The Eightfold Way — Question 6

Question 6

Equal spacing provides an approximate decuplet mass prediction

In an illustrative isospin-averaged decuplet, the first three strangeness rows have rest energies 1230, 1380 and 1530 MeV. Assume equal spacing per additional unit of negative strangeness. A comparison value for the last row is 1672 MeV.

1. Predict the last mass and verify the two input spacings.

2. Find the comparison-minus-prediction residual and fractional discrepancy relative to the comparison mass.

Question 6 - Solution

Equal spacing provides an approximate decuplet mass prediction

(a) Method and calculation

$$\boxed{\delta M=1380-1230=1530-1380=150\ {\mathrm{MeV}}/c^2}.$$$$\boxed{M_{\Omega}c^2=1530+150=1680\ {\mathrm{MeV}}}.$$

(b) Interpretation and further calculation

$$\boxed{r=(1672-1680)\ {\mathrm{MeV}}=-8\ {\mathrm{MeV}}}.$$$$\boxed{|r|/1672=0.00478469=0.478469\%}.$$

Physical check

Flavor symmetry is approximate; equal spacing is a useful mass relation, not an exact conservation law.