Pseudorapidity

Pseudorapidity on a 2D coordinate axis. For the coordinate system of the CMS detecter at the LHC, please see this post.

This is the simplest method with a for-loop in two variables: θ and η:

\documentclass[border=3pt,tikz]{standalone}
\tikzset{>=latex} % for LaTeX arrow head
\begin{document}
\begin{tikzpicture}[scale=3]
  \foreach \t/\e in {90/0,60/0.55,45/0.88,30/1.32,10/2.43,0/+\infty}{
    \pgfkeys{/pgf/number format/precision=2}
    \draw[->,thick] % eta lines
      (0,0) -- (\t:1.2) node[anchor=180+\t,black] {$\eta=\e$}
      node[black,pos=0.72,fill=white,scale=0.8,inner sep=2] {$\theta=\t^\circ$};
  }
\end{tikzpicture}
\end{document}

In the following method, η is calculated and rounded to two significant digits on the fly, with the exception for θ = 0:

\documentclass[border=3pt,tikz]{standalone}
\tikzset{>=latex} % for LaTeX arrow head
\begin{document}
\begin{tikzpicture}[scale=3]
  \foreach \t in {90,60,45,30,10,0}{
    \ifnum \t = 0
      \def\e{+\infty} % infinity symbol
    \else
      \pgfmathparse{-ln(tan(\t/2))} % pseudorapidity
      \pgfmathroundtozerofill{\pgfmathresult} % round with trailing zeroes
      \pgfmathsetmacro\e{\t==90?0:\pgfmathresult} % no trailing zeroes for theta = 90
    \fi
    \draw[->,thick] % eta lines
      (0,0) -- (\t:1.2) node[anchor=180+\t,black] {$\eta=\e$}
      node[black,pos=0.72,fill=white,scale=0.8,inner sep=2] {$\theta=\t^\circ$};
  }
\end{tikzpicture}
\end{document}

Full code to edit and compile if you like:

% Author: Izaak Neutelings (June 2017)
% Updated: December 2022
\documentclass[border=3pt,tikz]{standalone}
\tikzset{>=latex} % for LaTeX arrow head

\begin{document}

% PSEUDORAPIDITY with manual for-loop over theta, eta
\begin{tikzpicture}[scale=3]
  \def\R{1.2} % radius/length of lines
  \node[scale=1,below left=1] at (0,\R) {$y$}; % y axis
  \node[scale=1,below left=1] at (\R,0) {$z$}; % z axis
  \foreach \t/\e in {90/0,60/0.55,45/0.88,30/1.32,10/2.43,0/+\infty}{ % loop over theta/eta
    \pgfkeys{/pgf/number format/precision=2}
    \draw[->,black!60!red,thick,line cap=round] % eta lines
      (0,0) -- (\t:\R) node[anchor=180+\t,black] {$\eta=\e$}
      node[black,pos=0.7,fill=white,scale=0.8,inner sep=1.5pt] {$\theta=\t^\circ$};
  }
  %\draw[black!60!red,thick] (0,0.1*\R) |- (0.1*\R,0) ; % overlap in corner
\end{tikzpicture}

% PSEUDORAPIDITY with automatic calculation of eta
\begin{tikzpicture}[scale=3]
  \pgfkeys{/pgf/number format/precision=2} % two decimals
  \def\R{1.2} % radius/length of lines
  \node[scale=1,below left=1] at (0,\R) {$y$}; % y axis
  \node[scale=1,below left=1] at (\R,0) {$z$}; % z axis
  \foreach \t in {90,60,45,30,10,0}{ % loop over theta
    \ifnum \t = 0
      \def\e{+\infty} % infinity symbol
    \else
      \pgfmathparse{-ln(tan(\t/2))} % pseudorapidity
      %\pgfmathroundto{\pgfmathresult} % round without traling zeroes
      \pgfmathroundtozerofill{\pgfmathresult} % round with trailing zeroes
      \pgfmathsetmacro\e{\t==90?0:\pgfmathresult} % no trailing zeroes for theta = 0
    \fi
    \draw[->,black!60!red,thick,line cap=round] % eta lines
      (0,0) -- (\t:\R) node[anchor=180+\t,black] {$\eta=\e$}
      node[black,pos=0.7,fill=white,scale=0.8,inner sep=1.5pt] {$\theta=\t^\circ$};
  }
  %\draw[black!60!red,thick] (0,0.1*\R) |- (0.1*\R,0) ; % overlap in corner
\end{tikzpicture}

\end{document}

Click to download: axis2D_pseudorapidity.tex • axis2D_pseudorapidity.pdf
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