PHYSICS · Subjective · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Symmetry, groups and the quark model
Particle Physics, Ch SU(3) flavour and the hadron multiplets
Problem
Three light quarks, each independently a u, d or s, combine as 3⊗3⊗3, and the multiplet is stated to decompose as 27=10⊕8⊕8⊕1: a decuplet, two octets and a singlet. (a) Show that the total number of ways of assigning a flavour to each of the three quarks is 27. (b) The decuplet occupies four rows, by number of strange quarks 0,1,2,3, containing 4,3,2,1 states respectively (the familiar spin-3/2 pattern). Show that these four rows sum to the decuplet's size. (c) Once the decuplet's states are removed from the 27, how many remain, and check that this number equals the combined size of the two octets and the singlet.