Minimal Supersymmetric Standard Model

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

MSSM is an N=1 SUSY model in 3+1 Minkowski spacetime with $\frac{SU(3)\times SU(2) \times U(1)}{\mathbb{Z}_6}$ . 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	$(3,2) 1 / 6$	-
u^c	3	$(\bar{3},1)_{-2/3}$	-
d^c	3	$(\bar{3},1)_{1/3}$	-
l	3	$(1,2) - 1 / 2$	-
e^c	3	$(1,1) 1$	-
H_u	1	$(1,2) 1 / 2$	+
H_d	1	$(1,2) - 1 / 2$	+

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.