A Minimal Supersymmetric Standard Model is a class of proposed supersymmetric extensions to the Standard Model . Minimal supersymmetry assumes that the interaction between particles conserves R-parity and every particle has one superpartner .
Fermions have boson superpartners, and bosons have fermion superpartners.
Particle type
Particle
Symbol
Spin
Superpartner
Symbol
Spin
Fermions
Quark
q
1
2
{\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}
Squark
q
~
{\displaystyle {\tilde {q}}}
0
Neutrino
ν
1
2
{\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}
Sneutrino
ν
~
{\displaystyle {\tilde {\nu }}}
0
Electron
e
1
2
{\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}
Selectron
e
~
{\displaystyle {\tilde {e}}}
0
Muon
μ
1
2
{\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}
Smuon
μ
~
{\displaystyle {\tilde {\mu }}}
0
Tau
τ
1
2
{\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}
Stau
τ
~
{\displaystyle {\tilde {\tau }}}
0
Bosons
W
W
1
Wino
W
~
{\displaystyle {\tilde {W}}}
1
2
{\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}
Z
Z
1
Zino
Z
~
{\displaystyle {\tilde {Z}}}
1
2
{\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}
Photon
γ
1
Photino
γ
~
{\displaystyle {\tilde {\gamma }}}
1
2
{\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}
Gluon
g
1
Gluino
g
~
{\displaystyle {\tilde {g}}}
1
2
{\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}
Higgs bosons
Higgs
h , A ,
H
0
{\displaystyle H^{0}}
H
+
/
−
{\displaystyle H^{+/-}}
0
Higgsinos
h
~
,
A
~
,
H
0
~
,
H
+
/
−
~
{\displaystyle {\tilde {h}},{\tilde {A}},{\tilde {H^{0}}},{\tilde {H^{+/-}}}}
1
2
{\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}
MSSM is an N=1 SUSY model in 3+1 Minkowski spacetime with
S
U
(
3
)
×
S
U
(
2
)
×
U
(
1
)
Z
6
{\displaystyle {\frac {SU(3)\times SU(2)\times U(1)}{\mathbb {Z} _{6}}}}
SU(3)xSU(2)xU(1) , supersymmetric gauge theory .
MSSM contains vector superfields associated with the gauge group. It also contains the following chiral superfields :
field multiplicity representation Z 2 -parityq 3
(
3
,
2
)
1
/
6
{\displaystyle (3,2)_{1/6}}
- uc 3
(
3
¯
,
1
)
−
2
/
3
{\displaystyle ({\bar {3}},1)_{-2/3}}
- dc 3
(
3
¯
,
1
)
1
/
3
{\displaystyle ({\bar {3}},1)_{1/3}}
- l 3
(
1
,
2
)
−
1
/
2
{\displaystyle (1,2)_{-1/2}}
- ec 3
(
1
,
1
)
1
{\displaystyle (1,1)_{1}}
- Hu 1
(
1
,
2
)
1
/
2
{\displaystyle (1,2)_{1/2}}
+ Hd 1
(
1
,
2
)
−
1
/
2
{\displaystyle (1,2)_{-1/2}}
+
The electroweak symmetry is broken using the Higgs mechanism . There are also soft SUSY breaking terms in the action . Note that there is a PAIR of Higgs doublets. This is because MSSM forbids complex conjugation in the Yukawa potential. See holomorphy (SUSY)
The permissible (renormalizable and invariant ) terms in the superpotential are Hu Hd , Hu quc , Hd qdc and Hd lec . The constant term, of course, is unphysical.
This is just one of the many cancelations to the quadratic divergence to the mass squared of the Higgs boson which occurs in MSSM .
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