Someone argues: "the

PHYSICS · Subjective · 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

\Sigma^+

\Sigma^0

and

\Sigma^-

all belong to the same isospin multiplet with

I=1

, so isospin symmetry demands they have exactly the same mass. But the measured masses are

1189.4

1192.6

and

1197.4\,\mathrm{MeV}/c^2

(a spread of

8.1\,\mathrm{MeV}/c^2

), so isospin symmetry must be wrong." (a) Is this conclusion correct? Justify your answer. (b) State what isospin symmetry actually predicts about the masses within a multiplet, and check whether the

8.1\,\mathrm{MeV}/c^2

spread is consistent with that prediction.

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