The and baryons have quark content and respectively

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

\Xi^0

and

\Xi^-

baryons have quark content

uss

and

dss

respectively, and measured masses

M(\Xi^0) = 1314.9\,\mathrm{MeV}/c^2

and

M(\Xi^-) = 1321.7\,\mathrm{MeV}/c^2

. (a) Using the baryon number and the strangeness read off from the quark content of each particle (one unit of

S=-1

per strange quark), find the hypercharge

Y = B+S

of the

\Xi

doublet. (b) Using

Q = I_3 + Y/2

and the measured charges

Q(\Xi^0)=0

Q(\Xi^-)=-1

, find

I_3

for each particle, and state the isospin

I

of the pair, in the same way isospin doublets were built from charge and hypercharge previously. (c) Find the mass splitting

M(\Xi^-) - M(\Xi^0)

, and compare it with the roughly

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

that one extra strange quark costs a hadron (the decuplet row spacing) to decide whether this splitting is an example of isospin breaking or of three-flavour symmetry breaking.

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