Where Does the Proton’s Mass Come From? (Hint: Mostly Not the Higgs)

You are made mostly of protons and neutrons, and almost all of their mass is not the mass of the particles inside them. That sounds like a riddle, but it is one of the most solid results in modern physics. It also means the popular line “the Higgs gives everything its mass” is only a small part of the story for ordinary matter. This post builds on our explainer What Holds the Nucleus Together? and is drawn by Corekeeper, our strong-force character, from our Forces collection.

How heavy is a proton?

The CODATA 2022 value of the proton’s rest energy is mₚc² = 938.272 089 43(29) MeV (NIST^[1]), which is about 1.67 × 10⁻²⁷ kg. Particle physicists usually quote masses as energies in mega-electronvolts (MeV), using E = mc², where c is the speed of light. 1 MeV is 1.602 × 10⁻¹³ joules.

What is a proton made of, and how much do the quarks weigh?

A proton contains two up quarks and one down quark, held together by gluons, the carriers of the strong force. The Particle Data Group’s 2024 values are mᵤ = 2.16 ± 0.07 MeV and m_d = 4.70 ± 0.07 MeV (PDG 2024^[2]). Add them up:

2 × 2.16 MeV + 4.70 MeV ≈ 9 MeV

That is about 1% of 938 MeV. As the APS viewpoint on this question puts it, “the sum of these quark masses is a mere 1% of the proton mass” (Walker-Loud 2018^[3]). Quark masses are not measured the way you weigh a free particle, because quarks are never found alone (see Why Can’t Quarks Be Isolated?), but no definition makes them anywhere near large enough to explain the proton.

So where does the other 99% come from?

From energy. Einstein’s E = mc² works in both directions: any energy that stays bound inside a system counts towards that system’s mass. Inside a proton, quarks move at close to light speed and are tied together by an intensely energetic gluon field. That energy, divided by c², is most of the proton’s mass. Frank Wilczek summarises it this way: “Most of the mass of standard matter, by far, arises dynamically, from back-reaction of the color gluon fields of quantum chromodynamics (QCD)” (Wilczek 2012^[4]).

QCD is the theory of the strong force. One of its key features, asymptotic freedom, means quarks interact weakly at very short distances and ever more strongly as you try to pull them apart. Its discoverers shared the 2004 Nobel Prize in Physics (NobelPrize.org^[5]). That growing strength at larger distances is what keeps quarks confined and makes the field energy inside the proton so large.

Can physicists actually calculate the proton’s mass?

Yes, with lattice QCD, which puts the theory’s equations on a grid of points in space and time and solves them with supercomputers. In 2008 the BMW collaboration published a full ab initio calculation of the masses of the proton, neutron and other light hadrons, using three lattice spacings to extrapolate to the continuum. Their abstract notes that more than 99% of the mass of the visible universe is in protons and neutrons, and their results “completely agree with experimental observations” (Dürr et al. 2008^[6]).

The calculation is expensive. To remove errors from the grid, physicists repeat it at several lattice spacings a and extrapolate to a → 0, at a cost that rises roughly as a⁻⁶ (Walker-Loud 2018^[3]).

How is the proton’s mass split up?

In 1995 Xiangdong Ji showed how QCD lets you separate the nucleon mass into pieces: the energy of the quarks, the energy of the gluon field, the quark masses, and a quantum term known as the trace anomaly (Ji 1995^[7]). In 2018 Yi-Bo Yang and colleagues calculated each piece with lattice QCD, including at the physical pion mass (Yang et al. 2018^[8]). Their results, in the standard MS-bar scheme at a scale of 2 GeV, are:

• Quark energy (motion and interaction energy of the quarks): 32(4)(4)%
• Gluon field energy: 36(5)(4)%
• Trace anomaly (a quarter of it, a purely quantum effect of QCD): 23(1)(1)%
• Quark condensates (the part tied to the up, down and strange quark masses): 9(2)(1)%

The numbers in brackets are statistical and systematic uncertainties in the last digit. The viewpoint article accompanying the paper adds a striking consequence: “if the up, down, and strange quark masses were all zero, the proton would still have more than 90% of its experimental mass” (Walker-Loud 2018^[3]).

Open point: the exact percentages depend on the scheme and energy scale used to define them, which is why the paper states both. There is more than one way to write down a mass decomposition, and the physical interpretation of the individual terms is still discussed. The total, 938 MeV, is not in doubt; how you slice it is partly a choice of bookkeeping.

So what does the Higgs field do?

The Higgs field gives the elementary particles their masses. CERN describes it as a field “that fills the entire Universe and gives mass to all elementary particles” (CERN^[9]). That includes the up and down quarks and the electron. But the proton is not elementary. The Higgs field’s share of the proton mass runs through the quark masses: the naive sum of the three quark masses is about 1%, and the quark-condensate term in the breakdown above, which also counts the effect of strange quarks, is about 9%. The rest, more than 90%, would be there even if those quark masses were zero.

That does not make the Higgs unimportant for you. The electron, for example, is elementary, and its Higgs-given mass sets the size of every atom. Our Vevette sticker stands for the Higgs field and the Higgsby mug for the mechanism; they just are not where most of your weight comes from.

FAQ

Do quarks make up the proton’s mass?

Only about 1%. The up and down quark masses add to about 9 MeV against the proton’s 938 MeV.

Does the Higgs boson give the proton its mass?

Mostly no. The Higgs field gives quarks and electrons their masses, but more than 90% of the proton’s mass comes from the dynamics of quarks and gluons in QCD.

How can energy have mass?

By E = mc². Energy bound inside a system adds to its mass. A proton is a small, very energetic system of quarks and gluons, so its mass is mostly that energy divided by c².

Is the neutron’s mass explained the same way?

Yes. The neutron has one up and two down quarks and the same QCD dynamics, and lattice QCD calculates its mass along with the proton’s.

References

1. NIST CODATA 2022 recommended values: proton mass energy equivalent in MeV. https://physics.nist.gov/cgi-bin/cuu/Value?mpc2mev
2. Particle Data Group (2024), Review of Particle Physics: Quarks summary table. https://pdg.lbl.gov/2024/tables/rpp2024-sum-quarks.pdf
3. A. Walker-Loud (2018), “Viewpoint: Dissecting the Mass of the Proton,” Physics 11, 118 (APS). https://physics.aps.org/articles/v11/118
4. F. Wilczek (2012), “Origins of Mass,” Central Eur. J. Phys. 10, 1021 (arXiv:1206.7114). https://arxiv.org/abs/1206.7114
5. NobelPrize.org, The Nobel Prize in Physics 2004 (asymptotic freedom). https://www.nobelprize.org/prizes/physics/2004/summary/
6. S. Dürr et al. (BMW Collaboration) (2008), “Ab Initio Determination of Light Hadron Masses,” Science 322, 1224 (arXiv:0906.3599). https://arxiv.org/abs/0906.3599
7. X. Ji (1995), “A QCD Analysis of the Mass Structure of the Nucleon,” Phys. Rev. Lett. 74, 1071 (arXiv:hep-ph/9410274). https://arxiv.org/abs/hep-ph/9410274
8. Y.-B. Yang, J. Liang, Y.-J. Bi, Y. Chen, T. Draper, K.-F. Liu & Z. Liu (2018), “Proton Mass Decomposition from the QCD Energy Momentum Tensor,” Phys. Rev. Lett. 121, 212001 (DOI 10.1103/PhysRevLett.121.212001). https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.212001
9. CERN, “The Higgs boson”. https://home.cern/science/physics/higgs-boson

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.