Graphical representation of the weak hypercharge Y & isospin I3 quantum number (of U(1)Y and SU(2)L) of the Standard Model particles, as well as for different types of leptoquarks. Inspired by this image on Wikipedia.
All Standard Model fields:![SM_isospin_weak-001.png](https://tikz.net/wp-content/uploads/2023/09/SM_isospin_weak-001.png)
![SM_isospin_weak-002.png](https://tikz.net/wp-content/uploads/2023/09/SM_isospin_weak-002.png)
![SM_isospin_weak-003.png](https://tikz.net/wp-content/uploads/2023/09/SM_isospin_weak-003.png)
![SM_isospin_weak-004.png](https://tikz.net/wp-content/uploads/2023/09/SM_isospin_weak-004.png)
![SM_isospin_weak-005.png](https://tikz.net/wp-content/uploads/2023/09/SM_isospin_weak-005.png)
![SM_isospin_weak-006.png](https://tikz.net/wp-content/uploads/2023/09/SM_isospin_weak-006.png)
![SM_isospin_weak-007.png](https://tikz.net/wp-content/uploads/2023/09/SM_isospin_weak-007.png)
![SM_isospin_weak-008.png](https://tikz.net/wp-content/uploads/2023/09/SM_isospin_weak-008.png)
![SM_isospin_weak-009.png](https://tikz.net/wp-content/uploads/2023/09/SM_isospin_weak-009.png)
Edit and compile if you like:
% Author: Izaak Neutelings (June 2022) % Inspiration: % https://en.wikipedia.org/wiki/File:Electroweak.svg % https://commons.wikimedia.org/wiki/File:Standard_Model.svg % http://www.scientificlib.com/en/Physics/LX/WeakHypercharge.html % anti-fermions wrong ? % https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model#Field_content_in_detail % https://en.wikipedia.org/wiki/C-symmetry#Charge_conjugation_in_the_chiral_basis \documentclass[border=3pt,tikz]{standalone} \usepackage{tikz} \usepackage{amsmath} % for \text \usepackage[outline]{contour} % glow around text \usetikzlibrary{arrows.meta} % to control arrow size \tikzset{>={Latex[length=4,width=4]}} % for LaTeX arrow head \usetikzlibrary{calc} \usepackage{xcolor} % for colored text \contourlength{1.1pt} \colorlet{myblue}{blue!70!black} \colorlet{mydarkblue}{blue!40!black} \colorlet{mypurple}{blue!60!red!80!black} \colorlet{myred}{red!70!black} \colorlet{myred2}{red!75!blue!80!black!90} \colorlet{mydarkred}{red!50!black} \colorlet{mygreen}{green!60!black} \colorlet{mygreen2}{green!68!blue!70!black!90} \colorlet{mydarkgreen}{green!30!black} \colorlet{myorange}{orange!88!black} \colorlet{myorange2}{orange!75!black} \colorlet{myyellow}{yellow!80!orange!90!black} \def\tick#1#2{\draw[thick] (#1) ++ (#2:1pt) --++ (#2-180:2pt)} \renewcommand\bar{\overline} \renewcommand\tilde{\widetilde} \newcommand{\YW}{Y_\mathrm{W}} \newcommand{\ff}[2]{#1_\text{#2}} % fermion field \newcommand{\aff}[2]{\overline{#1}_\text{#2}} % anti-fermion field \tikzstyle{guide}=[ultra thin,black!15,line cap=round] \tikzstyle{myball}=[line width=0.05,ball color=#1] % COMMON MACROS \def\myball(#1)[#2]{ \fill[ball color=#2] (#1) circle(\r); \fill[#2,opacity=0.4] (#1) circle(\r); \draw[draw=#2!20!black,line width=0.04] (#1) circle(\r) } \def\quark(#1)[#2]#3{ \myball({#1)++(-30:0.8*\r})[red]; \myball({#1)++(-150:0.8*\r})[green!88!black]; \myball({#1)++(90:0.8*\r})[blue]; %\draw[myball=red] (#1)++(-30:0.8*\r) circle(\r); %\draw[myball=green] (#1)++(-150:0.8*\r) circle(\r); %\draw[myball=blue] (#1)++(90:0.8*\r) circle(\r); \node[#2] at (#1) {\strut#3} } \def\barwidth{0.015} % doublet thickness \def\doublet#1#2{\begin{pmatrix}#1\\#2\end{pmatrix}} \def\drawdoublet[#1,#2](#3){% % rectangle with fading color \fill[#2,left color=#1,right color=#2]% (-1/2,#3)++(0,-\barwidth/2) rectangle++ (1,\barwidth)% } \def\drawtriplet[#1,#2](#3){% % rectangle with fading color \fill[#2,left color=#1,right color=#2]% (-1,#3)++(0,-\barwidth/2) rectangle++ (2,\barwidth)% } \begin{document} % COMMON AXIS \def\r{0.7pt} % point radius \pgfmathsetmacro\qscale{1/sqrt(2)} % unit Q charge in (I3,YW/2) \def\TQYaxis{ % GUIDELINES \foreach \i [evaluate={\y=1.05*(1.2-abs(\i/2))}] in {1,2}{ % weak isospin T3 \draw[guide] (-\i/2,-\y) -- (-\i/2,\y); \draw[guide] ( \i/2,-\y) -- ( \i/2,\y); } \foreach \i [evaluate={\x=0.9*(1.1-abs(\i/6)^2)}] in {1,...,6}{ % weak hypercharge Y \draw[guide] (-\x,-\i/6) -- (\x,-\i/6); \draw[guide] (-\x, \i/6) -- (\x,\i/6); } \foreach \i [evaluate={\q=\qscale*\i/3}] in {-3,...,3}{ % EM charge Q %\draw[guide] (-1,\i/3) -- (1,\i/3); \draw[guide,rotate=-45] (-0.85,\q) -- (0.85,\q); \tick{45:\q}{135}; } \begin{scope}[every node/.style={scale=0.8,inner sep=1}] \tick{-1,0}{90} node[below] {$-1$}; \tick{-1/2,0}{90}; \tick{1/2,0}{90}; \tick{1,0}{90} node[below] {$+1$}; \tick{0,-2/3}{0}; \tick{0,-1/3}{0}; \tick{0,1/3}{0}; \tick{0,2/3}{0}; \tick{0,-1}{0} node[left] {$-1$}; \tick{0,1}{0} node[left] {$+1$}; \tick{45:-\qscale}{135} node[below] {$-1$}; \tick{0,0}{135} node[below right=0] {$0$}; \tick{45:\qscale}{135} node[below] {$+1$}; \end{scope} % AXES \draw[->,thick] (-1.05,0) -- (1.1,0) node[right] {$T_3$}; \draw[->,thick] (0,-1.05) -- (0,1.1) node[right=2,above=-2] {$\YW/2$}; \draw[->,thick] (45:-1) -- (45:1) node[left=18,above right=-3] {$Q=T_3+\frac{1}{2}\YW$}; } % ELECTROWEAK HYPERCHARGE \begin{tikzpicture}[scale=3.5] % AXES & GUIDELINES \TQYaxis % GAUGE BOSONS %\fill[myred] ( 0, 0) circle(\r) node[below right] {$\mathrm{Z}^+$}; \fill[myred,shift={(225:0.01)}] ( 0, 0) circle(\r) node[anchor=-23,inner sep=2.5] {$\gamma$, $g$, $Z^0$}; \fill[myred] ( 1, 0) circle(\r) node[right=2,above=2] {$W^+$}; \fill[myred] (-1, 0) circle(\r) node[right=2,above=2] {$W^-$}; % SCALAR BOSONS \fill[myorange,shift={(225:0.01)}] (-1/2, 1/2) circle(\r) node[left] {\strut$h^0$}; \fill[myorange,shift={(225:0.01)}] ( 