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. As the collision energy was scanned, the rate of Z decay products rose and fell, tracing a resonance peak with a measurable width.

The more ways a particle can decay, the larger its total decay rate can be and the shorter its life. That rate is expressed as a decay width. So the resonance carries information about every way 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 attributing the shape to the Z itself. A broad peak alone does not prove another neutrino.

Sources: [1] · [2] · [3]

First measure the decays that can be seen

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 leaving detectable energy. The line-shape method did not tag and count these pairs as empty events. It inferred the invisible part from the total width and the measured visible channels.

In words, the invisible width is the total width minus the hadronic and charged-lepton widths. The measurements share uncertainties and are correlated, so the subtraction is done inside a fit that includes detector efficiencies and theoretical corrections, not by simply tallying events.

Sources: [1] · [3] · [2]

How much should one light species add?

To turn the invisible width into a number of species, theory has to predict how much one light neutrino with the standard Z coupling contributes. If every 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 number of 2.9840, with an uncertainty of 0.0082. That figure comes from the 2006 report, not from the latest global electroweak fit.

A fitted number need not be a whole number. It is a continuous parameter extracted from measurements, with an uncertainty and model assumptions. Its small offset from three does not suggest a fraction of a neutrino species.

Sources: [1] · [3] · [2]

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

The Z can decay into a pair only if the pair’s mass fits within the available energy. A neutrino too heavy for that does not add to the width through this channel. So the familiar count comes with a mass condition.

A purely sterile neutrino has no direct standard weak coupling to the Z, so it would not add a full species to the count. Its mixing with active states, or extra interactions, can still be limited, but each case needs its own model and calculation.

Other invisible particles would also complicate the reading. That is why “three light active neutrinos with standard interactions” is more useful than a blanket claim that only three neutrinos can exist.

Sources: [1] · [4] · [3]

Counting the species and identifying one are different tasks

LEP had counted the light species before DONUT directly identified tau-neutrino interactions. The two answer different questions: the collider measured the combined contribution to Z decay, and DONUT recognized one flavor through a tau produced in a target.

Neither measurement gives the tiny absolute masses of neutrinos. A neutrino can be effectively massless at the Z energy scale and still have a mass that matters for beta-endpoint experiments or cosmology. Oscillation experiments measure yet another kind of mass information.

Together these results pin down an invisible particle from several directions. A decay peak can count the 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 2026-10-09; last revised 2026-10-09. 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.