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

The predicted-minus-measured differences areRelative to the measured masses, these are $+0.755\%$ and $-0.416\%$. The predicted spin-spin interaction splitting is $200.62\mathrm{MeV}$, compared with the measured $216.93\mathrm{MeV}$, a discrepancy of about $7.5\%$ in the splitting.

This is an effective constituent-quark model, with a common spatial contact factor and a nonrelativistic spin-dependent interaction applied to light quarks. Relativistic motion, different spatial wavefunctions, and omitted strong-interaction corrections prevent an expectation of accuracy at the experimental $0.2$--$0.3\mathrm{MeV}$ scale. Agreement at the level of several percent in absolute baryon masses would already be useful for such a simple formula; the sub-percent absolute-mass agreement here is better than that rough expectation.

No theoretical uncertainty or fitting prescription is supplied, so there is no unique numerical “expected error” or justified statistical significance to attach to the deviations. Small relative errors in the large spin-independent mass sum also need not imply equally small relative errors in the much smaller spin-spin interaction splitting.