 Solution

ID: past-exam-of-the-nuclear-and-particle-physics-course-of-the-university-of-oxford/2022/4/e/solution

Write the charge in units of

e

Q = a I_{z} + b (B + S)

. The proton and neutron have

(I_{z}, B + S) = (1/2, 1)

and

(- 1/2, 1)

, so their measured charges imply

1 = a /2 + b

and

0 = - a /2 + b

. Thus

a = 1

b = 1/2

Q = I_{z} + \frac{B + S}{2} .

Y = B + S

1/3

and the isospin and strangeness assignments from part (a),

Q_{u} = \frac{1}{2} + \frac{1}{6} = \frac{2}{3}, Q_{d} = - \frac{1}{2} + \frac{1}{6} = - \frac{1}{3}, Q_{s} = 0 + \frac{1/3 - 1}{2} = - \frac{1}{3} .

Physical electric charges are these numbers multiplied by the positive elementary charge

e

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