The Higgs Field
Why particles have mass
A field fills all of space. The way it settled gives particles their mass, and a rare particle, found among enormous numbers of collisions, showed that it is there. Each section ends with a closed block of details for engineers.
Space is not empty
Empty space is not quite empty. The Higgs field fills all of it, everywhere, all the time. Most fields, like the magnetic field around a magnet, fade to zero far from their source. The Higgs field does not: even in the deepest vacuum it keeps a steady value that is not zero. That steady value is what the rest of this page is about. Particles that interact with it have mass, and how strongly they interact sets how much.
For engineers
The field’s vacuum expectation value is fixed by the Fermi constant, which is measured in muon decay:
with = 1.1663787(6) × 10⁻⁵ GeV⁻² (CODATA 2022). The PDG review quotes the same relation and v ≃ 246 GeV.
The shape that breaks symmetry
The field’s energy depends on its value, and the shape of that dependence decides where the field settles. In the hot early universe the shape was a simple bowl, lowest at zero. As the universe cooled, the center rose and the bowl became a ring-shaped trough, like the bottom of a wine bottle. The field rolled off the center into the trough. Every point of the trough is equally low, but the field had to settle at one of them. That is spontaneous symmetry breaking.
For engineers
With one complex doublet Φ the potential is
For the minimum moves off zero to , that is
The figure is schematic. Its temperature control stands in for the thermal correction to , which grows with the square of the temperature and makes the effective mass term positive when the universe is hot.
How particles get mass
A particle’s mass measures how strongly it couples to the field. The electron couples weakly and is light; the top quark couples strongly and is heavy. People sometimes picture a crowd slowing someone who crosses a room. That is only an analogy: mass is not friction or drag, and nothing is slowed by a medium. Photons and gluons get no mass from the field and remain massless. Where neutrino masses come from is still an open question.
Top quark: coupling y ≈ 0.991, mass 172.60 GeV.
| Neutrinos | mass below 0.45 eV; its origin is an open question |
|---|---|
| Electron | coupling y ≈ 2.9 × 10⁻⁶, mass 0.51099895069 MeV |
| Up quark | coupling y ≈ 1.2 × 10⁻⁵, mass 2.16 MeV |
| Down quark | coupling y ≈ 2.7 × 10⁻⁵, mass 4.7 MeV |
| Strange quark | coupling y ≈ 5.3 × 10⁻⁴, mass 92.9 MeV |
| Muon | coupling y ≈ 6.1 × 10⁻⁴, mass 105.6583755 MeV |
| Charm quark | coupling y ≈ 7.3 × 10⁻³, mass 1.2729 GeV |
| Tau | coupling y ≈ 0.010, mass 1776.93 MeV |
| Bottom quark | coupling y ≈ 0.024, mass 4.186 GeV |
| W boson | gauge coupling g ≈ 0.653, mass 80.3625 GeV |
| Z boson | gauge couplings √(g² + g′²) ≈ 0.741, mass 91.1879 GeV |
| Higgs boson | self-coupling λ ≈ 0.129, mass 125.13 GeV |
| Top quark | coupling y ≈ 0.991, mass 172.60 GeV |
| Photon | no mass from the Higgs field: massless |
| Gluon | no mass from the Higgs field: massless |
For engineers
At tree level each mass is a coupling times the vacuum value:
From the measured masses, , , and . Of the doublet’s four real components, three are Goldstone modes that become the longitudinal polarizations of the W+, W− and Z. The fourth is the Higgs boson.
Photons and gluons have no direct mass-giving coupling to the Higgs field. They can still interact with the Higgs boson indirectly through quantum loops.
The mass ladder
Set the particles out by mass and the spread is enormous: the top quark is about 340,000 times heavier than the electron. Neutrinos are lighter still; their masses are not yet measured, only bounded from above. The chart uses a logarithmic scale, so each step to the right is ten times heavier.
Values in this chart
| Particle | Mass | Source |
|---|---|---|
| Neutrinos | below 0.45 eV | KATRIN Collaboration, Direct neutrino-mass measurement based on 259 days of KATRIN data, Science 388, 180 (2025) |
| Electron | 0.51099895069 MeV | PDG 2026: electron |
| Up quark | 2.16 MeV | PDG 2026: up-quark mass (MS-bar, 2 GeV) |
| Down quark | 4.7 MeV | PDG 2026: down-quark mass (MS-bar, 2 GeV) |
| Strange quark | 92.9 MeV | PDG 2026: strange-quark mass (MS-bar, 2 GeV) |
| Muon | 105.6583755 MeV | PDG 2026: muon |
| Charm quark | 1.2729 GeV | PDG 2026: charm-quark mass (MS-bar) |
| Tau | 1776.93 MeV | PDG 2026: tau |
| Bottom quark | 4.186 GeV | PDG 2026: bottom-quark mass (MS-bar) |
| W boson | 80.3625 GeV | PDG 2026: W boson mass |
| Z boson | 91.1879 GeV | PDG 2026: Z boson |
| Higgs boson | 125.13 GeV | PDG 2026: Higgs boson mass, OUR AVERAGE |
| Top quark | 172.60 GeV | PDG 2026: top-quark mass, direct measurements |
Most of your mass does not come directly from the Higgs field. A proton is two up quarks and a down quark, whose own masses add up to about 9.0 MeV, against the proton’s 938 MeV. Nearly all the rest is energy of the strong force that binds them.
