The Minimal Supersymmetric Standard Model
(MSSM) is an extension to the Standard Model
that realizes supersymmetry. MSSM is the minimal
supersymmetrical model as it considers only
"the [minimum] number of new particle states
and new interactions consistent with phenomenology".
Supersymmetry pairs bosons with fermions,
so every Standard Model particle has a superpartner
yet undiscovered. If we find these superparticles,
it equates to discovering such particles as
dark matter, could provide evidence for grand
unification, and provide hints as to whether
string theory describes nature. The failure
to find evidence for supersymmetry using the
Large Hadron Collider suggests a leaning to
abandon it.
== Background ==
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.
The Tevatron was actively looking for evidence
of the production of supersymmetric particles
before it was shut down on 30 September 2011.
Most physicists believe that supersymmetry
must be discovered at the 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 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 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 principal motivations for
the MSSM over other theoretical extensions
of the Standard Model, namely:
Naturalness
Gauge coupling unification
Dark MatterThese 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.
=== Naturalness ===
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.
In 2012, the Higgs particle was discovered
at the LHC, and its mass was found to be 125-126
GeV.
=== 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
where
α
1
−
1
{\displaystyle \alpha _{1}^{-1}}
is measured in SU(5) normalization—a factor
of
3
5
{\displaystyle {\frac {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 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 is about
3 standard deviations from the theoretical
expectations.
This prediction is generally considered as
indirect evidence for both the MSSM and SUSY
GUTs. It should be noted that gauge coupling
unification does not necessarily imply grand
unification and there exist other mechanisms
to reproduce gauge coupling unification. However,
if superpartners are found in the near future,
the apparent success of gauge coupling unification
would suggest that a supersymmetric grand
unified theory is a promising candidate for
high scale physics.
=== Dark matter ===
If R-parity is preserved, then the lightest
superparticle (LSP) of the MSSM is stable
and is a Weakly interacting massive particle
(WIMP) — i.e. it does not have electromagnetic
or strong interactions. This makes the LSP
a good dark matter candidate and falls into
the category of cold dark matter (CDM) particle.
== Predictions of the MSSM regarding hadron
colliders ==
The Tevatron and 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 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 the MSSM
will produce a 'missing energy' signal from
these particles leaving the detector.
=== Neutralinos ===
There are four neutralinos that are fermions
and are electrically neutral, the lightest
of which is typically stable. They are typically
labeled N͂01, N͂02, N͂03, N͂04 (although
sometimes
χ
~
1
0
,
…
,
χ
~
4
0
{\displaystyle {\tilde {\chi }}_{1}^{0},\ldots
,{\tilde {\chi }}_{4}^{0}}
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, 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 Z0 to a lighter neutralino or through a
W± to chargino. Thus a typical decay is
The mass splittings between the different
Neutralinos will dictate which patterns of
decays are allowed.
=== Charginos ===
There are two Charginos that are fermions
and are electrically charged. They are typically
labeled C
χ
~
{\displaystyle {\tilde {\chi }}}
±1 and C
χ
~
{\displaystyle {\tilde {\chi }}}
±2 (although sometimes
χ
~
1
±
{\displaystyle {\tilde {\chi }}_{1}^{\pm }}
and
χ
~
2
±
{\displaystyle {\tilde {\chi }}_{2}^{\pm }}
is used instead). The heavier chargino can
decay through Z0 to the lighter chargino.
Both can decay through a W± 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.
