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My understanding is that 'fundamental' pertains to there being a distinct quantum field corresponding to the particle. I ask the question above based on the fact that the heavier generations of particles decay. What reason do we have to believe that what was originally, say, a localised excitation of the tau field corresponding to a tau particle, was not a collective excitation of the particle fields it subsequently decays into? I would think of answering this question in two ways:

  1. Experimentally, I suspect we try to do scattering experiments. I should think that the theorists would have a prediction of the differential scattering cross section if the 'tau' were to be a collective excitation of several other fields which subsequently disperse. But i'm not so sure about how convincing this kind of evidence is.

    Another experimental factor may be acceleration experiments to 'observe' the particles with longer lifetimes in the lab frame, and we wouldn't expect a collective excitation of several fields to have the same behaviour.

  2. Theoretically. I am vaguely familiar with the group structure of the standard model, but not enough about the details to see how this answers the question above and, again, how convincingly.

Essentially, I am just interested in how someone who has much more knowledge in particle physics would answer this question. I have read through this post but I can't see it containing an answer. I know classical and (some) quantum field theory, and am presently taking a course in particle physics. But this hasn't been addressed.

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  • $\begingroup$ ? Heavy particles like the massive gauge bosons (W,Z) decay just like composite ones, like the neutron. They are all describable by quantum fields, coupled to others, which trigger said decay. $\endgroup$ – Cosmas Zachos Jan 27 at 17:09
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    $\begingroup$ In any case, compositeness is a purely experimental issue. You may cook up theoretical models of compositeness for any and all particles, but one need not heed such fantasies without experimental confirmation. The PDG is bursting with compositeness (negative) limits. $\endgroup$ – Cosmas Zachos Jan 27 at 17:12
  • $\begingroup$ Related, and also. $\endgroup$ – Cosmas Zachos Jan 27 at 17:15
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    $\begingroup$ Related question here. Compositeness is perfectly possible and has definitely been investigated, but at this moment there are no observations that require it to be explained. $\endgroup$ – knzhou Jan 27 at 17:36
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The standard model of particle physics is an encapsulation of a very large number of data, fitted with a specific theoretical model , a quantum field theory. In this theory,the table of particles , and the corresponding antiparticles are considered axiomatically as fundamental point particles of given mass and quantum numbers.

As in mathematics when one questions axioms the theory is changed, if one questions the particle table, one has to arrive at a new theory. The standard model is very successful in fitting and predicting data, it should be embedded in the new proposed theory.

At the moment the only theories that can embed the standard model are string theories, which go from point particles to strings or membranes, equally non composite.

I think the basic fact is conservation of lepton number, which is what has been established experimentally : that a negative muon is not a bound state of an electron, an electron antineutrino, and a muon neutrino, which is what it decays into.

In addition the standard model before electroweak symmetry breaking has all the fundamental particles massless, so they cannot decay into each other.

Field theory has to be based on the free wavefunctions of the corresponding equations ( Dirac for fermions, etc), so one has to consider the particles themselves, before setting up the field theory. All in all the simplest model at present is the standard model and there are absolutely no experimental indications of violations of lepton number conservation that might demand something mathematically much more complicated.

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I think the OP is touching a very subtle point of QFT which should not be too easily dismissed. The Hilbert space of any QFT is spanned by the asymptotic ('in' or 'out') states of all stable particles. For the SM these states include free elementary particles like the electron as well as bound states like the proton or even the hydrogen atom, but notably not the tau lepton. So, in this sense the initial "localised excitation of the tau field" (whatever that may be exactly) is necessarily just a superposition of the particles it decays into.

The formalism of QFT actually gives us the freedom to remove heavy unstable particles from the theory without changing the physics. This procedure is called 'integrating out the massive degrees of freedom' and is used in effective field theories. In the path integral formalism this just means what it says on the tin: you carry out the integral over, say, the W, Z and top-quark fields but leave the other fields alone. The price you pay for this is that you get non-local interactions between the remaining fields. In effective field theory one then proceeds by expanding the non-local interaction terms as an infinite series of local interaction terms. The higher order terms can be dropped if the kinematic energy scales we are interested in are well below the mass of the particles that were integrated out but after the truncation the theory is no longer renormalisable.

So, I would say the reason why we think the tau lepton (and the W, Z, top-quar, Higgs etc.) exist and are fundamental is that no-one has managed to write down a local and renormalisable theory which gets by without them and correctly re-produces the scattering cross sections of the particles we can observe.

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