The baryon has quark content and baryon number

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Symmetry, groups and the quark model

Particle Physics, Ch Isospin: a symmetry used as bookkeeping

Problem

The Σ−\Sigma^- baryon has quark content ddsdds and baryon number B=1B=1. It belongs, with Σ0\Sigma^0 and Σ+\Sigma^+, to a family of three states of equal spin and nearly equal mass. ((a)) Compute I3I_3 for the Σ−\Sigma^- from its quark content. ((b)) Compute the strangeness SS and hence the hypercharge Y=B+SY=B+S. ((c)) State the isospin II of the Σ\Sigma family from its number of members. ((d)) Check that Q=I3+Y/2Q = I_3 + Y/2 reproduces the known charge of the Σ−\Sigma^-, Q=−1Q=-1.

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