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MSSM-overview.tex
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MSSM-overview.tex
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\documentclass[11pt]{article}
\usepackage[margin=0cm,nohead]{geometry}
\usepackage[active,tightpage]{preview}
\usepackage{tikz,amsmath,amssymb,bm,color,cancel}
%\usepackage{newtxtext}
%\usepackage{newtxmath}
\usetikzlibrary{shapes,arrows}
\usetikzlibrary{calc}
\usetikzlibrary{positioning}
\usetikzlibrary{decorations.pathreplacing}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{-1mm}
\begin{document}
\begin{tikzpicture}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Macros
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\!\!{\tt #1}
\\[6pt]
~{\large \color{blue} #2}
}
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\!\!{\tt #1}
\\[6pt]
~{\large \color{blue} #2}
\\[6pt]
~{#3}
}
\newcommand{\tr}{\mathsf{{\scriptscriptstyle T}}}
\newcommand{\ii}{\mathrm{i}}
\newcommand{\ee}{\operatorname{e}}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\op}[1]{\operatorname{#1}}
\newcommand{\pL}{\mathsf{\scriptscriptstyle L}}
\newcommand{\pR}{\mathsf{\scriptscriptstyle R}}
\newcommand{\pC}{\mathsf{\scriptscriptstyle C}}
\newcommand{\bPsi}{\boldsymbol{\Psi}}
\newcommand{\bPhi}{\boldsymbol{\Phi}}
\newcommand{\suY}{\mathrm{\scriptscriptstyle Y}}
\newcommand{\suL}{\mathrm{\scriptscriptstyle L}}
\newcommand{\suC}{\mathrm{\scriptscriptstyle C}}
\newcommand{\dbar}[1]{\overline{#1}}
\newcommand{\sbar}[1]{\bar{#1}}
\newcommand{\anti}[1]{\bar{#1}}
\newcommand{\quantNo}[3]{\mathbf{#1},\mathbf{#2},#3}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Box styles
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% R/C styles
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Paper W/H
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%\draw [yellow] (-0.5*\paperWidth,-0.5*\paperHeight) rectangle (0.5*\paperWidth,0.5*\paperHeight);
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%\draw [blue!40] (-20.5,14.5) rectangle (20.5,-14.5);
\node at (-20.5,14.5) {}; \node at (20.5,-14.5) {};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Title
\node [color=black] at (0,14.25) {
\huge\sf The field content of the Minimal Supersymmetric Standard Model (MSSM)
};
\node [anchor=north, color=black] at (0,13.9) {
by M.B.Kocic ~--~ Version 1.05 (2016-01-25) ~--~ SUSYRC-HT15
};
\pdfinfo {
% /CreationDate (D:20160121124500)
/Title (The field content of the Minimal Supersymmetric Standard Model (MSSM))
/Author (Mikica B Kocic)
/Subject (SUSYRC-HT15)
/Keywords (QFT MSSM Supersymmetry)
/Creator (TeX-TikZ)
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Vector superm.
\tikzset{myRow/.style={boxRed,R10}}
\node [myRow,C30,align=center,inner sep=0] at (-20.5,13) {
\textsf{\textbf{Vector}\\[-0.3em]supermultiplets}
};
\node [boxRed,inner sep=0,minimum height=7.5mm,minimum width=30mm,rotate=90] at (-20.5,9) {
\textsf{Gauge fields}
};
\node [myRow,C20,align=center] at (-17.5,13) {
Superfield
};
\node [myRow,C20,align=center] at (-15.5,13) {
Adj.\,repr.
};
\node [myRow,C35,align=center] at (-13.5,13) {
Spin-1\\[-0.2em]\small (gauge bosons)
};
\node [myRow,C35,align=center] at (-10,13) {
Spin-1/2\\[-0.2em]\small (gauginos)
};
\node [myRow,C15,align=center] at (-6.5,13) {
Aux.
};
\node [myRow,C85,align=center] at (-5,13) {
~\hfill Vector superfield (in Wess-Zumino gauge) \hfill~
};
\node [minimum height=5mm] at (-14.5,-2.75) {\small
N.B. Quantum numbers of the fields in the MSSM
are the same as in the SM.
