Fundamental Interactions in the Standard Model

Question

The elementary particles of the Standard Model seem clearly enumerated and distinguished, totaling 17 (6 quarks, 6 leptons, 4 gauge bosons, and the Higgs). Is there a similar enumeration of the variety of fundamental interactions found in nature according to the Standard Model? If it is finite, how many particular interactions are there (ie, in terms of the 17 elementary particles), and is every such interaction expressible as a Feynman Diagram? Thanks.

EDIT: To clarify, I was asking about how many total interactions like ($e^- + e^+ \rightarrow \mu^- + \mu^+$) and ($e^- \rightarrow e^- + \gamma$) there are.

EDIT2: The Wikipedia article on "Fundamental interaction" says: "The interaction of any pair of fermions in perturbation theory can then be modelled thus: Two fermions go in --> interaction by boson exchange --> Two changed fermions go out." This seems to imply that the total number of possible interactions is $N(N-1)/2$ (if interactions of like particles are excluded). Since there are 12 fermions, the number of interactions amounts to 66. Are all such interactions found in nature?

Answer 1

There are two standard models, one of particle physics that focuses on elementary particles and the three fundamental so-called gauge forces: the weak, strong and electromagnetic force; the other is of cosmology, which focuses on very large scale phenomena mediated by gravity which is both taken to be a fundamental force and not a force at because, after General Relativity, it is seen as an expression of the curvature of spacetime. But this is chimerical, as the gauge forces can also be writren geometrically.

In particle physics, the four gauge bosons are the W, Z, photon and gluon. They mediate the three gauge forces. They are called gauge forces because they forces exhibit a symmetry called gauge symmetry. In fact, just as gravity can be formulated geometrically, so can these three forces through the notion of fibre bundles. Here, the physical notion of a gauge symmetry is encapsulated through a connection on the bundle. This in turn tells us how the bundle curves. Thus, we see the three gauge forces has a geometrical expression akin to that of General Relativity.

Now, the quanta of these forces are the gauge bosons: W, Z for the weak force; the gluon for the strong force and the photon for the electromagnetic force. All of these particles have been detected.

In the cosmological standard model, the only force is gravity. This has not yet been quantised successfully. Its hypothetical quanta is called the graviton. This too is a boson. It hasn't yet been detected.

Answer 2

The text Particles and Fundamental Interactions (2009) by Braibant, Giacomelli, and Spurio states that there are a total of 61 elementary particles in the Standard Model (p 314). The total consists of 24 fermions + 24 antifermions + 12 vector bosons + 1 Higgs boson.

Considering only fermion-fermion interactions then gives a total number of potential interactions of N(N+1)/2, where N=48. The maximum potential number of fermion-fermion interactions is thus 1176.

However, note that "the full theory includes perturbations beyond simply fermions exchanging bosons; these additional perturbations can involve bosons that exchange fermions, as well as the creation or destruction of particles ..." (ref: Wikipedia-Fundamental interaction).