Hadron Multiplets

Explore light-flavor multiplets

The diagram classifies states built from u, d and s flavors using approximate flavor SU(3) symmetry. Choose the pseudoscalar meson octet with J = 0, baryon octet with J = 1/2 or baryon decuplet with J = 3/2, then Show. These contain 8, 8 and 10 states. This is a classification model, not a calculation of QCD dynamics or hadron masses.

Every point is at its physical isospin projection I₃ and hypercharge Y. Select any state using the native list or its diagram label. Labels are also keyboard buttons: Tab to a label, then Enter or Space. Leader lines connect displaced labels to their actual weights. The marker and displayed values use the same selected state.

Quantum numbers

I is total isospin; I₃ is its projection. For these flavors, hypercharge is Y = B + S and electric charge in units of e is Q = I₃ + Y/2. The u, d and s quarks have charges +2/3, −1/3 and −1/3, and baryon number +1/3. Their I₃ values are +1/2, −1/2 and 0. The strange quark has S = −1; u and d have S = 0. Antiquarks have the opposite additive quantum numbers and are shown with overbars.

Valence contributions are summed in exact integer thirds and halves. For example, the neutron udd has I₃ = −1/2, Y = +1 and Q = 0. Negative half-integers retain their minus signs. The flavor content listed for a baryon is not a complete spin-flavor wavefunction.

Coincident weights and neutral mesons

Λ and Σ⁰ both occupy (I₃,Y) = (0,0), but Λ has I = 0 and Σ⁰ has I = 1. Similarly, π⁰ and η₈ share (0,0), with I = 1 and I = 0. Their physical points are not moved apart. Separate labels and the complete particle list make both states accessible.

The neutral mesons are superpositions: π⁰ = (uū − dd̄)/√2 and η₈ = (uū + dd̄ − 2ss̄)/√6. They are not each a single fixed quark-antiquark pair. η₈ is the pure octet basis state. The physical η involves mixing with the flavor singlet and is not identified with η₈ here; no physical η mass is assigned to η₈.

Quiz

Each question supplies total isospin I together with I₃ and Y, or Q and Y. The full set of clues identifies exactly one state, including the coincident center pairs. Choose a state, then check. Only the first answer counts; checking again cannot increase the score. Feedback names the correct state, marked by a dashed green label and marker. The solid red marker indicates the current selection.

Next question clears the selection and previous particle details. Questions follow a deterministic complete cycle through the multiplet, alternating the two clue forms. Changing multiplet or mode clears the old result and quiz and waits for Show. Navigation retains the current quiz in memory; reloading or changing language restores only valid settings, never quiz scores or answers.

Mass examples and scope

The optional mass values are rounded illustrative examples retained for comparison. They are not current PDG measurements, do not express experimental uncertainty, and are not predicted by this SU(3) diagram. η₈ has no assigned mass. Flavor SU(3) is approximate, in particular because the strange quark differs in mass from the up and down quarks.

Source

Particle Data Group, Quark Model review, 2025: light-flavor quantum numbers, meson octet and singlet mixing, and baryon representations.