NUC In the literature: partially resolved

Origin of the proton mass from quark and gluon energies

In plain words

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.

Precise statement

Using the QCD energy-momentum tensor $T^{\mu \nu}$ split into quark and gluon parts, determine for the proton at rest the quark mass (sigma-term) contribution, quark and gluon kinetic and potential contributions, and the trace-anomaly term $(\beta(g)/2g) F^{2}$, in MS-bar at $\mu = 2\,\mathrm{GeV}$, as fractions of $M_p = 938.27\,\mathrm{MeV}$. Also determine whether the split depends on the chosen decomposition (Ji 1995 versus Lorce 2018 and Metz-Pasquini-Rodini 2020) and which terms are measurable. Answer: numerical fractions with uncertainties plus a statement of which are scheme independent.

What would settle it

Lattice QCD computation of quark and gluon sigma terms and momentum fractions at the physical point, plus an experimental extraction of the gluon trace term from near-threshold heavy-quarkonium production.

Status in the literature

Unverified note

Lattice QCD produced a full decomposition in 2018 (Yang et al., chiQCD); the physical meaning and measurability of individual terms remained debated as of 2026.