Minimal Supersymmetric Standard Model

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	${\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}$	Squark	${\displaystyle {\tilde {q}}}$	0
	Neutrino	ν	${\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}$	Sneutrino	${\displaystyle {\tilde {\nu }}}$	0
	Electron	e	${\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}$	Selectron	${\displaystyle {\tilde {e}}}$	0
	Muon	μ	${\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}$	Smuon	${\displaystyle {\tilde {\mu }}}$	0
	Tau	τ	${\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}$	Stau	${\displaystyle {\tilde {\tau }}}$	0
Bosons	W	W	1	Wino	${\displaystyle {\tilde {W}}}$	${\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}$
	Z	Z	1	Zino	${\displaystyle {\tilde {Z}}}$	${\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}$
	Photon	γ	1	Photino	${\displaystyle {\tilde {\gamma }}}$	${\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}$
	Gluon	g	1	Gluino	${\displaystyle {\tilde {g}}}$	${\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}$
Higgs bosons	Higgs	h, A, ${\displaystyle H^{0}}$, ${\displaystyle H^{+/-}}$	0	Higgsinos	${\displaystyle {\tilde {h}},{\tilde {A}},{\tilde {H^{0}}},{\tilde {H^{+/-}}}}$	${\displaystyle {\begin{matrix}{\frac {1}{2}}\end{matrix}}}$

MSSM is an N=1 SUSY model in 3+1 Minkowski spacetime with ${\displaystyle {\frac {SU(3)\times SU(2)\times U(1)}{\mathbb {Z} _{6}}}}$. See 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	Z2-parity
q	3	${\displaystyle (3,2)_{1/6}}$	-
uc	3	${\displaystyle ({\bar {3}},1)_{-2/3}}$	-
dc	3	${\displaystyle ({\bar {3}},1)_{1/3}}$	-
l	3	${\displaystyle (1,2)_{-1/2}}$	-
ec	3	${\displaystyle (1,1)_{1}}$	-
Hu	1	${\displaystyle (1,2)_{1/2}}$	+
Hd	1	${\displaystyle (1,2)_{-1/2}}$	+

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 H_uH_d, H_uqu^c, H_dqd^c and H_dle^c. 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.

External links

• Particle Data Group review of MSSM and search for MSSM predicted particles