LEP: counting particles that leave no trace

Change the collision energy and watch a peak emerge

At CERN’s Large Electron–Positron collider, LEP, electrons and positrons collided at energies near the mass of the Z boson. The rate of producing its decay products rose and fell as the collision energy was scanned. The resulting resonance was a peak with a measurable width.

A particle with more available decay channels can have a larger total decay rate and a shorter lifetime. That rate is expressed as a decay width. The resonance therefore carries information about all the ways the Z can decay, including final states the detector cannot see.

The observed peak also depends on beam energy, radiation from the colliding particles and the apparatus. Physicists had to model these effects before assigning its shape to the Z itself. A broad peak is not automatically evidence for another neutrino.

Sources: [1] · [2] · [3]

Measure the visible pieces of the account

The ALEPH, DELPHI, L3 and OPAL experiments measured final states involving charged leptons and hadrons. Their detectors could recognize these products and determine how the visible event rates changed with energy.

A neutrino–antineutrino pair normally escaped without depositing detectable energy. In the line-shape method, those pairs were not counted one by one as tagged empty events. The invisible contribution was inferred from the total width and the measured visible channels.

The accounting can be written as the total width minus the hadronic and charged-lepton widths. The measurements share uncertainties and correlations, so this subtraction belongs to a fit with detector efficiencies and theoretical corrections, rather than a simple tally of photographs.

Sources: [1] · [3] · [2]

Use the predicted contribution of one light species

To turn an invisible width into a species count, a theory must predict the contribution of one light neutrino with the standard coupling to the Z. If every counted species has that coupling, their contributions add in a known way.

The first LEP results in 1989 favored three such species. A combined precision report published in 2006 gave a fitted effective count of 2.9840 with an uncertainty of 0.0082. This is a dated historical result, not a quotation of the latest global electroweak fit.

A fitted count need not be an integer. It is a continuous parameter extracted from measurements with uncertainty and model assumptions. Its small offset from three is not a proposal that a fraction of a neutrino species exists.

Sources: [1] · [3] · [2]

“Light” and “standard coupling” are part of the answer

The Z can only decay into a pair if the pair’s mass fits inside the available energy. A heavier neutrino beyond that threshold does not contribute through the same open channel. The familiar count therefore has a mass condition attached.

An exactly sterile neutrino has no direct standard weak coupling to the Z. It would not simply add one full species to this count. Mixing with active states or additional interactions can still produce constraints, but those require their own model and calculation.

Other invisible particles would also complicate the interpretation. This is why “three light active neutrinos with standard interactions” is more useful than an unrestricted statement that only three neutrinos can possibly exist.

Sources: [1] · [4] · [3]

Counting a family and recognizing its interaction do different jobs

LEP established the light-species count before DONUT directly identified tau-neutrino interactions. There is no contradiction: the collider measured a collective contribution to Z decay, while DONUT recognized a particular flavor through a tau produced in a target.

Neither measurement gives the tiny absolute neutrino masses. A species can be effectively massless on the Z-energy scale and still have a mass that matters in beta-endpoint experiments or cosmology. Oscillation experiments measure a different set of mass information again.

Together, these results show how an invisible particle becomes constrained from several directions. A decay peak can count allowed channels; a short track can identify tau flavor; a changing flavor probability can reveal mass differences. Each instrument asks a question the others cannot answer alone.

Sources: [1] · [5] · [4] · [6]

Primary sources & revision

1. LEP/SLD Collaborations and working groups · Precision Electroweak Measurements on the Z Resonance (2006)
2. CERN · Thirty years of LEP’s Z line shape (2019)
3. Barbara Mele · The Measurement of the Number of Light Neutrino Species at LEP (2015)
4. Particle Data Group · Neutrino Masses, Mixing, and Oscillations (2024)
5. DONUT Collaboration · Observation of Tau Neutrino Interactions (2000/2001)
6. Giunti & Laveder · Neutrino Mixing (2004)

First published and source-checked on 9 October 2026. Original explanatory text and diagrams by Sandbox Physics. Illustrations are schematic; no experimental event records are reproduced here. This is an independent educational publication, not an official Nobel or experiment collaboration publication.

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