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% U(1)
\tikzset{myRow/.style={boxYellow,R10}}
\node [myRow,C22c5,align=center] at (-19.75,12) {
$\op{U}(1)_\suY$
};
\node [myRow,C20,align=center] at (-17.5,12) {
$V_\suY$
};
\node [myRow,C20,align=center] at (-15.5,12) {
$\quantNo{1}{1}{0}$
};
\node [myRow,C35,align=center] at (-13.5,12) {
$B_\mu$,~ B-boson
};
\node [myRow,C35,align=center] at (-10,12) {
$\lambda_\suY \equiv \widetilde{B}$,~ bino
};
\node [myRow,C15,align=center] at (-6.5,12) {
$D_\suY$
};
\node [myRow,C85,align=left] at (-5,12) {\,
$ \displaystyle
V_\suY \equiv
\theta \, \sigma^\mu \, \sbar{\theta} \, B_\mu \,
+ \theta\theta\, \sbar{\theta}\sbar{\lambda}_\suY
+ \sbar{\theta}\sbar{\theta} \, \theta\lambda_\suY
+ \tfrac{1}{2} \theta\theta \, \sbar{\theta}\sbar{\theta} \, D_\suY
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% SU(2)
\tikzset{myRow/.style={boxYellow,R10}}
\node [myRow,C22c5,align=center] at (-19.75,11) {
$\op{SU}(2)_\suL$
};
\node [myRow,C20,align=center] at (-17.5,11) {
$V^i_\suL$
};
\node [myRow,C20,align=center] at (-15.5,11) {
$\quantNo{1}{3}{0}$
};
\node [myRow,C35,align=center] at (-13.5,11) {
$W^i_\mu$,~ W-bosons
};
\node [myRow,C35,align=center] at (-10,11) {
$\lambda^i_\suL \equiv \widetilde{W}^i$,~ winos
};
\node [myRow,C15,align=center] at (-6.5,11) {
$D^i_\suL$
};
\node [myRow,R10,C85,align=left] at (-5,11) {\,
$ \displaystyle
V^i_\suL \equiv
\theta \, \sigma^\mu \, \sbar{\theta} \, W^i_\mu \,
+ \theta\theta\, \sbar{\theta}\sbar{\lambda}^i_\suL
+ \sbar{\theta}\sbar{\theta} \, \theta\lambda^i_\suL
+ \tfrac{1}{2} \theta\theta \, \sbar{\theta}\sbar{\theta} \, D^i_\suL
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% SU(3)
\node [myRow,C22c5,align=center] at (-19.75,10) {
$\op{SU}(3)_\mathrm{\scriptscriptstyle C}$
};
\node [myRow,C20,align=center] at (-17.5,10) {
$V^a_\suC$
};
\node [myRow,C20,align=center] at (-15.5,10) {
$\quantNo{8}{1}{0}$
};
\node [myRow,C35,align=center] at (-13.5,10) {
$g^a_\mu$, gluons
};
\node [myRow,C35,align=center] at (-10,10) {
$\lambda^a_\suC \equiv \widetilde{g}^a$,~ gluinos
};
\node [myRow,C15,align=center] at (-6.5,10) {
$D^a_\suC$
};
\node [myRow,R10,C85,align=left] at (-5,10) {\,
$ \displaystyle
V^a_\suC \equiv
\theta \, \sigma^\mu \, \sbar{\theta} \, g^a_\mu \,
+ \theta\theta\, \sbar{\theta}\sbar{\lambda}^a_\suC
+ \sbar{\theta}\sbar{\theta} \, \theta\lambda^a_\suC
+ \tfrac{1}{2} \theta\theta \, \sbar{\theta}\sbar{\theta} \, D^a_\suC
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Lagrangian
\node [boxWhite,black!60!blue,minimum height=7.5mm,minimum width=162.5mm,text width=158mm,align=center] at (4.25,13) {
\color{white}\Large\textsf{\textbf{The MSSM Lagrangian}}
};
\tikzset{myRow/.style={boxRed,R10}}
\node [myRow,C80,align=center] at (4.25,12) {
The (matter) kinetic term
};
\node [myRow,C80,align=center] at (12.5,8.6) {
The Yukawa interaction term
};
\node [myRow,C80,align=center] at (12.5,12) {
The gauge kinetic term
};
\tikzset{myRow/.style={boxYellow,R10}}
\node [myRow,minimum height=50mm,C80,align=left] at (4.25,11) { \\[0.1em]
\hfill $ \displaystyle
\mathcal{L}^\mathrm{kin} =
\sum_{\Phi,\,gV}
\Phi^\dagger \ee^{2gV} \Phi \big\rvert_D
$ \hfill\! \\[0.3em]
$ gV $ runs over all the gauge superfields, \\[0.3em]
\hfill $
\{ \; g V_\suY, \; g_i V^i_\suL t^i, \; g_a V^a_\suC T^a \; \}
$,\hfill\!\\[0.5em]
$\Phi$ runs over all the matter superfields, \\[0.3em]
\hfill $
\{ \, Q_I,\, U_I,\, D_I,\, L_I,\, N_I,\, E_I,\, H_u,\, H_d \, \}
$, \hfill\!\\[0.3em]
in the appropriate respresentation where \\
$I=1,2,3$ is the family index.
