= Solution
The predicted-minus-measured differences are
$$
\Delta_\Xi=1324.79-1314.86=+9.93\,\mathrm{MeV},\qquad
\Delta_{\Xi^*}=1525.42-1531.79=-6.37\,\mathrm{MeV}.
$$
Relative 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; \b[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.
Back to article page
