Past exam of the mathematics course of the University of Cambridge 2022 iii Paper 305 1 iii Solution 2026-09-28
The near equality makes the QCD Lagrangian approximately invariant under the isospin group acting on . Treating as small compared with the hadronic scale enlarges this to approximate flavor symmetry, whose hadron multiplets form the eightfold way. The observed multiplet pattern motivated the quark model, while the need for a hidden three-valued quantum number and a consistent strong dynamics led to color and QCD.
QCD explains both symmetries because its gluon coupling is flavor blind; only the quark-mass matrix breaks flavor symmetry. There is no useful larger light-flavor symmetry because . Their mass terms break too strongly for hadrons containing them to join approximately degenerate extensions of the light-quark multiplets.