Minimal Supersymmetric Standard Model
Encyclopedia
The Minimal Supersymmetric Standard Model (MSSM) is the 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 these supersymmetric partners exist, it is likely that they will be observed at the Large Hadron Collider
, which began operations in 2009. If the superparticles are found, it is analogous to discovering antimatter
and depending on the details of what is found, it could provide evidence for grand unification and might even in principle provide hints as to whether string theory
describes nature.
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, 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. Currently the Tevatron
is actively looking for evidence of the production of supersymmetric particles. 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, gluino
s, chargino
s, neutralino
s, and sleptons. These superparticles have their interactions and subsequent decays described by 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 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 violating phases to vanish.
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 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 (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 VEV
-- roughly 100 GeV. This mass scale is being probed currently at the Tevatron
and will be more extensively explored at the LHC
.
where
is measured in SU(5) normalization—a factor of 
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
.
Remarkably, this is precisely satisfied to experimental errors in the values of
. 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 is about 3 standard deviations from the theoretical expectations.
This prediction is generally considered as indirect evidence for both the MSSM and SUSY GUT
s. 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.
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) particle.
and 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 squarks 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.
s that are fermions and are electrically neutral, the lightest of which is typically stable. They are typically labeled , , , (although sometimes
is used instead). These four states are mixtures of the Bino and the neutral 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.
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.
The heavier neutralinos typically decay through a to a lighter neutralino or through a to chargino. Thus a typical decay is
The mass splittings between the different Neutralinos will dictate which patterns of decays are allowed.
s that are fermions and are electrically charged. They are typically labeled and (although sometimes
and 
is used instead). The heavier chargino can decay through to the lighter chargino. Both can decay through a to neutralino.
On the other way, there may be a remakable left-right mixing of the stops
and of the sbottoms 
because of the high masses of the partner quarks top and bottom:
Same holds for bottom
with its own parameters 
and 
.
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. Squarks are typically pair produced and therefore a typical signal is
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 is a distinctive signature because it has same-sign di-leptons and has very little background in the Standard Model.
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
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 couplings
between the Higgs and both down-type quarks and up-type quarks; these are 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.
. 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 superfield
s for the Standard Model fermions and Higgs bosons (and their respective superpartners).
The constant term is unphysical in global supersymmetry (as opposed to supergravity
).
Where
are the gauginos and 
is different for the wino, bino and gluino.
where
are any of the scalars in the MSSM and 
are 
hermitean matrices for the squarks and sleptons of a given gauge quantum numbers. The eigenvalues of these matrices are actually the masses squared, rather than the masses.
The
terms are 
complex matrices much as the scalar masses are.
More recently physicists have become concerned about the non-discovery of the Higgs boson
, or any superpartner at LEP II or the Tevatron
; many nevertheless hold out hope on account of the possibility that the Large Hadron Collider
which began operation at CERN
in 2009 will discover it.
that produces the desired properties in the superpartner masses and interactions. The three most extensively studied mechanisms are:
, 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 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 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.
Gravity-Mediated Supersymmetry Breaking was assumed to be flavor universal because of the universality of gravity; however, in 1986 Hall, Kostelecky, and Raby showed that Planck-scale physics that are necessary to generate the Standard-Model Yukawa couplings spoil the universality of the supersymmetry breaking.
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
that realizes supersymmetry
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
, although non-minimal extensions do exist. Supersymmetry pairs boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
s with fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s; therefore every Standard Model particle has a partner that has yet to be discovered. If these supersymmetric partners exist, it is likely that they will be observed at the Large Hadron Collider
Large Hadron Collider
The Large Hadron Collider is the world's largest and highest-energy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....
, which began operations in 2009. If the superparticles are found, it is analogous to discovering antimatter
Antimatter
In particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...
and depending on the details of what is found, it could provide evidence for grand unification and might even in principle provide hints as to whether string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
describes nature.
The MSSM was originally proposed in 1981 to stabilize the weak scale, solving the hierarchy problem
Hierarchy problem
In theoretical physics, a hierarchy problem occurs when the fundamental parameters of some Lagrangian are vastly different than the parameters measured by experiment. This can happen because measured parameters are related to the fundamental parameters by a prescription known as renormalization...
. The Higgs boson
Higgs boson
The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
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
Higgs boson
The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
has a fermionic superpartner, the Higgsino
Higgsino
In particle physics, a Higgsino, symbol , is the hypothetical superpartner of the Higgs boson, as predicted by supersymmetry. The Higgsino is a Dirac fermion and that is a weak isodoublet with hypercharge half under the Standard Model gauge symmetries...
