Photograph taken at the Brookhaven National Laboratory, reproduced in The Particle Explosion by E. Swanson.

The photograph shows a proton-proton collision. The incoming high-energy proton (yellow line at the bottom) it collides with a proton at rest in the liquid hydrogen triggering the creation of a spray of particles. Seven positive pions, a proton, and a positive kaon curve off to the right, while seven negative pions move to the right. A neutral lambda is also created and travels upwards undetected until it decays into a proton and a negative pion An electron has been knocked out of its orbit by the passing proton before the collision producing the spiral at the bottom, left.

According to the Standard Model, the protons are composed of quarks and their interaction proceeds via the strong force carried by gluons. The mathematical image of the 8 gluons forms a basis for the Lie algebra of colour gauge group SU(3) and the quark triplet a basis its 3 dimensional irreducible representation:

Colour SU(3)
eight gluons	three quarks: u,d,s

The proton belongs to an octet of particles (including also the neutron, for example) forming a basis for an 8 dimensional irreducible representation of the flavour SU(3) group, the symmetry of the Eightfold Way, a physically completely different incarnation of the same mathematical object SU(3). The label S stands for ‘strangeness’, the eigenvalue of a distinguished operator from the Lie algebra; the label Q denotes the charge, the eigenvalue of another operator.

The pions and kaons created in the proton-proton collision belong to another octet of flavour SU(3):

Flavour SU(3)
proton, neutron,…	kaon, pion,…

The proton-electron interaction bottom left proceeds by the electromagnetic force carried by the photon. The photon is ‘the’ basis element of the one dimensional Lie algebra of the electromagnetic gauge group, a copy of U(1). Everything in sight is governed by the gauge group U(1) x SU(2) x SU(3) of the Standard Model.

To be continued…

WR