1/2,-1/2) circle(\r) node[left] {\strut$h^{0*}$}; \fill[myorange,shift={(225:0.01)}] (-1/2,-1/2) circle(\r) node[left] {\strut$\phi^-$}; \fill[myorange,shift={(225:0.01)}] ( 1/2, 1/2) circle(\r) node[left] {\strut$\phi^+$}; % QUARKS \fill[myblue] (-1/2,-1/6) circle(\r) node[right=1] {$\aff{u}{L}$}; \fill[mypurple] (-1/2, 1/6) circle(\r) node[right=1] {$\ff{d}{L}$}; \fill[myblue] ( 0 ,-2/3) circle(\r) node[right=1] {$\aff{u}{R}$}; \fill[mypurple] ( 0 ,-1/3) circle(\r) node[right=1] {$\ff{d}{R}$}; \fill[mypurple] ( 0 , 1/3) circle(\r) node[right=1] {$\aff{d}{R}$}; \fill[myblue] ( 0 , 2/3) circle(\r) node[right=1] {$\ff{u}{R}$}; \fill[mypurple] ( 1/2,-1/6) circle(\r) node[right=1] {$\aff{d}{L}$}; \fill[myblue] ( 1/2, 1/6) circle(\r) node[right=1] {$\ff{u}{L}$}; % LEPTONS \fill[mygreen] ( 0 ,-1 ) circle(\r) node[right=1] {$\ff{e}{R}$}; \fill[mygreen] ( 0 , 1 ) circle(\r) node[right=1] {$\aff{e}{R}$}; \fill[mygreen,shift={(45:0.01)}] ( 1/2, 1/2) circle(\r) node[right=2] {$\aff{e}{L}$}; \fill[mygreen,shift={(45:0.01)}] (-1/2,-1/2) circle(\r) node[right=1] {$\ff{e}{L}$}; \fill[mygreen2,shift={(45:0.01)}] (-1/2, 1/2) circle(\r) node[right=1] {$\aff{\nu}{L}$}; \fill[mygreen2,shift={(45:0.01)}] ( 1/2,-1/2) circle(\r) node[right=1] {$\ff{\nu}{L}$}; \fill[mygreen2,shift={(45:0.01)}] ( 0, 0) circle(\r) node[right=1,above right=-2] {\contour{white}{$\aff{\nu}{R}$, $\ff{\nu}{R}$}}; % not in SM \end{tikzpicture} % ELECTROWEAK HYPERCHARGE - bosons \begin{tikzpicture}[scale=3.5] % AXES & GUIDELINES \TQYaxis % GAUGE BOSONS \drawtriplet[myred,myred](0); %\fill[myred] ( 0, 0) circle(\r) node[anchor=-23,inner sep=2.5] {$\gamma$, $g$, $Z^0$}; \fill[myred,shift=(0:-0.01)] ( 0, 0) circle(\r) node[anchor=-42,inner sep=2.5] {$Z^0$}; \fill[myyellow,shift=(0:0.01)] ( 0, 0) circle(\r) node[anchor=-150,inner sep=3] {\contour{white}{$\gamma$, $g$}}; \fill[myred] ( 1, 0) circle(\r) node[right=2,above=2] {$W^+$}; \fill[myred] (-1, 0) circle(\r) node[right=2,above=2] {$W^-$}; % SCALAR BOSONS \drawdoublet[myorange2,myorange]( 1/2); \drawdoublet[myorange,myorange2](-1/2); \fill[myorange2] (-1/2, 1/2) circle(\r) node[left] {\strut$h^0$}; \fill[myorange2] ( 1/2,-1/2) circle(\r) node[right] {\strut$h^{0*}$}; \fill[myorange] (-1/2,-1/2) circle(\r) node[left] {\strut$\phi^-$}; \fill[myorange] ( 1/2, 1/2) circle(\r) node[anchor=-170,inner sep=4] {\strut$\phi^+$}; \end{tikzpicture} % ELECTROWEAK HYPERCHARGE - bosons with full field names \begin{tikzpicture}[scale=3.5] % AXES & GUIDELINES \TQYaxis % GAUGE BOSONS \drawtriplet[myred,myred](0); %\fill[myred] ( 0, 0) circle(\r) node[anchor=-23,inner sep=2.5] {$\gamma$, $g$, $Z^0$}; \fill[myred,shift=(0:-0.01)] ( 0, 0) circle(\r) node[anchor=-45,inner sep=2] {$Z^0_\mu$}; \fill[myyellow,shift=(0:0.01)] ( 0, 0) circle(\r) node[anchor=-157,inner sep=2.8] {\contour{white}{$A^0_\mu$, $G^i_\mu$}}; \fill[myred] ( 