};
\node [myRow,minimum height=16mm,C80,align=left] at (12.5,7.6) {
\\[0.1em]
\hfill $
\mathcal{L}^\mathrm{Yuk} =
\mathcal{W}(\Phi) \big\rvert_F + \mathrm{ h.c.}
$ \hfill\!\\[0.5em]
$\mathcal{W}$ is the superpotential (given below)
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Chiral superm.
\tikzset{myRow/.style={boxRed,R10}}
\node [myRow,C30,align=center,inner sep=0] at (-20.5,8.5) {
\textsf{\textbf{Chiral}\\[-0.3em]supermultiplets}
};
\node [boxRed,inner sep=0,minimum height=7.5mm,minimum width=70mm,rotate=90] at (-20.5,0.5) {
\textsf{Matter fields}
};
\node [boxRed,inner sep=0,minimum height=7.5mm,minimum width=30mm,rotate=90] at (-20.5,-2.5) {
\textsf{Higgs fields}
};
\node [myRow,C20,align=center] at (-17.5,8.5) {
Superfield
};
\node [myRow,C20,align=center] at (-15.5,8.5) {
Repr.
};
\node [myRow,C35,align=center] at (-13.5,8.5) {
Spin-1/2\\[-0.2em]\small (fermions)
};
\node [myRow,C35,align=center] at (-10,8.5) {
Spin-0\\[-0.2em]\small (sfermions)
};
\node [myRow,C15,align=center] at (-6.5,8.5) {
Aux.
};
\node [myRow,C85,align=center] at (-5,8.5) {
~\hfill Chiral superfield (in terms of $y^\mu = x^\mu - \ii\, \theta\sigma^\mu\sbar\theta$) \hfill~
};
\tikzset{myRow/.style={boxYellow,R10}}
\node [myRow,minimum height=35mm,C22c5,align=center,inner xsep=0] at (-19.75,7.5) {
\textsf{quarks,}\\
\textsf{s(calar) quarks}
};
\node [myRow,minimum height=35mm,C22c5,align=center,inner xsep=0] at (-19.75,4) {
\textsf{leptons,}\\
\textsf{s(calar) leptons}
};
\node [myRow,minimum height=30mm,C22c5,align=center,inner xsep=0] at (-19.75,0.5) {
\textsf{higgsinos,}\\
\textsf{higgs}
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Quark, L-doublet
\tikzset{myRow/.style={boxYellow,R15}}
\node [myRow,C20,align=center] at (-17.5,7.5) {
$ Q_I $
};
\node [myRow,C20,align=center] at (-15.5,7.5) {
$\quantNo{3}{2}{+\frac{1}{6}}$
};
\node [myRow,C35,align=center] at (-13.5,7.5) {
$ \renewcommand{\arraystretch}{1.2}
\begin{pmatrix} u_\pL \\ d_\pL \end{pmatrix}\!,~
\begin{pmatrix} \chi_u \\ \chi_d \end{pmatrix}
$
};
\node [myRow,C35,align=center] at (-10,7.5) {
$ \renewcommand{\arraystretch}{1.2}
\begin{pmatrix} \widetilde{u}_\pL \\ \widetilde{d}_\pL \end{pmatrix}\!,~
\begin{pmatrix} \widetilde{\phi}_u \\ \widetilde{\phi}_d \end{pmatrix}
$
};
\node [myRow,C15,align=center] at (-6.5,7.5) {
$ \renewcommand{\arraystretch}{1.2}
\begin{pmatrix} F_u \\ F_d \end{pmatrix}
$\!\!
