Pions

Quark Models of Pions

Here are some quark models of pions. All pions are built-up around the heart of familial seeds shown on the left. Particles with a different angular momentum or charge are modeled by including various quarks around this common kernel. Then excited states are obtained by adding even more quarks. The pions may share more quarks in addition to the familial pattern. But this nugget is the minimum necessary to distinguish the pions from other particle families.  Nuclear particles are classified on this basis. EthnoPhysics analyzes the mechanics of pions using chains of events  noted by where each repeated cycle is composed of the following quarks.

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.

Pion 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.  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 .

Pion Calculations

Here is a spreadsheet that shows a step-by-step calculation of charged-pion characteristics. For more detail about cell contents and formulae, click the download link at the bottom of the sheet. Then you can enter other quark-coefficients in the yellow cells to assess different particle models.

This sheet shows that has an angular-momentum quantum-number of Therefore its orbital radius is All the particle radii are zero too. So its quark flux vector and wavenumber in vacuo are both nil. Thus its wavelength is also zero. Finally, since both the shape of satisfies the definition of a point particle. Indeed, both and are perfect point-charges.

Now here are some calculations about neutral pions.

Both the foregoing pions have cores that do not include any dynamic quarks. So they do not have any electromagnetic or weak potential energy. And no work is required to assemble these pions. Their formation and binding is due to their thermal potential.