For engineers
Quark masses are scheme-dependent: u, d and s are MS-bar masses at 2 GeV, c and b are MS-bar masses at their own scale, and t is the average of direct measurements. The W and Z values use the PDG Breit–Wigner convention with a mass-dependent width; they are not pole-mass values. The other masses follow their cited PDG conventions. The neutrino band shows the direct upper limit from KATRIN, below 0.45 eV at 90% confidence.
A lattice-QCD decomposition of the proton mass (MS-bar at 2 GeV) finds quark energy 33%, gluon field energy 37%, the trace anomaly 23% and the u, d, s quark condensates 9%. The valence-quark masses alone are 1.0% of the proton mass.
Finding one in a billion
At the Large Hadron Collider, bunches of protons cross 40 MHz, forty million times a second. Only about one collision in a billion makes a Higgs boson. No system could record every crossing, so the experiments choose quickly. A hardware trigger built into the detector electronics keeps at most 100 kHz. ATLAS targets an average of about 3 kHz after software selection for storage and later study. The rest is gone for good.
For engineers
The Level-1 trigger accepts events at up to the 100 kHz maximum detector read-out rate; the High-Level Trigger’s target average physics output is 3 kHz in Run 3 (ATLAS), up from about 1 kHz in Run 2. CMS uses the same two-stage design.
The bump
In 2012 the experiments looked, among other things, at pairs of photons, one of the cleanest traces a Higgs boson can leave. For each pair they computed the mass it would have if it came from a single particle. Ordinary processes give a smooth, falling spread of masses. A new particle adds a small pile at one mass. With little data the pile hides in the noise; with more data it stands out. Collect more data with the slider.
Expected significance in the peak window: 1.6σ.
For engineers
For s expected signal and b expected background events, the median discovery significance (the Asimov approximation) is
which the figure evaluates in a window around the peak. 5σ corresponds to a one-sided p-value of about 2.87 × 10⁻⁷. ATLAS and CMS announced the discovery on 4 July 2012. Their subsequently published discovery papers report local significances of 5.9σ and 5.0σ respectively (Phys. Lett. B 716, 2012, pages 1 and 30). The most sensitive channels were γγ and ZZ*→4ℓ.
Meet the boson
The particle found in 2012 is a ripple in the field itself: the Higgs boson. It weighs about 133 times as much as a proton, has no spin, and lives for about 1.6 × 10⁻²² s before it decays. More than half the time it turns into a bottom quark and its antiquark. The rare decays to two photons and to four leptons are the ones that gave it away.
- Mass
- 125.13 ± 0.11 GeV
- Spin and parity
- 0+
- Total width (predicted)
- about 4.1 MeV
- Lifetime
- about 1.6 × 10⁻²² s
Values in this chart
| Decay products | Fraction |
|---|---|
| Bottom quark and antiquark | 58.1% |
| W boson pair (one off shell) | 21.5% |
| Gluon pair | 8.18% |
| Tau and antitau | 6.26% |
| Charm quark and antiquark | 2.88% |
| Z boson pair (one off shell) | 2.64% |
| Photon pair | 0.227% |
For engineers
Spin-parity 0+ is the Standard Model assignment; measurements agree with it and exclude a pure 0− state. The total width is too small to measure directly at the LHC. The value shown is the Standard Model prediction at mH = 125.10 GeV, and the lifetime follows from it:
Is our vacuum stable?
The field’s shape at very high energies depends on the masses we measure, above all the top quark’s and the Higgs boson’s. Calculations put our vacuum just past the edge of absolute stability. It may be metastable: a lower-energy state could exist far away in field space. Even if so, the expected lifetime vastly exceeds the age of the universe. Nothing here is a danger. Drag the point to see how the answer depends on the top quark’s mass.
For engineers
The running quartic coupling falls with energy, driven by the top Yukawa. At one loop, keeping the dominant terms (for V = −μ²|H|² + λ|H|⁴):
For the measured masses λ crosses zero at about 1010 GeV. Near the measured values the condition for absolute stability is well approximated by
The chart draws this line for αs(MZ) = 0.1184. The published analyses also map an unstable region at heavier top masses, but its edge is given only as a figure, so it is not drawn here. One estimate of the metastable vacuum’s lifetime is 10139 years, and more than 1058 years at 95% confidence.
