I do not know any (but I am also not an expert in QED)

Anyway, probably the basis for the support is just that 3-degree vertices is the simplest approach to depict the processes.

And simplicity is always a plus for any theory, explanation, description, etc...

Feynmann was also always looking for "simplicity" in a way.

Thanks, Samuel.

Let's weight for the clarification: I'm sure there is *some* substantive evidence. The only question is how much evidence.

The degree of the vertices is determined by the number of fields in the interaction terms in the lagrangian. The QED lagrangian contains up to 3rd order terms (coupling two charged particles and a photon), while the Standard Model, which is describes the interaction of all known particles (without gravity) contains up to 4th order terms, meaning that there are also quartic vertices for gauge bosons and for gauge bosons and the Higgs field. For example, there are interactions of four W bosons, or two W bosons with two neutral gauge bosons (photons and/or Z). However, the question concerned experimental observation, not theory. Quartic gauge boson couplings are difficult to measure, but studies are in progress at the LHC to test whether they agree with the Standard Model. I haven't seen conclusive results yet, but someone in CMS or ATLAS would know better.

Thanks, Scott!

I would appreciate it if you could answer several questions.

1. Why does the following Wiki list of Feynman diagrams (including Higgs boson production) contains only vertices of degree 3?

https://en.wikipedia.org/wiki/List_of_Feynman_diagrams

2. To which extent do Feynman diagrams capture *all possible* (real) particle interaction?

Thanks, again!

P.S. I did find at least one diagram, "catastrophic transition", (1952 paper by Marshak) which is a degree-4 vertex.

However, the thrust of the question is the *actual*, rather than theoretical, interactions.

In the wiki, you will find one Higgs diagram with a loop in the middle. That contains the quartic Higgs vertex. Experimental results are closely entwined with theory, since individual Feynman diagrams are not directly observed, but are used to calculate scattering rates. Changing the coefficient of a quartic vertex would affect the predicted rate for certain processes, so measuring these rates allows the coefficient to be determined. In practice, this usually requires collecting a lot of data on relatively rare processes, which is why I am not certain whether such results are available yet from the LHC, although I know the work is in progress. Most processes involving the Standard Model do not require the quartic vertices at low orders of perturbative calculations, which explains why you don't see them very often.

A toy model commonly used in teaching quantum field theory is the "phi^4" model, with a single type of particle (spinless) and a quartic self-interaction. This model yields diagrams with only quartic vertices.

Scott,

What do you know about the answer to the second, main, question?

Who are the right people (in general) to ask this question?

Since Feynman diagrams are a theoretical construct, it is always a matter of comparing a hypothesis about the interactions to some experimental measurement via a calculation. Right now, the LHC results are being used to test the Standard Model, which is holding up very well so far - so well that there are a few worries that the LHC won't find anything new. However, it is still early. Feynman diagrams are also used in other contexts, where many kinds of interaction may be represented, but from a particle physics perspective, right now, experimental evidence is making the Standard Model look very robust, apart from some discoveries about neutrinos that are not included in the original model. Thus, for the state of the art on all known elementary particle interactions, one should study the Standard Model. For a relatively readable account that will probably answer your questions in detail, look up Griffith's book on introductory particle physics. I've used this for an advanced undergraduate course. It is fairly self-contained in terms of background, with the main prerequisite being some exposure to special relativity and the most basic ideas of quantum mechanics.

Scott, from your answers I'm getting a preliminary impression (correct or incorrect ?) that there is no separate (from theory) experimental field investigating the structure of particle interactions.

Is this a correct state of affairs?

There is no way to separate the theory from the experimental t result. We can't directly observe all the quantum interactions that go into a scattering event. Even then, quantum mechanics only predicts probabilities, so a large number of scattering events must be analyzed to determine a distribution, which is compared to a theoretical distribution obtained by calculating Feynman diagrams. A little browsing through the CERN web site may clarify the nature of the observations. My own work involves calculating the theoretical distributions predicted for certain standard model processes so they can be compared to measured distributions.

Now, this is interesting: after so many years, we still have not developed the appropriate methodology and hardware to record in greater detail the corresponding elementary events.

Scott, the reason I'm interested in this is related to radically new (non-numeric, or structural) formalism proposed by us which suggests how to view and approach elementary---or for that matter non-elementary---events.

What are the difficulties involved in setting up the experiments to study magnified (compared, for example, to the bubble chamber) interaction events? Again, is it that difficult to see experimentally the more detailed structure of the corresponding elementary events?