The ( ) and the ( ) are both spin- baryons with the same quark content, .

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

\Lambda

(

1115.68\,\mathrm{MeV}/c^2

) and the

\Sigma^0

(

1192.64\,\mathrm{MeV}/c^2

) are both spin-

\tfrac12

baryons with the same quark content,

uds

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

I_3

and

Y=B+S

for each, and give the point

(I_3,Y)

at which each sits on the weight diagram. ((b)) The

\Sigma^0

has two charged partners of nearly equal mass and the same spin,

\Sigma^+

(

1189.37

) and

\Sigma^-

(

1197.45\,\mathrm{MeV}/c^2

). No spin-

\tfrac12

baryon of content

uus

dds

has been seen anywhere near

1116\,\mathrm{MeV}/c^2

. Use the size of each family to give

I

for the

\Sigma^0

and for the

\Lambda

. ((c)) Compute

m(\Sigma^0)-m(\Lambda)

and compare it with the splittings inside the pion, kaon, nucleon and

\Sigma

families. Explain why this difference shows that the two are not members of one family, and why their quark content alone could not have fixed

I

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