};
\node [myRow,C85,align=left] at (-5,7.5) {~
$ \renewcommand{\arraystretch}{1.2}
Q = Q_1 =
\begin{pmatrix}
\widetilde{\phi}_u + \sqrt2 \, \theta \chi_u + \theta\theta \, F_u \\
\widetilde{\phi}_d + \sqrt2 \, \theta \chi_d + \theta\theta \, F_d
\end{pmatrix}
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Anti-u, L
\tikzset{myRow/.style={boxBlue,R10}}
\node [myRow,C20,align=center] at (-17.5,6) {
$U_I$ ($\anti{u}_I$)
};
\node [myRow,C20,align=center] at (-15.5,6) {
$\quantNo{\overline3}{1}{-\frac{2}{3}}$
};
\node [myRow,C35,align=center] at (-13.5,6) {
$\anti{u}_\pL = (u_\pR)^\pC$,
$\chi_{\anti{u}}$
};
\node [myRow,C35,align=center] at (-10,6) {
$\widetilde{\anti{u}}_\pL$, $\widetilde{\phi}_{\anti{u}}$
};
\node [myRow,C15,align=center] at (-6.5,6) {
$F_{\anti{u}}$
};
\node [myRow,C85,align=left] at (-5,6) {~
$ \anti{u} = U_1 =
\widetilde{\phi}_{\anti{u}}
+ \sqrt2\, \theta \chi_{\anti{u}}
+ \theta\theta \, F_{\anti{u}}
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Anti-d, L
\tikzset{myRow/.style={boxBlue,R10}}
\node [myRow,C20,align=center] at (-17.5,5) {
$D_I$ ($\anti{d}_I$)
};
\node [myRow,C20,align=center] at (-15.5,5) {
$\overline{\mathbf{3}}, \mathbf{1}, +\frac{1}{3}$
};
\node [myRow,C35,align=center] at (-13.5,5) {
$\anti{d}_\pL = (d_\pR)^\pC$,
$\chi_{\anti{d}}$
};
\node [myRow,C35,align=center] at (-10,5) {
$\widetilde{\anti{d}}_\pL$, $\widetilde{\phi}_{\anti{d}}$
};
\node [myRow,C15,align=center] at (-6.5,5) {
$F_{\anti{d}}$
};
\node [myRow,C85,align=left] at (-5,5) {~
$ \anti{d} = D_1 =
\widetilde{\phi}_{\anti{d}}
+ \sqrt2\, \theta \chi_{\anti{d}}
+ \theta\theta \, F_{\anti{d}}
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Lepton, L-doublet
\tikzset{myRow/.style={boxYellow,R15}}
\node [myRow,C20,align=center] at (-17.5,4) {
$ L_I $
};
\node [myRow,C20,align=center] at (-15.5,4) {
$\quantNo{1}{2}{-\frac{1}{2}}$
};
\node [myRow,C35,align=center] at (-13.5,4) {
$ \renewcommand{\arraystretch}{1.2}
\begin{pmatrix} \nu_{e\pL} \\ e_\pL \end{pmatrix}\!,~
\begin{pmatrix} \chi_{\nu_e} \\ \chi_e \end{pmatrix}
$
};
\node [myRow,C35,align=center] at (-10,4) {
$ \renewcommand{\arraystretch}{1.2}
\begin{pmatrix} \widetilde{\nu}_{e\pL} \\ \widetilde{e}_\pL \end{pmatrix}\!,~
\begin{pmatrix} \widetilde{\phi}_{\nu_e} \\ \widetilde{\phi}_e \end{pmatrix}
$
};
\node [myRow,C15,align=center] at (-6.5,4) {
$ \renewcommand{\arraystretch}{1.2}
\begin{pmatrix} F_{\nu_e} \\ F_e \end{pmatrix}
$\!\!
