The states belong to the spin- decuplet

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 Σ∗(1385)\Sigma^*(1385) states belong to the spin-3/23/2 decuplet, with quark content Σ∗+=uus\Sigma^{*+}=uus, Σ∗0=uds\Sigma^{*0}=uds, Σ∗−=dds\Sigma^{*-}=dds, and measured masses M(Σ∗+)=1382.8 MeV/c2M(\Sigma^{*+})=1382.8\,\mathrm{MeV}/c^2, M(Σ∗0)=1383.7 MeV/c2M(\Sigma^{*0})=1383.7\,\mathrm{MeV}/c^2, M(Σ∗−)=1387.2 MeV/c2M(\Sigma^{*-})=1387.2\,\mathrm{MeV}/c^2. (a) Using the quark content, find the baryon number BB, strangeness SS and hypercharge Y=B+SY=B+S shared by the three states. (b) Using Q=I3+Y/2Q = I_3+Y/2 and the measured charges Q(Σ∗+)=+1Q(\Sigma^{*+})=+1, Q(Σ∗0)=0Q(\Sigma^{*0})=0, Q(Σ∗−)=−1Q(\Sigma^{*-})=-1, find I3I_3 for each state and identify the isospin II of the triplet, in the same way an isospin triplet was built from charge and hypercharge previously. (c) Find the spread M(Σ∗−)−M(Σ∗+)M(\Sigma^{*-})-M(\Sigma^{*+}) and compare it with the roughly 150 MeV/c2150\,\mathrm{MeV}/c^2 cost of one extra strange quark (the decuplet row spacing) to decide whether the spread inside this triplet is isospin breaking or three-flavour symmetry breaking.

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