The Proton Radius Puzzle

Plate 44 speaks for itself: “Two rulers.”

The Physics

A muon is about 207 times heavier than an electron, so in muonic hydrogen it orbits much closer to the proton and is far more sensitive to its size. The 2010 muonic result came out well below the value from ordinary hydrogen and scattering.

m_μ / m_e ≈ 207

• m_μ: muon mass, kg
• m_e: electron mass, kg
• r_p: proton charge radius, m (quoted in fm, 10⁻¹⁵ m)

Muonic H: r_p = 0.84184(67) fm. 5σ below then-CODATA 0.8768(69) fm.

Honest caveat: Later electronic measurements moved toward the smaller value, and CODATA 2018 adopted 0.8414 fm, so the puzzle is now largely considered resolved.

Sources

• R. Pohl et al., Nature 466, 213 (2010).
• CODATA 2006 and 2018 recommended values.

On the poster

Plate 044, “The Proton Radius Puzzle”: the pixel-art plate with its slogan “Two rulers.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.