, 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 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. Currently the Tevatron
Tevatron
The Tevatron is a circular particle accelerator in the United States, at the Fermi National Accelerator Laboratory , just east of Batavia, Illinois, and is the second highest energy particle collider in the world after the Large Hadron Collider...
is actively looking for evidence of the production of supersymmetric particles. Most physicists believe that supersymmetry must be discovered at the LHC
Large Hadron Collider
The Large Hadron Collider is the world's largest and highest-energy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....
if it is responsible for stabilizing the weak scale. There are five classes of particle that superpartners of the Standard Model fall into: squarks, gluino
Gluino
A gluino is the hypothetical supersymmetric partner of a gluon. Gluinos are expected by supersymmetry theorists to be pair produced in particle accelerators such as the Large Hadron Collider if they exist....
s, chargino
Chargino
In particle physics, the chargino is a hypothetical particle which refers to the mass eigenstates of a charged superpartner, i.e. any new electrically charged fermion predicted by supersymmetry. They are linear combinations of the charged wino and charged higgsinos...
s, neutralino
Neutralino
In particle physics, the neutralino is a hypothetical particle predicted by supersymmetry. There are four neutralinos that are fermions and are electrically neutral, the lightest of which is typically stable...
s, and sleptons. These superparticles have their interactions and subsequent decays described by the MSSM and each has characteristic signatures.
R-parity
R-parity is a concept in particle physics. In the supersymmetric extension of the Standard Model, baryon number and lepton number are no longer conserved by all of the renormalizable couplings...
to explain the stability of the proton
Proton decay
In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron...
. 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
Flavor changing neutral current
In theoretical physics, flavor-changing neutral currents are expressions that change the flavor of a fermion current without altering its electric charge. If they occur in the Lagrangian, they may induce processes that have not been observed in experiment...
s or large electric dipole moment
Electric dipole moment
In physics, the electric dipole moment is a measure of the separation of positive and negative electrical charges in a system of charges, that is, a measure of the charge system's overall polarity with SI units of Coulomb-meter...
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 violating phases to vanish.
Theoretical Motivations
There are three principle motivations for the MSSM over other theoretical extensions of the Standard Model, namely:- NaturalnessNaturalness (physics)Naturalness is the property that all parameters appearing in a theory take values of order 1...
- GaugeGauge theoryIn physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
coupling unification - Dark MatterDark matterIn astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
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
Tevatron
The Tevatron is a circular particle accelerator in the United States, at the Fermi National Accelerator Laboratory , just east of Batavia, Illinois, and is the second highest energy particle collider in the world after the Large Hadron Collider...
or the LHC
Large Hadron Collider
The Large Hadron Collider is the world's largest and highest-energy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....
.
Naturalness
Hierarchy problem
In theoretical physics, a hierarchy problem occurs when the fundamental parameters of some Lagrangian are vastly different than the parameters measured by experiment. This can happen because measured parameters are related to the fundamental parameters by a prescription known as renormalization...
). 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 VEV
Vacuum expectation value
In quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...
-- roughly 100 GeV. This mass scale is being probed currently at the Tevatron
Tevatron
The Tevatron is a circular particle accelerator in the United States, at the Fermi National Accelerator Laboratory , just east of Batavia, Illinois, and is the second highest energy particle collider in the world after the Large Hadron Collider...
and will be more extensively explored at the LHC
Large Hadron Collider
The Large Hadron Collider is the world's largest and highest-energy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....
.
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. The beta-functions for the MSSM gauge couplings are given by| Gauge Group |  |
 |
|---|---|---|
| SU(3) | 8.5 |  |
| SU(2) | 29.6 |  |
| U(1) | 59.2 |  |
where
is measured in SU(5) normalization—a factor of differentthan 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
.Remarkably, this is precisely satisfied to experimental errors in the values of
. 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 is about 3 standard deviations from the theoretical expectations.This prediction is generally considered as indirect evidence for both the MSSM and SUSY GUT
Grand unification theory
The term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at high-energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single...
s. 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-parityR-parity
R-parity is a concept in particle physics. In the supersymmetric extension of the Standard Model, baryon number and lepton number are no longer conserved by all of the renormalizable couplings...
is preserved, then the lightest superparticle (LSP
Lightest Supersymmetric Particle
In particle physics, the Lightest Supersymmetric Particle is the generic name given to the lightest of the additional hypothetical particles found in supersymmetric models. In models with R-parity conservation, the LSP is stable. There is extensive observational evidence for an additional...
