Appendix A. Constants and scales quick reference

Quantity	Symbol	Value	Comment
speed of light	$c$	$299\,792\,458\,\mathrm{m\,s^{-1}}$	exact SI definition
Planck constant	$h$	$6.62607015\times10^{-34}\,\mathrm{J\,s}$	exact
reduced Planck constant	$\hbar$	$1.054571817\ldots\times10^{-34}\,\mathrm{J\,s}$	derived exact
elementary charge	$e$	$1.602176634\times10^{-19}\,\mathrm{C}$	exact
Boltzmann constant	$k_B$	$1.380649\times10^{-23}\,\mathrm{J\,K^{-1}}$	exact
$\hbar c$		$197.3269804\ldots\,\mathrm{MeV\,fm}$	exact from defining constants
fine-structure constant	$\alpha^{-1}$	$137.035999177(21)$	measured dimensionless coupling
gravitational constant	$G$	$6.67430(15)\times10^{-11}\,\mathrm{m^3kg^{-1}s^{-2}}$	measured
electron rest energy	$m_ec^2$	$0.51099895069(16)\,\mathrm{MeV}$	measured
proton rest energy	$m_pc^2$	$938.27208943(29)\,\mathrm{MeV}$	measured
neutron rest energy	$m_nc^2$	$939.56542194(48)\,\mathrm{MeV}$	measured
Planck energy	$E_P$	$1.220890(14)\times10^{19}\,\mathrm{GeV}$	derived from $G,\hbar,c$
Higgs VEV	$v$	$\approx246.22\,\mathrm{GeV}$	derived from $G_F$
QCD crossover	$T_c$	$156.5\pm1.5\,\mathrm{MeV}$	definition-dependent pseudocritical temperature Chiral crossover in QCD at zero and non-zero chemical potentials (2019)
CMB temperature	$T_\gamma$	$2.7255\pm0.0006\,\mathrm K$	observational Cosmic Microwave Background (2025)