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Neutron–Proton Mass Difference: Why the Neutron Is Heavier

The neutron–proton mass gap is the small net result of competing quark-mass and electromagnetic effects, calculated using lattice QCD+QED.
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The neutron is heavier than the proton because two small effects pull their masses in opposite directions: the heavier down quark raises the neutron’s mass, while electromagnetism raises the mass of the electrically charged proton. The quark-mass effect wins, leaving a difference of about 0.14% of the average nucleon mass.

What is the neutron–proton mass difference?

A neutron and a proton are both nucleons, built from up and down quarks. A neutron contains two down quarks and one up quark (udd); a proton contains two up quarks and one down quark (uud). The neutron’s mass is slightly greater, but the gap is small: Borsanyi and colleagues described it in 2014 as about 0.14% of the average proton and neutron mass.

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This is a net difference, not a measure of where most of either particle’s mass comes from. Most proton and neutron mass is associated with strong-interaction energy. The mass splitting between them, by contrast, depends on small departures from the idealized symmetry between up and down quarks and on electromagnetism.

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Why do the two effects pull in opposite directions?

The down quark makes the neutron heavier

The down quark is heavier than the up quark. Since the neutron has two down quarks while the proton has only one, this quark-mass difference tends to make the neutron heavier. The Particle Data Group’s 2023 review gives an illustrative contribution of roughly 2.5 MeV in this direction.

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The proton’s electric charge pushes the other way

The proton carries electric charge, so electromagnetic effects contribute to its mass. This raises the proton’s mass relative to the neutron and therefore reduces the neutron–proton gap. The Particle Data Group’s 2023 review describes this contribution as roughly 1 MeV in the direction that makes the proton heavier.

Those rounded contributions are explanatory estimates, not exact, independently measured pieces of the mass difference. Separating electromagnetic and quark-mass effects depends on the calculation convention; the review also discusses finite-volume subtleties in lattice QED. The important result is the balance: the down–up quark-mass effect is larger, so the neutron remains heavier overall.

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How can physicists calculate such a small splitting?

In a strong-interaction-only idealization where up and down quarks have equal masses, proton and neutron would be degenerate. That calculation would leave out the ingredients needed to explain their different masses in nature. A realistic calculation must account for both the unequal up- and down-quark masses and electromagnetic effects.

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Lattice quantum chromodynamics (lattice QCD) represents spacetime on a discrete grid so that the equations of the strong interaction can be evaluated numerically. To calculate the neutron–proton splitting, researchers combine QCD with quantum electrodynamics (QED), while allowing the up and down quarks to have different masses.

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In a 2014 study, Borsanyi and collaborators used lattice QCD+QED with four non-degenerate Wilson fermion flavors. They reported an accuracy of 300 keV for the splitting and found it positive—meaning the neutron is heavier—by five standard deviations. These are the results reported by that study, not a claim that it provides the latest or best precision available today. The authors summarized the mechanism as a “competition between electromagnetic and mass isospin breaking effects.”

Is the difference caused by the Higgs?

Only indirectly, and it is important to distinguish two questions. The Higgs field gives elementary quarks their masses, including the different masses of the up and down quarks. But most of the mass of a proton or neutron comes from strong-interaction energy, not simply from adding up the masses of its quarks. The small difference between the two nucleons reflects the quark-mass contrast together with electromagnetic effects; it is not a direct measurement of the Higgs boson or an explanation for most ordinary matter’s mass.

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Why does the mass ordering matter?

The fact that a free neutron is heavier than a proton matters to decay energetics and to the conditions under which familiar atoms and nuclei exist. It is one important part of the picture, not a standalone explanation for the stability of every nucleus: nuclear binding and other physical factors also matter.

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