) 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
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
candidate and falls into the category of cold dark matter
Cold dark matter
Cold dark matter is the improvement of the big bang theory that contains the additional assumption that most of the matter in the Universe consists of material that cannot be observed by its electromagnetic radiation and whose constituent particles move slowly...
(CDM) particle.
Predictions of the MSSM Regarding Hadron Colliders
The TevatronTevatron
The Tevatron is a circular particle accelerator in the United States, at the Fermi National Accelerator Laboratory , just east of Batavia, Illinois, and is the second highest energy particle collider in the world after the Large Hadron Collider...
and LHC
Large Hadron Collider
The Large Hadron Collider is the world's largest and highest-energy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....
have active experimental programs searching for supersymmetric particles. Since both of these machines are hadron
Hadron
In particle physics, a hadron is a composite particle made of quarks held together by the strong force...
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 squarks or gluino
Gluino
A gluino is the hypothetical supersymmetric partner of a gluon. Gluinos are expected by supersymmetry theorists to be pair produced in particle accelerators such as the Large Hadron Collider if they exist....
s. Since the MSSM has R-parity
R-parity
R-parity is a concept in particle physics. In the supersymmetric extension of the Standard Model, baryon number and lepton number are no longer conserved by all of the renormalizable couplings...
, 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
Missing energy
In experimental particle physics, missing energy refers to energy which is not detected in a particle detector, but is not expected due to the laws of Conservation of Mass and Conservation of Momentum...
' signal from these particles leaving the detector.
Neutralinos
There are four NeutralinoNeutralino
In particle physics, the neutralino is a hypothetical particle predicted by supersymmetry. There are four neutralinos that are fermions and are electrically neutral, the lightest of which is typically stable...
s that are fermions and are electrically neutral, the lightest of which is typically stable. They are typically labeled , , , (although sometimes
is used instead). These four states are mixtures of the Bino and the neutral Wino (which are the neutral electroweak GauginoGaugino
In particle physics, a gaugino is the hypothetical superpartner of a gauge field, as predicted by gauge theory combined with supersymmetry. They are fermions.In the minimal supersymmetric extension of the standard model the following gauginos exist:...
s), and the neutral Higgsinos. As the neutralinos are Majorana fermion
Majorana fermion
In physics, a Majorana fermion is a fermion which is its own anti-particle. The term is used in opposition to Dirac fermion, which describes particles that differ from their antiparticles...
s, each of them is identical with its antiparticle
Antiparticle
Corresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The...
. 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
R-parity
R-parity is a concept in particle physics. In the supersymmetric extension of the Standard Model, baryon number and lepton number are no longer conserved by all of the renormalizable couplings...
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.
The heavier neutralinos typically decay through a to a lighter neutralino or through a to chargino. Thus a typical decay is
| → | + | → | Missing energy | + | + | |||||||||||
| → | + | → | + | + | → | Missing energy | + | + |
The mass splittings between the different Neutralinos will dictate which patterns of decays are allowed.
Charginos
There are two CharginoChargino
In particle physics, the chargino is a hypothetical particle which refers to the mass eigenstates of a charged superpartner, i.e. any new electrically charged fermion predicted by supersymmetry. They are linear combinations of the charged wino and charged higgsinos...
s that are fermions and are electrically charged. They are typically labeled and (although sometimes
and is used instead). The heavier chargino can decay through to the lighter chargino. Both can decay through a to neutralino.Squarks
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 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 remakable left-right mixing of the stops
and of the sbottoms because of the high masses of the partner quarks top and bottom:
Same holds for bottom
with its own parameters and .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. Squarks are typically pair produced and therefore a typical signal is
-
2 jets + missing energy -
2 jets + 2 leptons + missing energy
Gluinos
Gluinos are MajoranaMajorana
Majorana may refer to:* Majorana equation, a relativistic wave equation* Majorana fermion, a concept in particle physics* Majorana spinor, a concept in quantum field theory* Origanum majorana, a somewhat cold-sensitive perennial herb...
fermionic partners of the gluon
Gluon
Gluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
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
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
4 jets+ 
+ 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 leptonLepton
A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
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
MSSM Fields
FermionFermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s have boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
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
Gauge anomaly
In theoretical physics, a gauge anomaly is an example of an anomaly: it is an effect of quantum mechanics—usually a one-loop diagram—that invalidates the gauge symmetry of a quantum field theory; i.e...