1, 0) circle(\r) node[right=2,above=0] {$W^+_\mu$}; \fill[myred] (-1, 0) circle(\r) node[right=2,above=0] {$W^-_\mu$}; % SCALAR BOSONS \drawdoublet[myorange2,myorange]( 1/2); \drawdoublet[myorange,myorange2](-1/2); \fill[myorange2] (-1/2, 1/2) circle(\r) node[left] {\strut$\phi^0$}; \fill[myorange2] ( 1/2,-1/2) circle(\r) node[right] {\strut$\phi^{0*}$}; \fill[myorange] (-1/2,-1/2) circle(\r) node[left] {\strut$\phi^-$}; \fill[myorange] ( 1/2, 1/2) circle(\r) node[anchor=-170,inner sep=4] {\strut$\phi^+$}; \end{tikzpicture} % ELECTROWEAK HYPERCHARGE - bosons with full field names before SSB \begin{tikzpicture}[scale=3.5] % AXES & GUIDELINES \TQYaxis % GAUGE BOSONS \drawtriplet[myred,myred](0); %\fill[myred] ( 0, 0) circle(\r) node[anchor=-23,inner sep=2.5] {$\gamma$, $g$, $Z^0$}; \fill[myred,shift=(0:-0.01)] ( 0, 0) circle(\r) node[anchor=-45,inner sep=2] {$W^3_\mu$}; \fill[myyellow,shift=(0:0.01)] ( 0, 0) circle(\r) node[anchor=-157,inner sep=2.8] {\contour{white}{$B_\mu$, $G^i_\mu$}}; \fill[myred] ( 1, 0) circle(\r) node[right=2,above=0] {$W^+_\mu$}; \fill[myred] (-1, 0) circle(\r) node[right=2,above=0] {$W^-_\mu$}; % SCALAR BOSONS \drawdoublet[myorange2,myorange]( 1/2); \drawdoublet[myorange,myorange2](-1/2); \fill[myorange2] (-1/2, 1/2) circle(\r) node[left] {\strut$\phi^0$}; \fill[myorange2] ( 1/2,-1/2) circle(\r) node[right] {\strut$\phi^{0*}$}; \fill[myorange] (-1/2,-1/2) circle(\r) node[left] {\strut$\phi^-$}; \fill[myorange] ( 1/2, 1/2) circle(\r) node[anchor=-170,inner sep=4] {\strut$\phi^+$}; \end{tikzpicture} % ELECTROWEAK HYPERCHARGE - fermions % https://en.wikipedia.org/wiki/C-symmetry#Charge_conjugation_in_the_chiral_basis \begin{tikzpicture}[scale=3.5] \def\ns{\hspace{-0.1em}} % small negative space \def\NS{\hspace{-0.2em}} % large negative space \def\r{0.7pt} % point radius % AXES & GUIDELINES \TQYaxis % ISOSPIN DOUBLETS \drawdoublet[mygreen,mygreen2](-1/2); \drawdoublet[mygreen2,mygreen](1/2); \drawdoublet[myblue,mypurple](-1/6); \drawdoublet[mypurple,myblue](1/6); %% QUARKS %\fill[myblue] (-1/2,-1/6) circle(\r) node[left=1] {$\aff{u}{R}$}; %\fill[mypurple] (-1/2, 1/6) circle(\r) node[left=1] {$\ff{d}{L}$}; %\fill[myblue] ( 0 ,-2/3) circle(\r) node[right=1] {$\aff{u}{L}$}; %\fill[mypurple] ( 0 ,-1/3) circle(\r) node[right=1] {$\ff{d}{R}$}; %\fill[mypurple] ( 0 , 1/3) circle(\r) node[right=1] {$\aff{d}{L}$}; %\fill[myblue] ( 0 , 2/3) circle(\r) node[right=1] {$\ff{u}{R}$}; %\fill[mypurple] ( 1/2,-1/6) circle(\r) node[right=1] {$\aff{d}{R}$}; %\fill[myblue] ( 1/2, 1/6) circle(\r) node[right=1] {$\ff{u}{L}$}; % RGB QUARK BALLS \quark(-1/2,-1/6)[left=3,myblue] {$\aff{u}{L}$}; \quark(-1/2, 1/6)[left=3,mypurple] {$\ff{d}{L}$}; \quark( 0 ,-2/3)[right=3,myblue] {$\aff{u}{R}$}; \quark( 0 ,-1/3)[right=3,mypurple] {$\ff{d}{R}$}; \quark( 