# Why the muon is considered a fundamental particle?

intervoxel
This question arises from the fact that the muon has a mass close to the first excited state of the radial vibration of the electron (Prog. Theor. Vol. 47 (1972), No. 3 Cohesive force of electron and Nambu's mass-formula).

Mentor
It is not so far away but still completely inconsistent. Also, quantum field theory does a much better job describing the electron interactions, that 1972 paper is just outdated.
That theory cannot reproduce the muon g-2 value and the hundreds of other measurements done since 1972. They are all in excellent agreement with the muon as fundamental particle.
Also, where are all the other states predicted by that old theory? They would be impossible to miss in modern experiments.

intervoxel and Nugatory
Staff Emeritus
2021 Award
More to the point - and the author admits this - is that such a muon would decay via mu -> e gamma. This has never been observed, despite a LOT of looking. So, this theory predicts a) the wrong mass, b) the wrong decays, and c) new particles that experiment fails to find. Seems like a good reason to abandon it.

Astronuc, intervoxel, mfb and 1 other person
Mentor
This has never been observed, despite a LOT of looking.
At <5.7E-13, it should be the second best upper limit on a branching fraction ever set, at least according to the particle data group (checked kaons, pions and neutrons. The lowest upper limit is for a charge violating neutron decay that would make 71Ga unstable).

Astronuc and vanhees71
Gold Member
my question on the paper is why they call it the $\mu$-meson?

Staff Emeritus
2021 Award
It's an old terminology. ":Meson" means middleweight. The idea that a ~100 MeV particle mediates the nuclear force was proposed by Yukawa, and the muon's mass looked like it fit the bill. It was quickly apparent that this particle had the wrong properties, but then the pion came along: at the time they were called the mu-meson and pi-meson.

Astronuc and vanhees71
lpetrich
It's one of those terminology shifts, like deciding that the asteroids are not planets, and then that Pluto is not a planet. Or earlier redefining "star" and "planet".

The muon was likely changed from meson from lepton when lots of mesons were discovered, but with the muon acting much more like a 106-MeV electron than any of them. Using Google's n-gram viewer, I've discovered about when that terminology changed happened. "Mu-meson" rises from 1940 to a peak in 1960, and then declines at a similar rate to 1970, and after that, slowly declines further. "Muon" rises almost continuously from 1950 to 1990, and then drops.

Finally, about the muon as an excited state of the electron, what free parameters does that theory have? There have to be fewer free parameters than observations to get a meaningful fit.

Gold Member
2021 Award
I think the change is roughly related to the advent of the Standard Model or the discovery of Glashow-Salam-Weinberg model for the weak and electromagnetic interactions. The model was more or less finished in the mid 1960ies, but the real breakthrough came with 't Hooft's PhD thesis and the related papers of 1971, where he together with and building on work by his thesis adviser Veltman. In this thesis 't Hooft performed the first proof of the renormalizablility of superficially Dyson-renormalizable non-Abelian gauge theories, including the case of Higgsed ones, i.e., the electroweak GSW model. The key issue was the invention of dimensional regularization, which provides a gauge invariant regularization (with the caveat of chiral structures in the GSW model, related to the possible anomalies occuring in such models, but also this was solved by 't Hooft and Veltman).

Not much later came the idea of QCD to also describe the strong interactions and the next corner stone of the Standard Model: The discovery of asymptotic freedom by Gross and Wilczek and (independently) by Politzer.

In the Standard Model we have three families of quarks (carrying color charge) and leptons (carrying no color charge). So, nowadays we characterize the particles according to their participation in the strong and electroweak interaction rather than their mass. That's because today we know a pethora of particles over a large range of masses belonging to the various particle types.

Of course, due to confinement we don't see color-charged objects but only color-neutral bound states. These we call hadrons. For sure we only know mesons (bound state of a quark and an antiquark) and baryons (bound state of three quarks). There are hints that there should be glue balls and (perhaps even found) tetra-quark states.

The leptons are elementary (as far as we know today) and consist of the electrically charged ones (electron, muon, tau lepton and their anti-particles) and neutral ones (the neutrinos and perhaps their antiparticles; it's not clear yet whether neutrinos are strictly neutral Majorana or Dirac particles).

