Hydrogen, helium and positronium spectroscopy versus QED

5 problems

• Nine $\sigma$ discrepancy in the ionization energy of metastable helium

  Open

  Helium has two electrons, which makes its energy levels harder to compute than hydrogen's, but theory now claims sub-MHz accuracy. The measured binding energy of a long-lived excited state disagrees with this theory by nine standard errors.

• Helion-$\alpha$ charge radius difference from electronic versus muonic helium

  Contested

  The difference in size between helium-3 and helium-4 nuclei can be measured with ordinary helium atoms or with muonic helium ions. The two methods disagree by about four standard errors.

• Why two 1S-3S hydrogen measurements give different proton radii

  Open

  Two labs measured the same hydrogen line and extracted proton sizes that disagree by more than two standard errors. Finding why would tell which systematic effects affect such experiments.

• Positronium $2^3\mathrm{S}_1$ to $2^3\mathrm{P}_0$ interval disagrees with QED

  Open

  Positronium, an electron bound to its antiparticle, tests quantum electrodynamics (QED, the quantum theory of light and charges) with no proton involved. One of its microwave transitions came out 4.5 standard errors away from theory.

• Residual tensions in proton radius and Rydberg constant determinations

  Partially resolved

  In 2010 muonic hydrogen (a muon orbiting a proton) gave a proton about 4% smaller than electron measurements did. New hydrogen measurements now agree with the small value, but some older hydrogen and scattering results still give the large value.