The light vector mesons have the quark contents , , ,

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

The light vector mesons ρ+,ρ−,K∗+,K∗0,Kˉ∗0,K∗−\rho^+,\rho^-,K^{*+},K^{*0},\bar K^{*0},K^{*-} have the quark contents udˉu\bar d, duˉd\bar u, usˉu\bar s, dsˉd\bar s, sdˉs\bar d and suˉs\bar u respectively. Take the quark isospin components as I3(u)=+12I_3(u)=+\tfrac12, I3(d)=−12I_3(d)=-\tfrac12, I3(s)=0I_3(s)=0 (and the opposite sign for each antiquark), the quark strangeness as S(u)=S(d)=0S(u)=S(d)=0, S(s)=−1S(s)=-1 (and the opposite sign for each antiquark), and hypercharge Y=B+SY=B+S with B=0B=0 for a meson. (a) Add the quark and antiquark values to find (I3,Y)(I_3,Y) for each of the six mesons listed. (b) Plot the six points and state what shape they trace out on the (I3,Y)(I_3,Y) plane. (c) Say which multiplet decomposition, 3⊗3ˉ=8⊕13\otimes\bar3=8\oplus1, this hexagon belongs to, and what kind of state(s) would sit at the remaining (0,0)(0,0) point(s) not asked for here.

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