Quark Composition of Baryons and Mesons
Live values
The omega-minus: a prediction that came true
The prediction. By 1962 nine of the ten particles in the decuplet had been found, and the pattern had a gap at the bottom. At a conference at CERN in July 1962, Murray Gell-Mann predicted the missing particle: three strange quarks (in today’s language), a strangeness of −3, a charge of −1 and a mass of about 1680 MeV/c2. With that mass it could only decay by the weak interaction, so it would live long enough to leave a visible trail.
The search. A team at Brookhaven National Laboratory in New York fired a beam of K− mesons into the 80-inch liquid hydrogen bubble chamber and took about 100,000 photographs. In January 1964 one of them showed the chain of decays that only an omega-minus could produce.
The result. The team measured its mass as 1686 ± 12 MeV/c2, matching the prediction. The modern value is 1672 MeV/c2. The discovery convinced most physicists that the pattern was real, and it led to the quark model. Gell-Mann received the 1969 Nobel Prize in Physics.
Read more. The discovery paper is Barnes et al., Observation of a Hyperon with Strangeness Minus Three, Physical Review Letters 12, 204 (1964). HyperPhysics shows the bubble chamber photograph.
Equations
Hadrons. A meson is made of a quark and an antiquark, so its baryon number is +⅓ − ⅓ = 0. A baryon is made of three quarks, so its baryon number is +1. An antibaryon is made of three antiquarks.
Reading the diagrams. Particles on the same horizontal line have the same strangeness, and particles on the same sloping line have the same charge. Strangeness comes only from s quarks (−1 each) and s antiquarks (+1 each), so counting the s quarks gives the row.
The middle of each octet. Two particles share the centre. The Σ0 and Λ both have the quark content uds, but they are different particles with different masses, 1193 and 1116 MeV/c2. The π0 is a mixture of uu and dd, and the η is mainly ss mixed with uu and dd. This page accepts any of those combinations for the centre, and explains which is the main one.
Beyond A-level: why an octet and a decuplet? Quarks have a property called spin. In the octets the quarks’ spins partly cancel; in the decuplet all three spins line up, which gives those baryons more energy and so more mass. That is why the decuplet baryons are heavier than the octet baryons with the same quarks: the Δ+ (uud, 1232 MeV/c2) and the proton (uud, 938 MeV/c2). The different spin arrangements are also what make the Λ and the Σ0 different particles.
The kaons. K0 (d s) and K̄0 (s d) are both neutral, but they are different particles: each is the antiparticle of the other.
Strangeness and interactions. Strangeness is conserved in the strong and electromagnetic interactions. In a weak interaction it can change by 0 or ±1, which is why the omega-minus, the lightest particle with S = −3, decays slowly by the weak interaction in steps of one.