# Pseudoscalar Quindecuplet

Pseudoscalar Quindecuplet for usdc Quarks

By Daniel Boyce, August, 2023

\documentclass[tikz,border=10pt]{standalone}
\usepackage{tikz-3dplot}
\begin{document}

%  Constants
\newcommand*{\h}{4}%  Height difference between levels

%  Particle Ball
\newcommand\particle[1]{%
\begin{tikzpicture}
\node at (0,0) {#1};
\end{tikzpicture}
}

\begin{tikzpicture}[scale=0.9]
%  Coordinate System of the Quarks
\draw[->] ({-\rmid-4},0,0) --({-\rmid-2},0,0) node[below] {Charge};
\draw[->] ({-\rmid-4},0,0) -- ({-\rmid-4},0,-2) node[above right] {Strangeness};
\draw[->] ({-\rmid-4},0,0) -- ({-\rmid-4},2,0) node[right] {Charm};

%  Coordinates
%  Top Level
\coordinate (cs) at ({\rtop*cos(90)},\h,{-\rtop*sin(90)});
\coordinate (cu) at ({\rtop*cos(225)},\h,{-\rtop*sin(225)});
\coordinate (cd) at ({\rtop*cos(315)},\h,{-\rtop*sin(315)});

%  Middle Level
\coordinate (ud) at ({\rmid*cos(0)},0,{-\rmid*sin(0)});
\coordinate (us) at ({\rmid*cos(60)},0,{-\rmid*sin(60)});
\coordinate (ds) at ({\rmid*cos(120)},0,{-\rmid*sin(120)});
\coordinate (du) at ({\rmid*cos(180)},0,{-\rmid*sin(180)});
\coordinate (su) at ({\rmid*cos(240)},0,{-\rmid*sin(240)});
\coordinate (sd) at ({\rmid*cos(300)},0,{-\rmid*sin(300)});
\coordinate (uudd2ss) at (-0.8,0,0);
\coordinate (uudd) at (0,0,0);
\coordinate (uuddss) at (0.8,0,0);

%  Bottom Level
\coordinate (sc) at ({\rbot*cos(270)},-\h,{-\rbot*sin(270)});
\coordinate (uc) at ({\rbot*cos(45)},-\h,{-\rbot*sin(45)});
\coordinate (dc) at ({\rbot*cos(135)},-\h,{-\rbot*sin(135)});

%  Highlight Levels
\fill[lightgray] (cd) -- (cs) -- (cu) -- (cd) -- cycle;
\fill[lightgray] (ud) -- (us) -- (ds) -- (du) -- (su) -- (sd) -- (ud) -- cycle;
\fill[lightgray] (sc) -- (uc) -- (dc)  -- (sc) -- cycle;

%  Particles and Lines
%  Level Lines
\draw (cd) -- (cs) -- (cu) -- (cd);
\draw (ud) -- (us); \draw[dashed] (us) -- (ds) -- (du); \draw (du) -- (su) -- (sd) -- (ud);
\draw (sc) -- (uc); \draw[dashed] (uc) -- (dc)  -- (sc);

%  Need the eta prime:
\node at (uuddss) {\particle {$\eta^{\prime}$}};

%  Between Levels
\draw (cd) -- (sd); \draw (cd) -- (ud);
\draw (cs) -- (us); \draw[dashed] (cs) -- (ds);
\draw (cu) -- (du); \draw (cu) -- (su);

\draw (sc) -- (uc); \draw[dashed] (uc) -- (dc)  -- (sc);
\draw (sc) -- (sd); \draw (sc) -- (su);
\draw (uc) -- (ud); \draw[dashed] (uc) -- (us);
\draw[dashed] (dc) -- (ds); \draw[dashed] (dc) -- (du);

%  Top Level
\node at (cs) {\particle {$D_s^0$}};
\node at (cu) {\particle {$D^0$}};
\node at (cd) {\particle {$D^+$}};

%  Middle Level
\node at (ud) {\particle {$\pi^+$}};
\node at (us) {\particle {$K^+$}};
\node at (ds) {\particle {$K^0$}};
\node at (du) {\particle {$\pi^-$}};
\node at (su) {\particle {$K^-$}};
\node at (sd) {\particle {$\overline{K}^0$}};
\node at (uudd2ss) {\particle {$\eta$}};
\node at (uudd) {\particle {$\pi^0$}};

%  Bottom Level
\node at (sc) {\particle {$D_s^-$}};
\node at (uc) {\particle {$\overline{D}^0$}};
\node at (dc) {\particle {$D^-$}};

%  Title
\node[scale=2] at (-3,{\h+3},0) (title) {Pseudoscalar Quindecuplet for udsc quarks};
\end{tikzpicture}
\end{document}