};
\node [myRow,C85,align=left] at (-5,4) {~
$ \renewcommand{\arraystretch}{1.2}
L = L_1 =
\begin{pmatrix}
\widetilde{\phi}_{\nu_e} + \sqrt2\, \theta \chi_{\nu_e} + \theta\theta \, F_{\nu_e} \\
\widetilde{\phi}_e + \sqrt2\, \theta\chi_e + \theta\theta \, F_e
\end{pmatrix}
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Antineutrino, L
\tikzset{myRow/.style={boxGray,R10}}
\node [myRow,C20,align=center] at (-17.5,2.5) {
$N_I$ ($\anti{\nu}_I$)
};
\node [myRow,C20,align=center] at (-15.5,2.5) {
$\quantNo{1}{1}{0}$
};
\node [myRow,C35,align=center] at (-13.5,2.5) {
$\anti{\nu}_{e\pL} = (\nu_{e\pR})^\pC$,
$\chi_{\anti{\nu}_e}$
};
\node [myRow,C35,align=center] at (-10,2.5) {
$\widetilde{\anti{\nu}}_{e\pL}$, $\widetilde{\phi}_{\anti{\nu}_e}$
};
\node [myRow,C15,align=center] at (-6.5,2.5) {
$F_{\anti{\nu}_e}$
};
\node [myRow,C85,align=left] at (-5,2.5) {~
$ \anti{\nu} = N_1 =
\widetilde{\phi}_{\anti{\nu}_e}
+ \sqrt2\, \theta \chi_{\anti{\nu}_e}
+ \theta\theta \, F_{\anti{\nu}_e}
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Positron, L
\tikzset{myRow/.style={boxBlue,R10}}
\node [myRow,C20,align=center] at (-17.5,1.5) {
$E_I$ ($\anti{e}_I$)
};
\node [myRow,C20,align=center] at (-15.5,1.5) {
$\quantNo{1}{1}{+1}$
};
\node [myRow,C35,align=center] at (-13.5,1.5) {
$\anti{e}_\pL = (e_\pR)^\pC$,
$\chi_{\anti{e}}$
};
\node [myRow,C35,align=center] at (-10,1.5) {
$\widetilde{\anti{e}}_\pL$, $\widetilde{\phi}_{\anti{e}}$
};
\node [myRow,C15,align=center] at (-6.5,1.5) {
$F_{\anti{e}}$
};
\node [myRow,C85,align=left] at (-5,1.5) {~
$ \anti{e} = E_1 =
\widetilde{\phi}_{\anti{e}}
+ \sqrt2\, \theta \chi_{\anti{e}}
+ \theta\theta \, F_{\anti{e}}
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% u-Higgs, L-doublet
\tikzset{myRow/.style={boxYellow,R15}}
\node [myRow,C20,align=center] at (-17.5,0.5) {
$ H_u $
};
\node [myRow,C20,align=center] at (-15.5,0.5) {
$\quantNo{1}{2}{+\frac{1}{2}}$
};
\node [myRow,C35,align=center] at (-13.5,0.5) {
$ \renewcommand{\arraystretch}{1.2}
\begin{pmatrix} \widetilde{H}^+_u \\ \widetilde{H}^0_u \end{pmatrix}
$
};
\node [myRow,C35,align=center] at (-10,0.5) {
$ \renewcommand{\arraystretch}{1.2}
\begin{pmatrix} H^+_u \\ H^0_u \end{pmatrix}
$
};
\node [myRow,C15,align=center] at (-6.5,0.5) {
$ \renewcommand{\arraystretch}{1.2}
\begin{pmatrix} F^+_{H_u} \\ F^0_{H_u} \end{pmatrix}
$\!\!
};
\node [myRow,C85,align=left] at (-5,0.5) {~
$ \renewcommand{\arraystretch}{1.2}
H_u =
\begin{pmatrix}
H^+_u + \sqrt2\, \theta \widetilde{H}^+_u + \theta\theta \, F^+_{H_u} \\
H^0_u + \sqrt2\, \theta \widetilde{H}^0_u + \theta\theta \, F^0_{H_u}
\end{pmatrix}
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% d-Higgs, L-doublet
\tikzset{myRow/.style={boxYellow,R15}}
\node [myRow,C20,align=center] at (-17.5,-1) {
$ H_d $
};
\node [myRow,C20,align=center] at (-15.5,-1) {
$\quantNo{1}{2}{-\frac{1}{2}}$
};
\node [myRow,C35,align=center] at (-13.5,-1) {
$ \renewcommand{\arraystretch}{1.2}
\begin{pmatrix} \widetilde{H}^0_d \\ \widetilde{H}^-_d \end{pmatrix}
$
};
\node [myRow,C35,align=center] at (-10,-1) {
$ \renewcommand{\arraystretch}{1.2}
\begin{pmatrix} H^0_d \\ H^-_d \end{pmatrix}
$
};
\node [myRow,C15,align=center] at (-6.5,-1) {
$ \renewcommand{\arraystretch}{1.2}
\begin{pmatrix} F^+_{H_d} \\ F^0_{H_d} \end{pmatrix}
$\!\!