0 , 1/3)[right=3,mypurple] {$\aff{d}{R}$}; \quark( 0 , 2/3)[right=3,myblue] {$\ff{u}{R}$}; \quark( 1/2,-1/6)[right=3,mypurple] {$\aff{d}{L}$}; \quark( 1/2, 1/6)[right=3,myblue] {$\ff{u}{L}$}; % LEPTONS \fill[mygreen] ( 0 ,-1 ) circle(\r) node[right=1] {$\ff{e}{R}$}; \fill[mygreen] ( 0 , 1 ) circle(\r) node[right=1] {$\aff{e}{R}$}; \fill[mygreen] ( 1/2, 1/2) circle(\r) node[right=2] {$\aff{e}{L}$}; \fill[mygreen] (-1/2,-1/2) circle(\r) node[left=1] {$\ff{e}{L}$}; \fill[mygreen2] (-1/2, 1/2) circle(\r) node[left=1] {$\aff{\nu}{L}$}; \fill[mygreen2] ( 1/2,-1/2) circle(\r) node[right=1] {$\ff{\nu}{L}$}; \fill[mygreen2] ( 0, 0) circle(\r) node[right=1,above right=-2] {\contour{white}{$\ff{\nu}{R}$, $\aff{\nu}{R}$}}; \end{tikzpicture} % ELECTROWEAK HYPERCHARGE - fermions (with doublets) \begin{tikzpicture}[scale=3.5] \def\ns{\hspace{-0.1em}} % small negative space \def\NS{\hspace{-0.2em}} % large negative space \def\r{0.7pt} % point radius % AXES & GUIDELINES \TQYaxis % ISOSPIN DOUBLETS \drawdoublet[mygreen,mygreen2](-1/2) node[scale=0.9,below=1,right=24] {$\ff{L}{L}=\doublet{\nu}{e}_\text{\NS L}$}; \drawdoublet[mygreen2,mygreen](1/2) node[scale=0.9,below=1,right=24] {$\aff{L}{L}=(\bar{\nu},\bar{e})_\text{\ns L}$}; \drawdoublet[myblue,mypurple](-1/6) node[scale=0.9,below=2,right=24] {$\aff{Q}{L}=\left(\bar{u},\bar{d}\right)_\text{\ns L}$}; \drawdoublet[mypurple,myblue](1/6) node[scale=0.9,above=1,right=24] {$\ff{Q}{L}=\doublet{u}{d}_\text{\NS L}$}; % QUARKS \fill[myblue] (-1/2,-1/6) circle(\r) node[left=1] {$\aff{u}{L}$}; \fill[mypurple] (-1/2, 1/6) circle(\r) node[left=1] {$\ff{d}{L}$}; \fill[myblue] ( 0 ,-2/3) circle(\r) node[right=1] {$\aff{u}{R}$}; \fill[mypurple] ( 0 ,-1/3) circle(\r) node[right=1] {$\ff{d}{R}$}; \fill[mypurple] ( 0 , 1/3) circle(\r) node[right=1] {$\aff{d}{R}$}; \fill[myblue] ( 0 , 2/3) circle(\r) node[right=1] {$\ff{u}{R}$}; \fill[mypurple] ( 1/2,-1/6) circle(\r) node[right=1] {$\aff{d}{L}$}; \fill[myblue] ( 1/2, 1/6) circle(\r) node[right=1] {$\ff{u}{L}$}; % LEPTONS \fill[mygreen] ( 0 ,-1 ) circle(\r) node[right=1] {$\ff{e}{R}$}; \fill[mygreen] ( 0 , 1 ) circle(\r) node[right=1] {$\aff{e}{R}$}; \fill[mygreen] ( 1/2, 1/2) circle(\r) node[right=2] {$\aff{e}{L}$}; \fill[mygreen] (-1/2,-1/2) circle(\r) node[left=1] {$\ff{e}{L}$}; \fill[mygreen2] (-1/2, 1/2) circle(\r) node[left=1] {$\aff{\nu}{L}$}; \fill[mygreen2] ( 1/2,-1/2) circle(\r) node[right=1] {$\ff{\nu}{L}$}; \fill[mygreen2] ( 0, 0) circle(\r) node[right=1,above right=-2] {\contour{white}{$\ff{\nu}{R}$, $\aff{\nu}{R}$}}; \end{tikzpicture} % ELECTROWEAK HYPERCHARGE - fermions \begin{tikzpicture}[ scale=3.5, ] \def\ns{\hspace{-0.1em}} % small negative space \def\NS{\hspace{-0.2em}} % large negative space \def\r{0.7pt} % point radius \def\xmin{-0.8} % guideline