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
Yukawa interaction
In particle physics, Yukawa's interaction, named after Hideki Yukawa, is an interaction between a scalar field \phi and a Dirac field \Psi of the typeV \approx g\bar\Psi \phi \Psi or g \bar \Psi \gamma^5 \phi \Psi ....
between the Higgs and both down-type quarks and up-type quarks; these are 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
Complex conjugate
In mathematics, complex conjugates are a pair of complex numbers, both having the same real part, but with imaginary parts of equal magnitude and opposite signs...
(which has Y=+1/2). However in a supersymmetric theory this is not allowed, so two types of Higgs fields are needed.
| SM Particle type | Particle | Symbol | Spin Spin (physics) In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,... |
R-Parity | Superpartner | Symbol | Spin | R-parity |
|---|---|---|---|---|---|---|---|---|
| Fermions | Quark Quark A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly... |
 |
 |
+1 | Squark |  |
0 | -1 |
| Lepton Lepton A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral... |
 |
 |
+1 | Slepton |  |
0 | -1 | |
| Bosons | W W and Z bosons The W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own... |
 |
1 | +1 | Wino |  |
 |
-1 |
| B W and Z bosons The W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own... |
 |
1 | +1 | Bino |  |
 |
-1 | |
| Gluon Gluon Gluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles.... |
 |
1 | +1 | Gluino Gluino A gluino is the hypothetical supersymmetric partner of a gluon. Gluinos are expected by supersymmetry theorists to be pair produced in particle accelerators such as the Large Hadron Collider if they exist.... |
 |
 |
-1 | |
| Higgs bosons | Higgs Higgs boson The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model... |
 |
0 | +1 | Higgsinos |  |
 |
-1 |
MSSM Superfields
In supersymmetric theories, every field and its superpartner can be written together as a superfieldSuperfield
In theoretical physics, one often analyzes theories with supersymmetry in which superfields play a very important role. In four dimensions, the simplest example - namely the minimal N=1 supersymmetry - may be written using a superspace with four extra fermionic coordinates...
. 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 superfield
Chiral superfield
In theoretical physics, one often analyzes theories with supersymmetry in which chiral superfields play an important role. In four dimensions, the minimal N=1 supersymmetry may be written using the notion of superspace...
s for the Standard Model fermions and Higgs bosons (and their respective superpartners).
| field | multiplicity | representation | Z2-parity | Standard Model particle |
|---|---|---|---|---|
| Q | 3 |  |
− | left-handed Chirality (physics) A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity... quark |
| Uc | 3 |  |
− | left-handed Chirality (physics) A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity... up-type anti-quark |
| Dc | 3 |  |
− | left-handed Chirality (physics) A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity... down-type anti-quark |
| L | 3 |  |
− | left-handed Chirality (physics) A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity... lepton |
| Ec | 3 |  |
− | left-handed Chirality (physics) A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity... charged anti-lepton |
| Hu | 1 |  |
+ | Higgs |
| Hd | 1 |  |
+ | 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 superpotentialSuperpotentialSuperpotential is a concept from particle physics' supersymmetry.-Example of superpotentiality:Let's look at the example of a one dimensional nonrelativistic particle with a 2D internal degree of freedom called "spin"...
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-parityR-parityR-parity is a concept in particle physics. In the supersymmetric extension of the Standard Model, baryon number and lepton number are no longer conserved by all of the renormalizable couplings...
, the renormalizable, gauge invariant operators in the superpotential are
The constant term is unphysical in global supersymmetry (as opposed to supergravity
Supergravity
In theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...
).
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
Where
are the gauginos and is different for the wino, bino and gluino.- The next are the soft masses for the scalar fields
where
are any of the scalars in the MSSM and are hermitean matrices for the squarks and sleptons of a given gauge quantum numbers. The eigenvalues of these matrices are actually the masses squared, rather than the masses.- Finally there are the
and 
terms which are given by
The
terms are complex matrices much as the scalar masses are.Problems with the MSSM
There are several problems with the MSSM — most of them falling into understanding the parameters.- The mu problemMu problemIn theoretical physics, the μ problem is a problem of supersymmetric theories, concerned with understanding the parameters of the theory.The supersymmetric Higgs mass parameter μ appears as the following term in the superpotential: μHuHd. It is necessary to provide a mass for the fermionic...
