---
title: "Alvarez’s group finds short-lived particles in combinations of tracks"
description: "How can a particle be discovered when it decays before it can leave a visible track?"
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last_modified: "2026-10-24"
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Particles · Experiments · Discovery

# Alvarez’s group finds short-lived particles in combinations of tracks

How can a particle be discovered when it decays before it can leave a visible track?

Sandbox Physics · 2026-10-24

Nobel contribution: 1968-1

1. Photograph interactions in hydrogen
2. Measure three-dimensional tracks
3. Combine daughter energies and momenta
4. Look for repeated masses

A resonance is inferred from a distribution of reconstructed combinations across many events.

## The missing track can leave measurable daughters

Some particles decay far too quickly to draw a separate line in a bubble chamber. In 1960, Luis Alvarez’s Berkeley group showed how such a particle could emerge from measurements of the particles it produced. The group studied interactions photographed in hydrogen and combined the measured energies and momenta of suitable outgoing particles. Particular combinations repeatedly gave a mass close to one and a half proton masses, the strange resonance now called Sigma(1385).

The word resonance describes an unstable state that appears especially often at a particular combined energy. It can be found even when no camera resolves the distance it travels. The evidence is a pattern across events: outgoing particles are more likely to appear together with one characteristic combined mass. The invisible parent has left a statistical signature in its visible daughters.

This required a substantial instrument behind each plotted point. A hydrogen bubble chamber supplied a proton target and recorded charged-particle paths. Different camera views made three-dimensional reconstruction possible. A known magnetic field linked curvature to momentum. Scanners and measuring systems then turned the photographs into numerical descriptions of individual events. A striking photograph began a much longer measurement.

Sources: [1] [2] [3]

## Mass belongs to the pair as a whole

Add the two daughter energies and add their momentum vectors. Those sums describe the pair as one physical system. Imagine observing it from a frame in which its total momentum is zero. The energy left in that frame corresponds to the pair’s invariant mass. The word invariant means that observers moving relative to one another agree on this mass, even though they assign different energies to the individual daughters.

Simply adding the individual rest masses would miss the point. Two identical particles moving apart quickly have more combined energy than the same pair nearly at rest together. Their kinetic energy in the pair’s rest frame contributes to the invariant mass. Both the amount of momentum and the angle between the tracks matter, so the reconstruction needs the geometry as well as the particle identification.

For a parent that decays into that pair, conservation of energy and momentum ties the pair’s combined mass to the parent’s mass. Repeat the calculation for many events and fill a histogram, a plot that counts how many combinations fall into each mass interval. A parent state produces an excess in a particular region, superposed on combinations that arise in other ways. The particle can thus be sought as a feature of a distribution.

A useful check is to imagine the same decay seen from a moving train. Each daughter’s measured energy changes, but the reconstructed parent should keep the same mass. That shared value lets events with different overall motions contribute to one mass spectrum. Without the momentum subtraction implicit in the calculation, simply adding laboratory energies would mix the parent’s motion with its identity.

Sources: [1] [2]

## A peak has to survive the choice of combinations

Not every visible pair comes from the decay one hopes to find. An event may contain several particles, allowing several pairings. Selecting a pair after seeing that its mass lies near an attractive value can manufacture the pattern being sought. A useful analysis therefore states the reaction and selection first, applies them consistently, and compares the resulting spectrum with plausible alternatives.

Measurement uncertainty also broadens a mass feature. So does a short-lived state’s natural spread in energy. These are different effects. Knowing the chamber’s momentum resolution helps separate instrumental blurring from properties of the state. The position of a peak alone also does not supply every quantum property: spin and parity require additional observations, such as angular distributions and competing decay channels.

The 1961 follow-up by Margaret Alston and colleagues illustrates that next stage. It compared decay possibilities for the Sigma(1385) state and discussed what was still needed to identify its character. Discovery was followed by tests that distinguished explanations for the same new mass feature. A distribution could reveal a state before its full identity was known.

Sources: [2] [3] [1]

## The photograph becomes a population of events

Alvarez’s 1968 prize recognised decisive contributions to particle physics, especially resonance discoveries made possible by hydrogen bubble chambers and data analysis. The apparatus and the analysis were inseparable. Better chambers produced useful events; better measuring systems made enough of those events available for distributions to reveal new structures.

The method also changed what it meant to see a particle. A long-lived charged particle might announce itself by one clear trajectory. A very short-lived state could announce itself through many combinations, each individually ordinary-looking. The task was to preserve the event information accurately enough that the same hidden mass could appear again and again.

Sources: [1]

Continue with the physics

## Try the related models

### [Read a collision event](https://sandboxphysics.com/labs/particle-collider/)

Select a curved track and compare it with the detector layers it crosses.

A parametric generator supplies synthetic tracks and detector signals.

## Sources and reading notes

1. [L. W. Alvarez, Recent developments in particle physics (1968)](https://www.nobelprize.org/uploads/2018/06/alvarez-lecture.pdf)

   The lecture explains hydrogen chambers, scanning and measurement, and the strange-resonance discoveries.

2. [M. Alston et al., Resonance in the Lambda–pi system (1960)](https://doi.org/10.1103/PhysRevLett.5.520)

   The original resonance report combines reconstructed particle momenta; read with its 1961 erratum.

3. [M. H. Alston et al., The Sigma/Lambda branching ratio of Y1\* (1961)](https://doi.org/10.1103/PhysRevLett.6.698)

   The follow-up discusses the 1385 MeV resonance and the need for additional spin and parity information.

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