Omega Minus Discovery and the Eightfold Way Mass Prediction

Find the line that has to explain itself.

A charged particle leaves a production vertex, travels far enough to draw a line, then ends at a second vertex. Choose that segment. The sums below are made from the particle assignments each time, not stored verdicts.

Choose the candidate

It must begin at the production vertex and end at the decay kink.

No candidate selected.

Vertex ledger

Production charge waiting

Production strangeness waiting

Decay charge waiting

Decay strangeness waiting

Authored topology diagram based on the reaction assignment in Barnes et al. It is not a geometric reconstruction and does not preserve the photograph's angles, curvature, scale, or camera view. The dashed neutral paths are inferred from the event assignment because neutral particles leave no direct bubble trail.

Leave the tenth place out.

The nine known charge states supplied three rounded isospin-multiplet mass levels. Fit only those levels. Omega-minus is locked outside the fit, where a prediction can still fail.

Historical inputs from the discovery paper

Delta, S = 0 1238 MeV/c² Sigma-star, S = −1 1385 MeV/c² Xi-star, S = −2 1532 MeV/c² Omega-minus, S = −3, held out not fitted

Fit rule

The view switch changes only the held-out comparison. It never changes the fit inputs.

Fitted line calculating three input levels

Missing level at S = −3 calculating Omega-minus remains held out

Rounded-input residual RMS calculating Zero can be caused by rounding or two-point interpolation

Calculating the historical fit.

The strong-decay gate

current ground-state masses

Choose which Omega-minus mass to place below the lightest ground-state two-body channel with the same charge, baryon number, and strangeness.

calculating

Calculating the threshold.

The check

Every result here is recomputed from the source values below. Published values remain labelled as published. The arithmetic beside them is live.

Held-out prediction

calculating

Current threshold

calculating

Vertex sums

calculating

Three mass statements

Paper prediction: about 1680 MeV/c²

First event: 1686 ± 12 MeV/c²

PDG 2026 fit: 1672.45 ± 0.29 MeV/c²

Uncertainties and free choices

The historical inputs 1238, 1385, and 1532 MeV/c² are whole-MeV labels printed in the discovery paper. Their exact 147 MeV/c² spacing is exact only at that displayed precision. Equal spacing is an approximate broken-SU(3) rule, not an exact law.
The paper said "about 1680 MeV/c²." The 1679 value is our arithmetic from its displayed levels. Neither has a published uncertainty in this form, so none is invented.
The 1686 ± 12 MeV/c² first-event value is published, not recovered from this flat diagram. The chamber analysis used three camera views, field and geometry calibration, track identification, and kinematic constraints.
The current threshold uses the 2026 PDG Xi-zero fit, 1314.86 ± 0.20 MeV, and charged-kaon average, 493.677 ± 0.013 MeV. Root-sum-square propagation assumes their errors are independent. The kaon average error already includes a PDG scale factor of 2.4.
The current Omega-minus fit assumes equal Omega-minus and anti-Omega-plus masses and averages them. Its 0.29 MeV uncertainty is combined with the threshold uncertainty only when the current gap is displayed.
Your free choices are which historical levels enter least squares, which of two fit rules is shown, and which held-out mass is compared. Omega-minus cannot be included in its own prediction.

Vacuous settings, named

Any least-squares line through only two selected levels has zero residual and zero residual degrees of freedom. The page marks it as interpolation, not evidence for equal spacing.
The all-three residual is also exactly zero because the paper's displayed inputs were rounded to a perfect spacing. It does not show that modern resonance masses are exactly equally spaced.
Strangeness minus three is inferred by applying conservation at production to the assigned particles. Reusing that same balance is not an independent confirmation, so the page calls it an inference.

Source update. The candidate spec carried Xi-zero as 1314.82 ± 0.21 MeV. The cited 2026 PDG listing now prints 1314.86 ± 0.20 MeV. This page uses the listing, which changes the threshold to calculating MeV/c² and the current gap to calculating MeV/c².

What this plate cannot establish

Not from pixels alone. Charge sign follows curvature only after the magnetic-field direction and camera geometry are known. Momentum needs calibrated curvature in three dimensions. Particle identity also uses range, ionisation, decay assignments, and constrained kinematics.

One event, cautiously stated. Barnes et al. reported an event they believed to be the postulated particle and said the charge, inferred strangeness, and reconstructed mass justified the identification. They deferred a detailed mass discussion until more events and systematic errors were better understood.

Not a spin measurement. The decuplet supplied the spin-parity assignment. The photographed event itself did not measure spin-parity; later angular analyses tested spin.

Not the quark model's mature prediction. The 1964 event tested the Eightfold Way classification and unitary symmetry. Quark proposals appeared in the same year.

The event

V. E. Barnes et al., "Observation of a Hyperon with Strangeness Minus Three", Physical Review Letters 12, 204 to 206 (1964).

The classification

Murray Gell-Mann, "Symmetries of Baryons and Mesons", Physical Review 125, 1067 to 1084 (1962).

The mass formula

Susumu Okubo, "Note on Unitary Symmetry in Strong Interactions", Progress of Theoretical Physics 27, 949 to 966 (1962).

Current masses

F. Takahashi et al. (Particle Data Group), 2026 particle listings. This is an online data release cited as forthcoming in International Journal of Modern Physics A 41, 2630011.

The photograph

Brookhaven National Laboratory, "Omega Minus", uploaded 29 December 2008, CC BY-NC-ND 2.0. It is linked rather than loaded, so this page makes no third-party request and does not modify the image.

Independent reproduction

The no-dependency verifier in research/omega-minus/verify-omega-minus.mjs independently transcribes the source anchors, recomputes every physical result displayed here, checks vertex quantum numbers, and fails on drift.