Particle mass versus lifetime & decay length

Standard Model particles plotted as mass versus lifetime to show its stability in the context of high-energy physics detectors such as the CMS detector.

Note the average decay length is given by L = γβcτ = (pc/mc²)(cτ), because β = v/c and the average distance traveled by a particle is L = v(γτ), where the lifetime is dilated due to a boost with a Lorentz factor γ = 1/sqrt(1-β²). We can write γβ = pc/mc², because the relativistic momentum is given by p = γmv.

Mass versus proper lifetime, including the electron mass:

Zoomed in so the electron falls outside the mass range:

The average decay length L = γβcτ, assuming a momentum of p = 10 GeV/c:

Assuming a momentum of p = 20 GeV/c:

Assuming a momentum of p = 50 GeV/c:

Assuming a momentum of p = 100 GeV/c:

Assuming a momentum p between 1 and 50 GeV/c to show the full variation of the decay length:

Animating the average decay length for momenta between 1 and 50 GeV/c:

Edit and compile if you like:

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% Author: Izaak Neutelings (December 2022)
% Inspired by
%   https://www.sciencedirect.com/science/article/pii/S0146641019300109
%   https://iopscience.iop.org/article/10.1088/1361-6471/ab4574/pdf
\documentclass[border=3pt,tikz]{standalone}
\usepackage{siunitx}
\usepackage[outline]{contour} % glow around text
\usepackage{xfp} % needed for accuracy with \fpeval
\usepackage{pgfplots} % for the axis environment
\contourlength{1.1pt}
\tikzset{>=latex} % for LaTeX arrow head
% redraw axis on top / in front (over filled areas)
\makeatletter \newcommand{\pgfplotsdrawaxis}{\pgfplots@draw@axis} \makeatother
\pgfplotsset{axis line on top/.style={after end axis/.append code={\pgfplotsdrawaxis}}}
% UNSLANT GREEK LETTERS for particle symbols
% https://tex.stackexchange.com/questions/145926/upright-greek-font-fitting-to-computer-modern
% https://tex.stackexchange.com/questions/236915/adjust-custom-made-upright-greek-letters-when-used-in-subscripts
\usepackage{scalerel}
\newsavebox{\foobox}
\newcommand{\slantbox}[2][0]{\mbox{%
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}}
\newcommand\unslant[2][-.25]{%
  \mkern1.2mu%
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\newcommand{\PJpsi}{J\!/\!$\unslant\psi$}
% COLORS
\colorlet{boscol}{red!80!black} % boson color
\colorlet{mescol}{blue!70!cyan!90!black} % meson color
\colorlet{barcol}{blue!80!cyan!65!red!85} % baryon color
\colorlet{lepcol}{green!80!black} % lepton color
 
 
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