: The supersymmetric HiggsHiggsThe term Higgs appears in:* Alan Higgs, English businessman and philanthropist* Sir Derek Higgs, an English business leader and merchant banker* Eric Sidney Higgs, English archaeologist*Griffin Higgs...
mass parameter μ appears as the following term in the superpotentialSuperpotentialSuperpotential is a concept from particle physics' supersymmetry.-Example of superpotentiality:Let's look at the example of a one dimensional nonrelativistic particle with a 2D internal degree of freedom called "spin"...
: μHuHd. It should have the same order of magnitude as the electroweak scale, many orders of magnitude smaller than that of the planck scalePlanck scaleIn particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 1019 GeV at which quantum effects of gravity become strong...
, which is the natural 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 naturalnessNaturalness (particle physics)Naturalness is the property that all parameters appearing in a theory take values of order 1...
: why are these scales so much smaller than the cutoff scale yet happen to fall so close to each other? - Flavor universality of soft masses and A-terms: since no flavor mixing additional to that predicted by the standard modelStandard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
has been discovered so far, the coefficients of the additional terms in the MSSM Lagrangian must be, at least approximately, flavorFlavorFlavor or flavour is the sensory impression of a food or other substance, and is determined mainly by the chemical senses of taste and smell. The "trigeminal senses", which detect chemical irritants in the mouth and throat as well as temperature and texture, are also very important to the overall...
invariant (i.e. the same for all flavors). - Smallness of CP violating phases: since no CP violationCP violationIn particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...
additional to that predicted by the standard modelStandard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
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.
More recently physicists have become concerned about the non-discovery of the Higgs boson
Higgs boson
The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
, or any superpartner at LEP II or the Tevatron
Tevatron
The Tevatron is a circular particle accelerator in the United States, at the Fermi National Accelerator Laboratory , just east of Batavia, Illinois, and is the second highest energy particle collider in the world after the Large Hadron Collider...
; many nevertheless hold out hope on account of the possibility that the Large Hadron Collider
Large Hadron Collider
The Large Hadron Collider is the world's largest and highest-energy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....
which began operation at CERN
CERN
The European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
in 2009 will discover it.
Theories of Supersymmetry breaking
A large amount of theoretical effort has been spent trying to understand the mechanism for soft supersymmetry breakingSupersymmetry breaking
In particle physics, supersymmetry breaking is the process to obtain a seemingly non-supersymmetric physics from a supersymmetric theory which is a necessary step to reconcile supersymmetry with actual experiments. It is an example of spontaneous symmetry breaking...
that produces the desired properties in the superpartner masses and interactions. The three most extensively studied mechanisms are:
Gravity-Mediated Supersymmetry Breaking
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 mechanismHiggs mechanism
In particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking....
, the gravitino
Gravitino
The gravitino is the supersymmetric partner of the graviton, as predicted by theories combining general relativity and supersymmetry; i.e. supergravity theories...
, 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 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
Supergravity
In theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...
framework where supersymmetry breaking is communicated through the supergravity interactions was carried out by Ali Chamseddine, Richard Arnowitt
Richard Arnowitt
Richard Lewis Arnowitt is an American physicist known for his contributions to theoretical particle physics and to general relativity.Arnowitt is a Distinguished Professor at Texas A&M University, where he is a member of the Department of Physics....
, and Pran Nath
Pran Nath
Pran Nath is a theoretical physicist working at Northeastern University, with research focus in elementary particle physics. He holds a Matthews Distinguished University Professor chair.-Research:...
in 1982. mSUGRA is one of the most widely investigated models of particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
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.
Gravity-Mediated Supersymmetry Breaking was assumed to be flavor universal because of the universality of gravity; however, in 1986 Hall, Kostelecky, and Raby showed that Planck-scale physics that are necessary to generate the Standard-Model Yukawa couplings spoil the universality of the supersymmetry breaking.
Gauge Mediated Supersymmetry Breaking (GMSB)
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.Anomaly Mediated Supersymmetry Breaking (AMSB)
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.External links
- MSSM on arxiv.org
- A Supersymmetry Primer by Stephen P. Martin
- Particle Data Group review of MSSM and search for MSSM predicted particles
- Supersymmetry and the MSSM: An Elementary Introduction by Ian J R Aitchison