};
\node [myRow,C85,align=left] at (-5,-1) {~
$ \renewcommand{\arraystretch}{1.2}
H_d =
\begin{pmatrix}
H^0_d + \sqrt2\, \theta \widetilde{H}^0_d + \theta\theta \, F^+_{H_d}\\
H^-_d + \sqrt2\, \theta \widetilde{H}^-_d + \theta\theta \, F^0_{H_d}
\end{pmatrix}
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Superpotential
\tikzset{myRow/.style={boxYellow,R10}}
\node [boxRed,R10,C80,align=center] at (4.25,5.75) {
The Superpotential, Part I (`good' terms)
};
\node [boxGreen,R20,C80,align=left] at (4.25,4.75) {
\hspace{1mm} $
\mathcal{W}_1 = y^{IJ}_u \, U_I \, (Q_J \circ H_u)
- y^{IJ}_d \, D_I \, (Q_J \circ H_d)
$
\\[0.3em]
\hspace{12mm} $
+ \, y^{IJ}_\nu \, N_I \, (L_J \circ H_u)
- y^{IJ}_e \, E_I \, (L_J \circ H_d)
$
\\[0.2em]
\hspace{12mm} $
+ \, \mu \, (H_u \circ H_d)
$
};
\node [boxRed2,R10,C80,align=center] at (12.5,5.75) {\small
The Superpotential, Part II \\[-0.25em](terms that violate lepton/baryon numbers)
};
\node [boxGray,R20,C80,align=left] at (12.5,4.75) {
\hspace{1mm} $
\mathcal{W}_2 = \lambda^{IJK} \, E_I \, ( L_J \circ L_K )
+ \lambda^{\prime\,IJK} \, D_I \, ( L_J \circ Q_K )
$
\\[0.5em]
\hspace{12mm} $
+ \, \mu^{\prime\,I}_0 \, ( L_I \circ H_u )
+ \lambda^{\prime\prime\,IJK}_3 \, U_I D_J D_K
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Building superp.
\node [boxWhite,minimum width=162.5mm, minimum height=147.5mm] at (4.25,2.5) {
};
\node [anchor=south,align=left] at (17.5,1.75) {
\textsf{\textbf{Superpotential} (construction)}
};
\draw (9,1.5) -- (6.5,0.75) -- (6.5,-1.5);
\draw (11.25,1.5) -- (11.75,1);
\draw (8.75,-3) -- (6.5,-3.5) -- (6.5,-5.5);
\draw (11,-3) -- (13.5,-3.5);
\draw (10,-3) -- (10,-5);
\draw (8.75,-7) -- (8.25,-7.5) -- (8.25,-8.75);
\draw (11.25,-7) -- (11.75,-7.5) -- (11.75,-10);
\draw (10.5,0.5) -- (10,0) -- (10,-1.5);
\draw (13,0.5) -- (13.5,0) -- (13.5,-1.5);
\draw (18.5,-7) -- (18.5,-10.25);
\draw (18.5,0.5) -- (18.5,-2.25);
\draw (13.5,-4) -- (13.5,-4.5) -- (13.5,-5.75);
\draw (14.5,-4) -- (16,-4.5) -- (17,-4.75);
%%%%
\tikzset{myRow/.style={boxYellow,C30,minimum height=7.5mm,inner sep=0,align=center}}
\node [myRow,boxRed] at (8.5,2) {
$Q$ : $( \quantNo{3}{2}{+\frac{1}{6}} )$
};
\node [myRow] at (5,0.75) {
$\anti{u}$ : $( \quantNo{3}{1}{-\frac{2}{3}} )$
};
\node [myRow] at (10.25,1) {
$\anti{d}$ : $( \quantNo{3}{1}{+\frac{1}{3}} )$
};
\node [myRow] at (5,0) {
$H_u$ : $( \quantNo{1}{2}{+\frac{1}{2}} )$
};
\node [myRow] at (8.5,0) {
$H_d$ : $( \quantNo{1}{2}{-\frac{1}{2}} )$