minimum % GUIDELINES \foreach \i [evaluate={ % weak isospin T3 \y=1.05*(1.1-abs(\i/2))} ] in {-1,0,+1}{ \draw[guide] (\i/2,\y) -- (\i/2,-1.2) node[black,below=-1,scale=0.85] {\strut$\i$}; } \foreach \i [evaluate={ % EM charge Q \q=\qscale*\i/3; \qmin=-min(0.85,abs(\xmin*sqrt(2)-\q); \m=mod(\i,3)==0; % \i is divisible by 3 \num=int(\i/(\m==0?1:3); % numerator }% ] in {-3,...,3}{ \draw[guide,rotate=-45] (\qmin,\q) -- (0.9,\q) node[black,anchor=135,inner sep=1,scale=0.85] { \ifnum\i=0 $\phantom{+}0$ \else $\pgfmathprintnumber[print sign=true]{\num} \ifnum\m=0 /3 \fi$ \fi }; } \foreach \i [evaluate={ % weak hypercharge YW \x=0.55*(1.3-abs(\i/6)^2); \gcd=(mod(\i,2)==0?2:1)*(mod(\i,3)==0?3:1); % greatest common divisor \den=int(6/\gcd); % denominator \num=int(\i/\gcd); % simplified numerator }% ] in {-6,...,6}{ \draw[guide] (\xmin,\i/6) -- (\x,\i/6); \node[black,right=0,scale=0.85] at (-1.06,\i/6) { \ifnum\i=0 $\phantom{+}0$ % indent Y = 0 \else $\pgfmathprintnumber[print sign=true]{\num} \ifnum\den=1 \else /\den \fi$ \fi }; } \node[right=0] at (-1.06,1.15) {$\YW/2$}; \node[right,below=-3] at (0.9,-1.2) {\strut$T_3$}; \path[rotate=-45] (0.9,1.3*\qscale) node[black,anchor=135,inner sep=1] {$Q$}; % ISOSPIN DOUBLETS \drawdoublet[mygreen,mygreen2](-1/2); %node[scale=0.9,below=1,right=24] {$L_R=\doublet{\nu}{e}_{\NS L}$}; \drawdoublet[mygreen2,mygreen](1/2); %node[scale=0.9,below=1,right=24] {$\bar{L}_R=(\bar{\nu},\bar{e})_{\ns R}$}; \drawdoublet[myblue,mypurple](-1/6); %node[scale=0.9,below=0,right=24] {$\bar{Q}_R=\left(\bar{u},\bar{d}\right)_{\ns R}$}; \drawdoublet[mypurple,myblue](1/6); %node[scale=0.9,below=0,right=24] {$Q_L=\doublet{u}{d}_{\NS L}$}; % RGB QUARK BALLS \quark(-1/2,-1/6)[left=3,myblue] {$\aff{u}{L}$}; \quark(-1/2, 1/6)[left=3,mypurple] {$\ff{d}{L}$}; \quark( 0 ,-2/3)[right=3,myblue] {$\aff{u}{R}$}; \quark( 0 ,-1/3)[right=3,mypurple] {$\ff{d}{R}$}; \quark( 0 , 1/3)[right=3,mypurple] {$\aff{d}{R}$}; \quark( 0 , 2/3)[right=3,myblue] {$\ff{u}{R}$}; \quark( 1/2,-1/6)[right=3,mypurple] {$\aff{d}{L}$}; \quark( 1/2, 1/6)[right=3,myblue] {$\ff{u}{L}$}; % LEPTONS \myball( 0 ,-1 )[mygreen] node[mygreen,right=1] {$\ff{e}{R}$}; \myball( 0 , 1 )[mygreen] node[mygreen,right=1] {$\aff{e}{R}$}; \myball( 1/2, 1/2)[mygreen] node[mygreen,right=2] {$\aff{e}{L}$}; \myball(-1/2,-1/2)[mygreen] node[mygreen,left=1] {$\ff{e}{L}$}; \myball(-1/2, 1/2)[mygreen2] node[mygreen2,left=1] {$\aff{\nu}{L}$}; \myball( 1/2,-1/2)[mygreen2] node[mygreen2,right=1] {$\ff{\nu}{L}$}; \myball( 0, 0)[mygreen2] node[mygreen2,right=1,above right=-2] {$\ff{\nu}{R}$, $\aff{\nu}{R}$}; \end{tikzpicture} % WEAK NEUTRAL-CURRENT COUPLINGS \begin{tikzpicture}[scale=2.4] \def\r{1.0pt} % point radius \def\thetaW{28.8} % weak mixing angle / Weinberg angle \def\sW{0.23153} % sin(theta_W)^2 \def\sinthetaW{\sin^2\theta_\mathrm{W}} %\pgfmathsetmacro\sW{sin(\thetaW)^2} % sin(theta_W) \pgfmathsetmacro\qscale{4*\sW/(sqrt(2))} % unit Q charge in (I3,YW/2) % GUIDELINES \foreach \i in {2}{ % axial-vector cV coupling \draw[guide] (-\i/2,-1) -- (-\i/2,1); \draw[guide] ( \i/2,-1) -- ( \i/2,1); } \foreach \i in {1,...,3}{ % vector cA coupling \draw[guide] (-1,-\i/3) -- (1,-\i/3); \draw[guide] (-1, \i/3) -- (1, \i/3); } \begin{scope} \clip (-1.1,-1.1) rectangle (1.1,1.1); \foreach \i [evaluate={\q=\qscale*\i/3;}] in {-3,...,3}{ % EM charge Q \draw[guide,rotate=45] (-1.5,\q) -- (1.5,\q); \tick{135:\q}{45}; } \end{scope} \foreach \i in {1,...,3}{ % ticks \tick{0,-\i/3}{0}; \tick{0, \i/3}{0}; } \begin{scope}[every node/.style={scale=0.8,inner sep=1}] \tick{-1,0}{-90} node[above] {$-1/2$}; \tick{1,0}{-90} node[above] {$+1/2$}; \tick{0,-1}{0} node[left] {$-1/2$}; \tick{0,1}{0} node[left] {$+1/2$}; \tick{-45:-\qscale}{45} node[below left] {$-1$}; \tick{-45:\qscale}{45} node[below left] {$+1$}; \end{scope} % AXES \draw[->,thick] (-1.1,0) -- (1.2,0) node[right=8,below] {$c_A = T_3$}; \draw[->,thick] (0,-1.1) -- (0,1.15) node[right=25,above=-2] {$c_V = T_3 - 2\sinthetaW Q$}; \draw[->,thick] (-45:-0.9) -- (-45:0.9) node[above=-2,right=-1] {$Q = \cfrac{c_A - c_V}{2\sinthetaW}$}; % QUARKS \fill[mygreen] ( 1, 1) circle(\r) node[right=1] {$\nu$}; \fill[mygreen2] (-1,-1+4*\sW) circle(\r) node[left=1] {$e$} node[below=1,right=1,scale=0.85] {$-\frac{1}{2}+2\sinthetaW$}; \fill[myblue] ( 1, 1-8/3*\sW) circle(\r) node[right=1] {$u$} node[left=1,scale=0.85] {$\frac{1}{2}-\frac{4}{3}\sinthetaW$}; \fill[mypurple] (-1,-1+4/3*\sW) circle(\r) node[left=1] {$d$} node[right=1,scale=0.85] {$-\frac{1}{2}+\frac{2}{3}\sinthetaW$}; \end{tikzpicture} % LEPTOQUARK SU(2)_L x U(1)_Y QUANTUM NUMBERS % Inspired by % "Physics of leptoquarks in precision experiments and at particle colliders" % I. Dorsner, S. Fajfer, A. Greljo, J. F. Kamenik, N. Kosnik % https://arxiv.org/abs/1603.04993 \begin{tikzpicture}[scale=3.5] % GUIDELINES \begin{scope} \clip (0,0.21) ellipse({1.12} and 1.3) (0,0.34) ellipse({1.12} and 1.4); \foreach \i in {1,2}{ % weak isospin T3 \draw[guide] (-\i/2,-1.6) -- (-\i/2,1.6); \draw[guide] ( \i/2,-1.6) -- ( \i/2,1.6); } \foreach \i in {1,...,8}{ % weak hypercharge Y \draw[guide] (-1.2,-\i/6) -- (1.2,-\i/6); \draw[guide] (-1.2, \i/6) -- (1.2,\i/6); } \foreach \i in {-4,...,5}{ % charge Q \draw[guide,rotate=-45] (-1.3,\qscale*\i/3) -- (1.1,\qscale*\i/3); } \end{scope} \begin{scope}[ every node/.style={scale=0.8,inner sep=1}, qlab/.style={anchor=130,inner