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 the high masses of the partner
quarks top and bottom:
t
~
1
=
e
+
i
ϕ
cos
⁡
(
θ
)
t
L
~
+
sin
⁡
(
θ
)
t
R
~
{\displaystyle {\tilde {t}}_{1}=e^{+i\phi
}\cos(\theta ){\tilde {t_{L}}}+\sin(\theta
){\tilde {t_{R}}}}
t
~
2
=
e
−
i
ϕ
cos
⁡
(
θ
)
t
R
~
−
sin
⁡
(
θ
)
t
L
~
{\displaystyle {\tilde {t}}_{2}=e^{-i\phi
}\cos(\theta ){\tilde {t_{R}}}-\sin(\theta
){\tilde {t_{L}}}}
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 a typical signal is
q
~
q
¯
~
→
q
N
~
1
0
q
¯
N
~
1
0
→
{\displaystyle {\tilde {q}}{\tilde {\bar {q}}}\rightarrow
q{\tilde {N}}_{1}^{0}{\bar {q}}{\tilde {N}}_{1}^{0}\rightarrow
}
2 jets + missing energy
q
~
q
¯
~
→
q
N
~
2
0
q
¯
N
~
1
0
→
q
N
~
1
0
ℓ
ℓ
¯
q
¯
N
~
1
0
→
{\displaystyle {\tilde {q}}{\tilde {\bar {q}}}\rightarrow
q{\tilde {N}}_{2}^{0}{\bar {q}}{\tilde {N}}_{1}^{0}\rightarrow
q{\tilde {N}}_{1}^{0}\ell {\bar {\ell }}{\bar
{q}}{\tilde {N}}_{1}^{0}\rightarrow }
2 jets + 2 leptons + missing energy
=== Gluinos ===
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
g
~
g
~
→
(
q
q
¯
~
)
(
q
¯
q
~
)
→
(
q
q
¯
N
~
1
0
)
(
q
¯
q
N
~
1
0
)
→
{\displaystyle {\tilde {g}}{\tilde {g}}\rightarrow
(q{\tilde {\bar {q}}})({\bar {q}}{\tilde {q}})\rightarrow
(q{\bar {q}}{\tilde {N}}_{1}^{0})({\bar {q}}q{\tilde
{N}}_{1}^{0})\rightarrow }
4 jets + Missing energyBecause 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
g
~
g
~
→
(
q
¯
q
~
)
(
q
¯
q
~
)
→
(
q
q
¯
C
~
1
+
)
(
q
q
¯
C
~
1
+
)
→
(
q
q
¯
W
+
)
(
q
q
¯
W
+
)
→
{\displaystyle {\tilde {g}}{\tilde {g}}\rightarrow
({\bar {q}}{\tilde {q}})({\bar {q}}{\tilde
{q}})\rightarrow (q{\bar {q}}{\tilde {C}}_{1}^{+})(q{\bar
{q}}{\tilde {C}}_{1}^{+})\rightarrow (q{\bar
{q}}W^{+})(q{\bar {q}}W^{+})\rightarrow }
4 jets+
ℓ
+
ℓ
+
{\displaystyle \ell ^{+}\ell ^{+}}
+ Missing energyThis 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 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 a charginos and neutralinos if they are
light enough to be a decay product.
C
~
+
→
ℓ
~
+
ν
{\displaystyle {\tilde {C}}^{+}\rightarrow
{\tilde {\ell }}^{+}\nu }
N
~
0
→
ℓ
~
+
ℓ
−
{\displaystyle {\tilde {N}}^{0}\rightarrow
{\tilde {\ell }}^{+}\ell ^{-}}
== MSSM fields ==
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 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.
=== MSSM superfields ===
In supersymmetric theories, every field and
its superpartner can be written together as
a superfield. The superfield formulation of
supersymmetry is very convenient to write
down manifestly supersymmetric theories (i.e.
one does not have to tediously check that
the theory is supersymmetric term by term
in the Lagrangian). The MSSM contains vector
superfields associated with the Standard Model
gauge groups which contain the vector bosons
and associated gauginos. It also contains
chiral superfields for the Standard Model
fermions and Higgs bosons (and their respective
superpartners).
=== MSSM Higgs Mass ===
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 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 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.
==== Formulas ====
The only susy-preserving operator that creates
a quartic coupling for the Higgs in 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
m
h
0
2
≤
m
Z
0
2
cos
2
⁡
2
β
{\displaystyle m_{h^{0}}^{2}\leq m_{Z^{0}}^{2}\cos
^{2}2\beta }
.
