Eightfold way - Aetherwisp

The eightfold way is a 1961 theoretical model to classify and organize hadrons in a structured manner. It depicts mesons and baryons in geometric groups reminiscent of group theory. It also highlights the divide between ground state particles and resonances. It was developed by American physicist Murray Gell-Mann and led to the development of the quark model.

Development#

The eightfold way starts with the proposition that hadrons should be shown on a plot with the $z$ -projection of the isospin $I_{z}$ on the $x$ axis and the hypercharge $Y=B+S$ on the $y$ axis. This seems somewhat random at first, but it leads to surprising results. The Gell-Mann-Nishijima rule shows that mixing these two in just the right way gives the electric charge:

Q=I_{z}+ \frac{Y}{2}

This equation can be interpreted as a line of slope 1/2 and intercept $I_{z}$ . Particles take place on this line based on their charge and end up forming the following geometric shapes.

Baryon_octet.png|500

The baryon octet ( $J^{P}=1/2^{+}$ ), containing the baryonic ground states. By Laurascudder, CC BY-SA 3.0, from Wikipedia.

Baryon_decuplet.png|500

The baryon decuplet ( $J^{P}=3/2^{+}$ ), containing baryonic resonances. Note that the time of creation of the eightfold way, the $\Omega^{-}$ particle had not been discovered. It does, in fact, exist and was predicted through this plot, including its mass $m_{\Omega^{-}}=1672\text{ MeV}$ and lifetime $\tau_{\Omega^{-}}\sim 10^{-16}\text{ s}$ . It was detected through the tracks of its decay products (too short-lived to detect directly). By Laurascudder, CC BY-SA 3.0, from Wikipedia.

Meson_octet.png|500

The (pseudoscalar) meson octet ( $J^{P}=0^{-}$ ), containing meson ground states. In modern day we know that this is actually a nonet, with a ninth particle ( $\eta'$ ) in the middle (a resonance, anomalously). The meson resonances are found in the vector meson nonet ( $J^{P}=0^{-}$ ), not shown here. By Laurascudder, CC BY-SA 3.0, from Wikipedia.

Despite these results being extremely interesting, it leaves some things to be desired. The major step forward historically was to take the considerations from the eightfold way and step into the domain of quarks with the quark model.