Muon-electron mass ratio

The muon is a carbon copy of the electron with 207 times the mass: identical charge, identical spin, identical couplings. The Standard Model accommodates the mass but does not explain it, and the pattern repeats with the tau at 3477 electron masses. This unexplained hierarchy of lepton masses is one of the sharpest open questions in particle physics.

The ratio has practical consequences. Bohr radii scale as 1/mass, so a muon captured by a proton orbits 207 times closer — muonic atoms probe the nuclear charge distribution directly, and muon-catalysed fusion works because a muonic molecular ion brings two nuclei close enough to tunnel. The ratio also enters the muon's anomalous magnetic moment, where sensitivity to heavy virtual particles grows as (m_μ/m_e)² ≈ 43 000, which is why the Fermilab g−2 experiment uses muons rather than electrons to look for new physics.