sep=0}, ] \tick{-1,0}{90} node[below] {$-1$}; \tick{-1/2,0}{90} node[below=-1] {$-\frac{1}{2}$}; \tick{1/2,0}{90} node[below=-1] {$+\frac{1}{2}$}; \tick{1,0}{90} node[below] {$+1$}; \tick{0,-1}{0} node[left] {$-1$}; \tick{0,-1/2}{0} node[left] {$-\frac{1}{2}$}; \tick{0,1/2}{0} node[left] {$+\frac{1}{2}$}; \tick{0,1}{0} node[left] {$+1$}; \tick{0,3/2}{0} node[left] {$+\frac{3}{2}$}; \tick{45:-4*\qscale/3}{135} node[qlab] {$-\frac{4}{3}$}; \tick{45:-\qscale}{135} node[qlab] {$-1$}; \tick{45:-2*\qscale/3}{135} node[qlab] {$-\frac{2}{3}$}; \tick{45:-\qscale/3}{135} node[qlab] {$-\frac{1}{3}$}; \tick{0,0}{135} node[below right=0] {$0$}; \tick{45:\qscale/3}{135} node[qlab] {+$\frac{1}{3}$}; \tick{45:2*\qscale/3}{135} node[qlab] {+$\frac{2}{3}$}; \tick{45:\qscale}{135} node[qlab] {$+1$}; \tick{45:4*\qscale/3}{135} node[qlab] {+$\frac{4}{3}$}; \tick{45:5*\qscale/3}{135} node[qlab] {+$\frac{5}{3}$}; \end{scope} % AXES \draw[->,thick] (-1.05,0) -- (1.1,0) node[right] {$T_3$}; \draw[->,thick] (0,-1.05) -- (0,1.8) node[right=2,above=-2] {$\YW/2$}; \draw[->,thick] (45:-1.1) -- (45:1.4) node[left=18,above right=-2] {$Q=T_3+\frac{1}{2}\YW$}; % Scalar S3 (3,3,1/3) \drawtriplet[myred2,myred](1/3) node[right=2] {$S_3^i$}; \fill[myred2] (-1 ,1/3) circle(\r); \fill[myred!50!myred2] (-0.01,1/3) circle(\r); \fill[myred] ( 1 ,1/3) circle(\r); % Scalar R2 (3,2,7/6) \drawdoublet[mypurple,myblue](7/6) node[right=2] {$R_2$}; \fill[mypurple] (-1/2,7/6) circle(\r); %node[right=2,above=2] {$R_3$}; \fill[myblue] ( 1/2,7/6) circle(\r); % Scalar R2~ (3,2,1/6) \drawdoublet[mypurple,myblue](1/6) node[right=2] {$\tilde{R}_2$}; \fill[mypurple] (-1/2,1/6) circle(\r); %node[right=2,above=2] {$\tilde{R}_3$}; \fill[myblue] ( 1/2,1/6) circle(\r); % Scalar S1~ (3,1,4/3) \fill[mygreen] (0,4/3) circle(\r) node[right=1] {$\tilde{S}_1$}; % Scalar S1 (3,1,1/3) \fill[mygreen] (0.01,1/3) circle(\r) node[anchor=-135,inner sep=2] {$S_1$}; % Scalar S1- (3,1,-2/3) \fill[mygreen] (0,-2/3) circle(\r) node[right=1] {$\overline{S}_1$}; % Vector U3 (3,3,2/3) \drawtriplet[myred,myred2](2/3) node[below=0.5,right=2] {$U_{3\mu}^i$}; \fill[myred] (-1 ,2/3) circle(\r); \fill[myred!50!myred2] (-0.01,2/3) circle(\r); \fill[myred2] ( 1 ,2/3) circle(\r); % Vector V2 (3,2,5/6) \drawdoublet[myblue,mypurple](5/6) node[below=0.5,right=2] {$V_{2\mu}$}; \fill[myblue] (-1/2,5/6) circle(\r); \fill[mypurple] ( 1/2,5/6) circle(\r); % Vector V2~ (3,2,-1/6) \drawdoublet[myblue,mypurple](-1/6) node[below=1,right=2] {$\tilde{V}_{2\mu}$}; \fill[myblue] (-1/2,-1/6) circle(\r); \fill[mypurple] ( 1/2,-1/6) circle(\r); % Vector U1~ (3,1,5/3) \fill[mygreen] (0,5/3) circle(\r) node[below=0.5,right=1] {$\tilde{U}_{1\mu}$}; % Vector U1 (3,1,2/3) \fill[mygreen] (0.01,2/3) circle(\r) node[below=0.5,anchor=-145,inner sep=1.7] {$U_{1\mu}$}; % Vector U1- (3,1,-1/3) \fill[mygreen] (0,-1/3) circle(\r) node[below=0.5,right=1] {$\overline{U}_{1\mu}$}; \end{tikzpicture} \end{document}
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