Since supersymmetry is broken, there are radiative
corrections to the quartic coupling that can
increase the Higgs mass. These dominantly
arise from the 'top sector'
m
h
0
2
≤
m
Z
0
2
cos
2
⁡
2
β
+
3
π
2
m
t
4
sin
4
⁡
β
v
2
log
⁡
m
t
~
m
t
{\displaystyle m_{h^{0}}^{2}\leq m_{Z^{0}}^{2}\cos
^{2}2\beta +{\frac {3}{\pi ^{2}}}{\frac {m_{t}^{4}\sin
^{4}\beta }{v^{2}}}\log {\frac {m_{\tilde
{t}}}{m_{t}}}}
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 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
L
=
y
t
m
t
~
a
h
u
q
~
3
u
~
3
c
{\displaystyle {\mathcal {L}}=y_{t}\,m_{\tilde
{t}}\,a\;h_{u}{\tilde {q}}_{3}{\tilde {u}}_{3}^{c}}
where
a
{\displaystyle a}
is a dimensionless number. This contributes
an additional term to the Higgs mass at loop
level, but is not logarithmically enhanced
m
h
0
2
≤
m
Z
0
2
cos
2
⁡
2
β
+
3
π
2
m
t
4
sin
4
⁡
β
v
2
(
log
⁡
m
t
~
m
t
+
a
2
(
1
−
a
2
/
12
)
)
{\displaystyle m_{h^{0}}^{2}\leq m_{Z^{0}}^{2}\cos
^{2}2\beta +{\frac {3}{\pi ^{2}}}{\frac {m_{t}^{4}\sin
^{4}\beta }{v^{2}}}\left(\log {\frac {m_{\tilde
{t}}}{m_{t}}}+a^{2}(1-a^{2}/12)\right)}
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 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 MSSM Lagrangian ==
The Lagrangian for the MSSM contains several
pieces.
The first is the Kähler potential for the
matter and Higgs fields which produces the
kinetic terms for the fields.
The second piece is the gauge field superpotential
that produces the kinetic terms for the gauge
bosons and gauginos.
The next term is the superpotential for the
matter and Higgs fields. These produce the
Yukawa couplings for the Standard Model fermions
and also the mass term for the Higgsinos.
After imposing R-parity, the renormalizable,
gauge invariant operators in the superpotential
are
W
=
μ
H
u
H
d
+
y
u
H
u
Q
U
c
+
y
d
H
d
Q
D
c
+
y
l
H
d
L
E
c
{\displaystyle W_{}^{}=\mu H_{u}H_{d}+y_{u}H_{u}QU^{c}+y_{d}H_{d}QD^{c}+y_{l}H_{d}LE^{c}}
The constant term is unphysical in global
supersymmetry (as opposed to supergravity).
=== 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
L
⊃
m
1
2
λ
~
λ
~
+
h.c.
{\displaystyle {\mathcal {L}}\supset m_{\frac
{1}{2}}{\tilde {\lambda }}{\tilde {\lambda
}}+{\text{h.c.}}}
Where
λ
~
{\displaystyle {\tilde {\lambda }}}
are the gauginos and
m
1
2
{\displaystyle m_{\frac {1}{2}}}
is different for the wino, bino and gluino.
The next are the soft masses for the scalar
fields
L
⊃
m
0
2
ϕ
†
ϕ
{\displaystyle {\mathcal {L}}\supset m_{0}^{2}\phi
^{\dagger }\phi }
where
ϕ
{\displaystyle \phi }
are any of the scalars in the MSSM and
m
0
{\displaystyle m_{0}}
are
3
×
3
{\displaystyle 3\times 3}
Hermitian matrices for the squarks and sleptons
of a given set of gauge quantum numbers. The
eigenvalues of these matrices are actually
the masses squared, rather than the masses.
There are the
A
{\displaystyle A}
and
B
{\displaystyle B}
terms which are given by
L
⊃
B
μ
h
u
h
d
+
A
h
u
q
~
u
c
~
+
A
h
d
q
~
d
c
~
+
A
h
d
l
~
e
c
~
+
h.c.
