The foregoing quark models completely specify the quantum numbers of pions. The charge, angular momentum, baryon-number, lepton-number and strangeness are all correct. These models also produce accurate calculated values for the lifetime, width and mass. Results that fall outside of experimental uncertainty are noted with an X in all tables. There are just a handful of these errors from among hundreds of particles.

## Particle Cores

Some highly excited states contain so many quarks that it may be difficult to see how the models work. So to view the underlying pattern, we ignore most of the quark/anti-quark pairs. The pairs are needed for stability. But these field quarks obscure the minimum number of quarks required to identify a particle and account for its mass.ย So we remove them and the remaining core quarks are shown in the table below.

Fixing attention on the core shows more clearly how excited pions are built-up over blocks of the same baryonic quarks. The mass depends on not . So is unchanged by any variation in the field of pairs. A particle’s rest mass is completely determined by its core quarks.

Experimentally observed values are taken from this reference .

## Sample Calculations for Pions

Here is a spreadsheet that shows a step-by-step calculation for a specific pion. For more detail about cell contents and formulae, you can see a read-only, on-line version by clicking the icon in the black bar at the bottom of the sheet. To get a copy of the spreadsheet click the download link at the bottom of this page. Then you can enter other quark-coefficients in the yellow cells to assess other particle models.