Then there are the gauge bosons, which are Gluons (8 adjoint color charges), weakons (charged W's and the neutral Z), and photons. Last but not least there's (at least one) Higgs boson.

All these particles are discovered by now and show astoningishly the validity of the Standard Model at high accuracy. There might be a deviation of the Standard Model in the prediction of the anomalous moment of the muon, but that's with around 3 standard deviations only evidence no discovery according to the standards in HEP, where a signifcance of 5 standard deviations is necessary to claim a discovery.

intervoxel
Gold Member
The names hadron/meson/lepton are really abused in terms of their meanings.E.g. the tau lepton can by no-means be considered lighter than some mesons, and its mass is comparable to hadrons (protons/neutrons).
That's why they have changed their meanings, leptons are "those" , mesons are the quark-antiquarks, hadrons are the triquarks etc...

vanhees71
Mentor
The names hadron/meson/lepton are really abused in terms of their meanings.E.g. the tau lepton can by no-means be considered lighter than some mesons, and its mass is comparable to hadrons (protons/neutrons).
That's why they have changed their meanings, leptons are "those" , mesons are the quark-antiquarks, hadrons are the triquarks etc...
To make it worse, all the mesons with heavy quarks are heavier than the light baryons, so yes, the original idea that lead to their names is not right any more.

edpell
What is meant by first excited state of the electron? I have never heard of this. An electron with no measurable size of structure how does it get excited?

Gold Member
2021 Award
Where did you get this idea from? Indeed, as far as we know today, the electron is elementary and thus there are no excited states of an electron. What should that be?

intervoxel
Hi,

I think that my original question "Why the muon is considered a fundamental particle?" was not answered yet.

Second, I'm sorry but I think I've posted to the wrong forum. I forgot that this forum refers strictly to quantum mechanics which considers leptons as fundamental pointlike particles. My question was motivated by that curious old article referred above where the electron may be seen as a distributed entity and not a pointlike one. Considering that recent research using tunnelling microscopy shows clear evidence of the distributed nature of particles, far bypassing the uncertainty principle, it all suggests that QM gives an exact (although necessarily based on probabilities) but slightly blurred picture of nature and a deeper theory (incorporating gravity, of course) must be sought.

Last edited:
Gold Member
2021 Award
Again, the muon is, according to what we know today, an elementary particle. Of course, it's not a particle in the classical sense but a quantum, described by a quantized Dirac field.

Staff Emeritus
2021 Award
All evidence is that the muon is elementary. It doesn't mean it really is, but it does mean that it is such a good approximation we are unable find discrepancies. As for the article that was posted, this theory predicts a) the wrong mass, b) the wrong decays, and c) new particles that experiment fails to find. A track record like that is not going to convince anyone of anything.

vanhees71 and intervoxel
Mentor
I think that my original question "Why the muon is considered a fundamental particle?" was not answered yet.
There are hundreds of experiments consistent with the muon as a fundamental particle, with incredible precision. There is no theory of a muon as something else that would be consistent with all (or even just half) of those measurement results.

A very prominent example is the muon g-factor:
2.0023318366 <- theoretical prediction for an elementary muon
2.0023318418 <- experimental result
With uncertainties of the order of this tiny difference.

Various other experimental results are summarized http://pdg8.lbl.gov/rpp2014v1/pdgLive/Particle.action?node=S004 [Broken]. The idea you linked to in post 1 cannot predict even a single of those experimental values (apart from the trivial muon/antimyon asymmetry predictions), while the standard model allows to calculate all of them.

See precision tests of QED for more examples. All those tests would fail horribly if the muon was not a fundamental particle, or if the electron would be something different from the point-like standard model particle.

Considering that recent research using tunnelling microscopy shows clear evidence of the distributed nature of particles
You don't need recent research for that, this is standard quantum mechanics and known for over 80 years now. Quantum electrodynamics is over 50 years old, too.

Last edited by a moderator:
vanhees71 and intervoxel
Larry Pendarvis
... recent research using tunnelling microscopy shows clear evidence of the distributed nature of particles, far bypassing the uncertainty principle
As mfb pointed out, the uncertainty principle has been around a long time. But you imply that recent results show clear evidence of greater "distributed nature of particles". Do you have a reference for that?

intervoxel
Elements of physics for the 21st century - Werner A. Hofer
arXiv:1311.5470v1

Larry Pendarvis
Mentor