};
\node [myRow] at (12,0) {
$L$ : $( \quantNo{1}{2}{-\frac{1}{2}} )$
};
\node [myRow,boxGreen,thin] at (5,-1) {
$U_I \, (Q_J \circ H_u$)
};
\node [myRow,boxGreen,thin] at (8.5,-1) {
$D_I \, (Q_J \circ H_d$)
};
\node [myRow,boxGray,thin] at (12,-1) {
$D_I \, (L_J \circ Q_K$)
};
%%%%
\node [myRow,boxRed,C30] at (8.5,-2.5) {
$H_u$ : $( \quantNo{1}{2}{+\frac{1}{2}} )$
};
\node [myRow,C30] at (5,-3.5) {
$H_u$ : $( \quantNo{1}{2}{+\frac{1}{2}} )$
};
\node [myRow,C30] at (5,-4.25) {
$L$ : $( \quantNo{1}{2}{-\frac{1}{2}} )$
};
\node [myRow,C30] at (5,-5) {
$L$ : $( \quantNo{1}{2}{-\frac{1}{2}} )$
};
\node [anchor=north] at (6.5,-5.75) {
$[F] \text{ in } \Phi^4 = \mathsf{M}^5$
};
\node [myRow] at (8.5,-3.5) {
$H_d$ : $( \quantNo{1}{2}{-\frac{1}{2}} )$
};
\node [myRow,boxGreen,thin] at (8.5,-4.5) {
$H_u \circ H_d$
};
\node [myRow] at (12,-3.5) {
$L$ : $( \quantNo{1}{2}{-\frac{1}{2}} )$
};
\node [myRow,boxGray,thin] at (15.5,-4.25) {
$L_I \circ H_u$
};
\node [myRow] at (12,-4.5) {
$\anti{\nu}$ : $( \quantNo{1}{1}{0} )$
};
\node [myRow,fill=black!40!green!3,thin] at (12,-5.5) {
$N_I \, (L_J \circ H_u)$
};
\node [myRow,boxRed] at (8.5,-6.5) {
$H_d$ : $( \quantNo{1}{2}{-\frac{1}{2}} )$
};
\node [myRow] at (6.75,-7.5) {
$H_d$ : $( \quantNo{1}{2}{-\frac{1}{2}} )$
};
\node [myRow] at (6.75,-8.25) {
$\anti{e}$ : $( \quantNo{1}{1}{+1} )$
};
\node [anchor=north] at (8.25,-9) {
$H_d \circ H_d = 0$
};
\node [myRow] at (10.25,-7.5) {
$L$ : $( \quantNo{1}{2}{-\frac{1}{2}} )$
};
\node [myRow] at (10.25,-8.25) {
$\anti{e}$ : $( \quantNo{1}{1}{+1} )$
};
\node [myRow,boxGreen,thin] at (10.25,-9.25) {
$E_I \, (L_J \circ H_d)$
};
\node [myRow,boxRed] at (17,-6.5) {
$\anti{u}$ : $( \quantNo{\overline3}{1}{-\frac{2}{3}} )$
};
\node [myRow,boxBlue] at (17,-7.5) {
$\overline{\mathbf{3}} \otimes \overline{\mathbf{3}} =
\mathbf{3} \oplus \overline{\mathbf{6}}$
};
\node [myRow] at (17,-8.25) {
$\anti{d}$ : $( \quantNo{\overline3}{1}{+\frac{1}{3} })$
};
\node [myRow] at (17,-9) {
$\anti{d}$ : $( \quantNo{\overline3}{1}{+\frac{1}{3}} )$
};
\node [myRow,boxGray,thin] at (17,-10) {
$U_I D_J D_K$
};
\node [myRow,boxRed] at (17,1) {
$L$ : $( \quantNo{1}{2}{-\frac{1}{2}} )$
};
\node [myRow] at (17,0) {
$L$ : $( \quantNo{1}{2}{-\frac{1}{2}} )$
};
\node [myRow] at (17,-0.75) {
$\anti{e}$ : $( \quantNo{1}{1}{+1} )$
};
\node [myRow,boxGray,thin] at (17,-1.75) {
$E_I \, (L_J \circ L_K$)
};
%%%%%
\tikzset{circled/.style={anchor=north,fill=black!60!blue,thin,circle,inner sep=2pt}}
