Proton spin, mass and charge radius

7 problems

• Disagreement between electron-scattering values of the proton charge radius

  Partially resolved

  Muonic hydrogen (a proton orbited by a muon, a heavy cousin of the electron) and the most precise hydrogen measurements give a proton radius of about $0.84\,\mathrm{fm}$ ($1\,\mathrm{fm} = 10^{-13}\,\mathrm{cm}$). Electron-scattering experiments disagree with each other, one giving $0.83\,\mathrm{fm}$ and an older one $0.88\,\mathrm{fm}$, and the cause is not identified.

• Gluon gravitational form factors and the proton mass radius

  Contested

  How mass and pressure are spread inside the proton can be read from its response to gravity-like probes, approximated in practice by producing heavy $J/\psi$ mesons just above threshold. Early extractions disagree on whether mass is more concentrated than charge.

• Total gluon spin contribution $\Delta G$ to the proton spin

  Open

  Gluons, the particles that bind quarks, can carry spin aligned with the proton's. Collider data show a positive contribution from medium-momentum gluons, but the part from very low-momentum gluons is unknown.

• Origin of the proton mass from quark and gluon energies

  Partially resolved

  The quarks in a proton weigh about one percent of the proton; the rest comes from the motion and interaction energy of quarks and gluons. How much comes from each source, including the trace anomaly (a mass scale generated purely by quantum effects in a theory with no built-in scale), is debated.

• Measuring quark and gluon orbital angular momentum in the proton

  Open

  Quarks and gluons circulate inside the proton, and this circulating motion carries part of its spin. No experiment has yet measured this orbital part directly.

• Pion-nucleon $\sigma$ term: lattice QCD versus pion-nucleon scattering

  Contested

  The $\sigma$ term measures how much of the proton mass comes from the small masses of the up and down quarks. Extractions from pion-proton scattering give about 59 MeV, while several lattice QCD calculations (QCD solved numerically on a space-time grid) give about 40 to 45 MeV.

• How the proton spin divides among quarks and gluons

  Partially resolved

  The proton spin of $1/2$ (in units of $\hbar$) must be the sum of quark spins, gluon spins and the orbital motion of both. Only the quark-spin part is measured well, at about 30 percent.