, with the weak S U ( 2 ) {\displaystyle SU(2)} fields, and with

11988-421: The worry that a future theory of fundamental particles, in which the Higgs boson mass will be calculable, should not have excessive fine-tunings. There have been many proposed solutions by many experienced physicists. Some physicists believe that one may solve the hierarchy problem via supersymmetry . Supersymmetry can explain how a tiny Higgs mass can be protected from quantum corrections. Supersymmetry removes

12099-427: The “Missing energy” byproduct represents the mass-energy of the neutralino (  N͂ 1  ) and in the second line, the mass-energy of a neutrino - antineutrino pair (  ν + ν  ) produced with the lepton and antilepton in the final decay, all of which are undetectable in individual reactions with current technology. The mass splittings between

12210-488: 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 LHC if it is responsible for stabilizing the weak scale. There are five classes of particle that superpartners of the Standard Model fall into: squarks , gluinos , charginos , neutralinos , and sleptons . These superparticles have their interactions and subsequent decays described by

12321-391: Was discovered at the LHC , and its mass was found to be 125–126 GeV. 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. The beta-functions for the MSSM gauge couplings are given by where α 1 − 1 {\displaystyle \alpha _{1}^{-1}}

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