Past exam of the particle and nuclear physics course of the University of Cambridge / 2022 / Section B / 5 / d

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- Solution d

Solution

Use GeV consistently with the supplied

A^{'}

:

m_{u} = 0.362 GeV, m_{s} = 0.537 GeV, A^{'} = 0.026 Ge V^{3} .

The spin-independent sum is

m_{u} + 2 m_{s} = 1.436 GeV

. The spin-spin interaction corrections are

Δ M_{1/2} Δ M_{3/2} = 0.026 [\frac{1}{4 ( 0.537 ) ^{2}} - \frac{1}{( 0.362 ) ( 0.537 )}] GeV = - 0.111208 GeV, = 0.026 [\frac{1}{4 ( 0.537 ) ^{2}} + \frac{1}{2 ( 0.362 ) ( 0.537 )}] GeV = + 0.0894151 GeV .

Thus

M (Ξ^{0}) ≃ 1324.8 MeV, M (Ξ^{* 0}) ≃ 1525.4 MeV .

The displayed decimal places document the calculation, rather than asserting that this simple constituent-quark model has sub-MeV predictive precision.

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