{\displaystyle {\mathcal {L}}\supset B_{\mu
}h_{u}h_{d}+Ah_{u}{\tilde {q}}{\tilde {u^{c}}}+Ah_{d}{\tilde
{q}}{\tilde {d^{c}}}+Ah_{d}{\tilde {l}}{\tilde
{e^{c}}}+{\text{h.c.}}}
The
A
{\displaystyle A}
terms are
3
×
3
{\displaystyle 3\times 3}
complex matrices much as the scalar masses
are.
Although not often mentioned with regard to
soft terms, to be consistent with observation,
one must also include Gravitino and Goldstino
soft masses given by
L
⊃
m
3
/
2
Ψ
μ
α
(
σ
μ
ν
)
α
β
Ψ
β
+
m
3
/
2
G
α
G
α
+
h.c.
{\displaystyle {\mathcal {L}}\supset m_{3/2}\Psi
_{\mu }^{\alpha }(\sigma ^{\mu \nu })_{\alpha
}^{\beta }\Psi _{\beta }+m_{3/2}G^{\alpha
}G_{\alpha }+{\text{h.c.}}}
The reason these soft terms are not often
mentioned are that they arise through local
supersymmetry and not global supersymmetry,
although they are required otherwise if the
Goldstino were massless it would contradict
observation. The Goldstino mode is eaten by
the Gravitino to become massive, through a
gauge shift, which also absorbs the would-be
"mass" term of the Goldstino.
== Problems with the MSSM ==
There are several problems with the MSSM — most
of them falling into understanding the parameters.
The mu problem: The Higgsino mass parameter
μ appears as the following term in the superpotential:
μHuHd. It should have the same order of magnitude
as the electroweak scale, many orders of magnitude
smaller than that of the Planck scale, which
is the natural cutoff scale. The soft supersymmetry
breaking terms should also be of the same
order of magnitude as the electroweak scale.
This brings about a problem of naturalness:
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 model has been discovered
so far, the coefficients of the additional
terms in the MSSM Lagrangian must be, at least
approximately, flavor invariant (i.e. the
same for all flavors).
Smallness of CP violating phases: since no
CP violation additional to that predicted
by the standard model has been discovered
so far, the additional terms in the MSSM Lagrangian
must be, at least approximately, CP invariant,
so that their CP violating phases are small.
== Theories of supersymmetry breaking ==
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
===
Gravity-mediated supersymmetry breaking is
a method of communicating supersymmetry breaking
to the supersymmetric Standard Model through
gravitational interactions. It was the first
method proposed to communicate supersymmetry
breaking. In gravity-mediated supersymmetry-breaking
models, there is a part of the theory that
only interacts with the MSSM through gravitational
interaction. This hidden sector of the theory
breaks supersymmetry. Through the supersymmetric
version of the Higgs mechanism, the gravitino,
the supersymmetric version of the graviton,
acquires a mass. After the gravitino has a
mass, gravitational radiative corrections
to soft masses are incompletely cancelled
beneath the gravitino's mass.
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. The most widely
used set of parameters is:
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. Requiring stop
squarks below 2 TeV, the maximum Higgs boson
mass predicted is just 121.5GeV. With the
Higgs being discovered at 125GeV - this model
requires stops above 2 TeV.
=== 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. Requiring
stop squarks below 2 TeV, the maximum Higgs
boson mass predicted is just 121.0GeV. With
the Higgs being discovered at 125GeV - this
scenario requires stops heavier than 2 TeV.
== Phenomenological MSSM (pMSSM) ==
The unconstrained MSSM has more than 100 parameters
in addition to the Standard Model parameters.
This makes any phenomenological analysis (e.g.
finding regions in parameter space consistent
with observed data) impractical. Under the
following three assumptions:
no new source of CP-violation
no Flavour Changing Neutral Currents
first and second generation universalityone
can reduce the number of additional parameters
to the following 19 quantities of the phenomenological
MSSM (pMSSM):
The large parameter space of pMSSM makes searches
in pMSSM extremely challenging and makes pMSSM
difficult to exclude.
== Experimental tests ==
=== Terrestrial detectors ===
XENON1T (a dark matter WIMP detector - being
commissioned in 2016) is expected to explore/test
supersymmetry candidates such as CMSSM.
== See also ==
Desert (particle physics