\node [circled] at (8.25,2) {\color{white}
\textbf{1}
};
\node [circled] at (8.25,-2.5) {\color{white}
\textbf{2}
};
\node [circled] at (8.25,-6.5) {\color{white}
\textbf{3}
};
\node [circled] at (16.75,1) {\color{white}
\textbf{4}
};
\node [circled] at (16.75,-6.5) {\color{white}
\textbf{5}
};
\node [anchor=north west,C30,align=center,red] at (12,-1.75) {
$\Delta L = 1$
};
\node [anchor=north west,C30,align=center,red] at (17,-2.5) {
$\Delta L = 1$
};
\node [anchor=north west,C30,align=center,red] at (15.5,-5) {
$\Delta L = 1$
};
\node [anchor=north west,C30,align=center,red] at (17,-10.75) {
$\Delta B = 1$
};
\node [anchor=north west,C80,align=left] at (4.5,-10.25) {
$\circ \equiv$ SU(2) invariant product of doublets: \\[0.5em]
~~$
\begin{pmatrix} \Phi_1 \\ \Phi_2 \end{pmatrix} \circ
\begin{pmatrix} \Psi_1 \\ \Psi_2 \end{pmatrix}
\equiv \Phi_1 \Psi_2 - \Phi_2 \Psi_1
$
};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Vector sf
\node [anchor=south west,align=left] at (-20.25,-4) {\large
\textsf{\textbf{Superspace Formalism}}
};
\node [boxWhite,R20,C80] at (-20.5,-4) {
A \textsf{\textbf{vector superfield}}, SU($n$), in WZ gauge: \\[0.5em]
\hfill $
V^i(x,\theta,\sbar{\theta}) ~\equiv~
\theta \sigma^\mu \sbar{\theta} \, V^i_\mu(x) \,
+ \theta\theta \, \sbar{\theta}\sbar{\lambda}^i(x)
$ \hfill\! \\[0.2em ]
\hfill $
+\, \sbar{\theta}\sbar{\theta} \, \theta\lambda^i(x)
+ \tfrac{1}{2} \theta\theta \, \sbar{\theta}\sbar{\theta} \, D^i(x),
~~ V \equiv V^i T^i
$ \hfill\!
};
\node [boxWhite,R15,C80] at (-20.5,-6) {
The \textsf{\textbf{field strength superfield}}: \\[0.5em]
\hfill $
\mathcal{V}_\alpha \equiv \mathcal{V}^i_\alpha T^i \equiv -\tfrac{1}{4} \sbar D_{\dot\beta} \sbar D^{\dot\beta}
\left( \ee^{-2gV} D_\alpha \ee^{2gV} \right)
$ \hfill\!
};
\node [boxYellow,R15,C80] at (-20.5,-7.75) {
The gauge kinetic term: \\[0.5em]
\hfill $
\tfrac{1}{4} (\mathcal{V}^{i\,\alpha} \mathcal{V}^i_\alpha) \big\rvert_F + \mathrm{h.c.}
$ \hfill\!
};
\node [boxWhite,minimum height=15mm,C80] at (-20.5,-9.5) {
$\tfrac{1}{4} (\mathcal{V}^{i\,\alpha} \mathcal{V}^i_\alpha) \big\rvert_F $
~(mod tot.\,der.) $=$ \\[0.5em]
\hfill $
\tfrac{1}{2} D^i D^i
+ \ii \sbar\lambda^i \sbar\sigma^\mu D_\mu \lambda^i
- \tfrac{1}{4} F^i_{\mu\nu} F^{i\,\mu\nu}
$ \hfill\! \\[0.8em]
};
\node [boxGray,R15,C80] at (-4,-12) {
Opt.\;Fayet-Iliopoulos $D$-term (in U(1) only) \\[0.5em]
\hfill $
-2\kappa V \big\rvert_D = - \kappa D
$ \hfill (not in MSSM)