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

\Sigma^+

baryon has quark content

uus

and baryon number

B=1

. It belongs, with

\Sigma^0

and

\Sigma^-

, to a family of three states of equal spin and nearly equal mass. ((a)) Compute

I_3 = \tfrac12(n_u-n_{\bar u}) - \tfrac12(n_d-n_{\bar d})

for the

\Sigma^+

. ((b)) Compute the strangeness

S

(minus the number of

s

quarks, plus the number of

\bar s

quarks) and hence the hypercharge

Y = B+S

. ((c)) State the isospin

I

of the

\Sigma

family from its number of members. ((d)) Check that

Q = I_3 + Y/2

reproduces the known charge of the

\Sigma^+

Q=+1

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