The baryons have quark content and

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

\Xi

baryons have quark content

\Xi^0 = uss

and

\Xi^- = dss

, with measured masses

1314.86\,\mathrm{MeV}/c^2

and

1321.71\,\mathrm{MeV}/c^2

respectively. ((a)) From the quark content, compute

I_3

and

Y=B+S

for each state, and give their coordinates

(I_3,Y)

on the weight diagram. ((b)) State the isospin

I

of this family and confirm that the number of members found matches

2I+1

. ((c)) Compute the mass splitting

\Delta m = m(\Xi^-)-m(\Xi^0)

and compare it with the electromagnetic scale of

1.44\,\mathrm{MeV}

that two unit charges separated by

1\,\mathrm{fm}

would store.

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