Open questions
The Higgs boson completed the Standard Model, and it also opened new questions. None of the answers below is known yet.
- How strongly does the Higgs boson couple to itself? Pairs of Higgs bosons would show it. Under stated assumptions, ATLAS and CMS together project measuring this self-coupling to better than 30% with 3 ab⁻¹ per experiment at the High-Luminosity LHC.
- Why is the Higgs boson so light? Quantum corrections should pull its mass toward the highest energy scales unless something cancels them. This is the hierarchy problem.
- Where do neutrino masses come from? They may arise from the Higgs field in a different way, or from something else entirely.
- Is the Higgs boson elementary? Its measured properties so far match an elementary particle, but it could be built from something smaller.
- Is it a link to dark matter? If dark matter couples to the Higgs field, the Higgs boson could decay into particles the detectors cannot see. Searches for such invisible decays continue.
For engineers
The quoted self-coupling precision assumes the Standard Model value and the combined ATLAS–CMS S3 scenario, including improved reconstruction performance, with 3 ab⁻¹ per experiment.
In the Standard Model the trilinear self-coupling is fixed by the Higgs mass and the vacuum value:
The hierarchy problem in one line: with a cutoff Λ, the top-quark loop shifts the Higgs mass parameter by
so a cutoff far above the weak scale needs a cancellation, or new physics near it. A dark sector could couple through the Higgs portal, a term for a new scalar S, which would add invisible decays to the Higgs boson’s total width.
Sources and further reading
The field was proposed in 1964 by the theorists Robert Brout, François Englert and Peter Higgs. The 2013 Nobel Prize in Physics went to Englert and Higgs; Brout died in 2011.
Every number on this page comes from one of these sources, or is computed from them where a formula is shown. Figures marked simulated or approximate say so on the figure.
- Particle Data Group, Review of Particle Physics (2026), Int. J. Mod. Phys. A 41, 2630011
- PDG 2026 review: Status of Higgs boson physics
- PDG 2026 listing: Higgs boson mass, OUR AVERAGE
- PDG 2026 listing: top-quark mass, direct measurements
- PDG 2026 listing: W boson mass
- PDG 2026 listing: Z boson
- PDG 2026 listing: electron
- PDG 2026 listing: muon
- PDG 2026 listing: tau
- PDG 2026 listing: up-quark mass (MS-bar, 2 GeV)
- PDG 2026 listing: down-quark mass (MS-bar, 2 GeV)
- PDG 2026 listing: strange-quark mass (MS-bar, 2 GeV)
- PDG 2026 listing: charm-quark mass (MS-bar)
- PDG 2026 listing: bottom-quark mass (MS-bar)
- PDG 2026 review: Statistics
- CODATA 2022 (NIST): Fermi coupling constant
- CODATA 2022 (NIST): proton mass energy equivalent in MeV
- CODATA 2022 (NIST): reduced Planck constant in eV s
- LHC Higgs Working Group, CERN Yellow Report 4: branching ratios and total width (arXiv:1610.07922)
- KATRIN Collaboration, Direct neutrino-mass measurement based on 259 days of KATRIN data, Science 388, 180 (2025)
- Y.-B. Yang et al., Proton mass decomposition from the QCD energy momentum tensor, Phys. Rev. Lett. 121, 212001 (2018)
- CERN: The Higgs boson
- ATLAS: New measurements of the Higgs boson find strength in unity
- CMS: Triggering and data acquisition
- ATLAS Collaboration, Operation of the ATLAS trigger system in Run 2, JINST 15 (2020) P10004
- ATLAS Collaboration, The ATLAS trigger system for LHC Run 3 and trigger performance in 2022, JINST 19 (2024) P06029
- ATLAS Collaboration, Observation of a new particle in the search for the Standard Model Higgs boson, Phys. Lett. B 716 (2012) 1
- CMS Collaboration, Observation of a new boson at a mass of 125 GeV, Phys. Lett. B 716 (2012) 30
- The Nobel Prize in Physics 2013: François Englert and Peter W. Higgs
- Physics Today obituary: Robert Brout (1928–2011)
- G. Cowan, K. Cranmer, E. Gross, O. Vitells, Asymptotic formulae for likelihood-based tests of new physics, Eur. Phys. J. C 71 (2011) 1554
- G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098
- D. Buttazzo et al., Investigating the near-criticality of the Higgs boson, JHEP 12 (2013) 089 (arXiv v4, eq. 64, section 4)
- A. Andreassen, W. Frost, M. D. Schwartz, Scale invariant instantons and the complete lifetime of the Standard Model, Phys. Rev. D 97, 056006 (2018)
- ATLAS and CMS Collaborations, Highlights of the HL-LHC physics projections by ATLAS and CMS (2025), arXiv:2504.00672