# Why are muons considered to be elementary particles in the Standard Model?

According to this article, a muon decays into one electron and two neutrinos.

According to this article, elementary particles or fundamental particles are particles "whose substructure is unknown, thus it is unknown whether it is composed of other particles." I have also seen somewhere that it is a particle that cannot be reduced into other constituent particles.

While perhaps not a sure thing, seems like the decay indicates that the muon may be just a composite particle, perhaps consisting of one electron and two neutrinos?

Based on this, why does the muon fit with the above definition of an elementary or fundamental particle?

I realize there are much more complicated, historical reasons as to why it was included in the Standard Model, but this question is just related so how it fits (or doesn't fit) the stated definition above.

It seems to me that we really can only get solid evidence of elementary vs. composite when we smash the particles together and see what comes out and compare that to all the masses, energies and momentum before and after? Until we do that with muons, how can we know with much certainty?

And perhaps we'll have a better answer with a Muon collider: http://en.wikipedia.org/wiki/Muon_collider/ http://map.fnal.gov/

To that point, seems that electrons may not be fundamental after all: https://www.sciencedaily.com/releases/2016/04/160404111559.htm

• Comments are not for extended discussion; this conversation has been moved to chat. – David Z Aug 20 '16 at 4:18
• I rolled back your question; please don't add new questions or comments by editing. Edits are generally meant for clarifying the original question. – David Z Aug 20 '16 at 5:29
• The muon collider article has been moved to - en.wikipedia.org/wiki/Muon_collider – Ed999 Feb 2 '19 at 15:34

First, I address some misconceptions in your question.

the decay indicates that the muon may be just a composite particle

The fact that the muon decays at all is not evidence that it's composite. It's tempting to say that if a particle $$A$$ can decay into $$B$$ and $$C$$, then it must be "made of" $$B$$ and $$C$$. However, this doesn't work out, because almost all particles have multiple decay channels. For example, hydrogen in the $$2s$$ state can release a photon to go to the $$1s$$ state, but it can also rarely do this by releasing two photons. As a more extreme example, parapositronium can completely annihilate, turning into two photons, but it can also turn into four.

We think about particle decay in terms of couplings of quantum fields to each other: an excitation in one field can decay into excitations in others. As Feynman put it, those final excitations don't exist "inside" the original one, any more than the word "cat" is bouncing around inside you because you can spend energy to say it.

To that point, seems that electrons may not be fundamental after all: https://www.sciencedaily.com/releases/2016/04/160404111559.htm

This article is about some of the weird ways that large collections of electrons in solids can behave collectively, but it's not related to whether or not electrons themselves are composite. It's important to keep this in mind when reading news releases, because the people who study what electrons in solids do unfortunately tend to give the resulting phenomena the same names as the particles we search for in colliders, leading to a lot of popular confusion.

## Answering the question

With that in mind, you're still right, in the sense that it's completely natural to think that the muon might be composite. If you were a scientist in the 1950s, for example, the muon would be just one more particle discovered along with a zoo of mesons and hadrons. Today, we know that all of those mesons and hadrons turned out to be composites of quarks. So why not think of the muon as composite as well?

Indeed, in the early days, the similarity of the muon and electron was taken as possible evidence that the muon was an excited state of the electron, just like the $$2s$$ state is an excited state of hydrogen. If this were the case, one would expect the muon to often decay by emitting a photon, $$\mu \to e \gamma$$, but this was found not to be the case. Instead, the decays involving neutrinos dominate.

Now you might ask, why can't the muon be a composite of the electron bound to some neutrinos? This idea doesn't work out because there's no force we know of that would do the job: even in the 1950s it was known that neutrinos interacted extremely weakly. Getting a neutrino to interact with an electron at all is less likely than winning the lottery, so it seems extremely unlikely that it would be simultaneously possible to bind them together.

Another difficulty of any composite muon theory is explaining the muon g-factor, which determines its magnetic moment. Elementary particles are expected to have $$g \approx 2$$. The composite proton and neutron violate this by a good margin, $$g_p \approx 5.59, \quad g_n \approx -3.82$$ while the electron and muon have $$g_e \approx 2.002, \quad g_\mu \approx 2.002.$$ That $$0.002$$ isn't evidence for compositeness either, because it's precisely what you would expect for a perfectly elementary particle, once you include quantum field theoretic effects. In fact, the electron and muon $$g$$-factors have been measured to far more decimal places than I've shown, and the results match the Standard Model prediction to great precision. Making the electron and muon composite without upsetting this agreement would seem to require a seriously contrived model, or a miracle.

## A meta-difficulty

These already are big difficulties, but if you imagine being a scientist in the 1950s, the quark model had its own problems (such as the complete nonobservability of individual quarks), but it earned support because of its ability to account for huge numbers of hadrons, and predict new ones. And today, people consider theories where the Higgs boson is composite, because it helps give it an appropriate mass.

The meta-difficulty for the muon is that it's only worth trying to make it composite if there's some payoff you expect, such as (1) the completion of a theoretical picture, (2) new predictions, or (3) ways to calculate quantities (such as the muon mass) that we otherwise have to take as inputs.

The first reason doesn't apply, because the muon already has a perfectly good place in the Standard Model: it has to be there because of the family structure of the theory, and this structure is rigid enough that without the muon, the Standard Model would be mathematically inconsistent because of gauge anomalies.

The second reason doesn't apply, either. It's not like we have a series of weird particles lying around that could be explained as further composites of the electron. And since we've measured properties of the muon to exquisite precision, just about any theory of muon compositeness will make "predictions" that we already know to be wrong! You have to work extremely hard just to avoid that. (Admittedly, the muon $$g$$-factor does seem to deviate a bit from the predicted value, and this does receive attention -- it's just that compositeness isn't the kind of thing that would help here.)

The third reason could potentially apply. However, explaining the masses of particles like the electron and muon is an infamously hard problem, even if you don't take them as composite. Certainly, heads would turn if you came up with a simple theory that gave the muon-electron mass ratio to many decimal places, but decades of failed attempts have made this seem unlikely.

If you just disregarded these reasons, and made a contrived model where the muon was composite, tuning all the constants involved to precisely the values needed to hide all deviations from the Standard Model, then it would "work"... but it would also be scientifically useless.

Of course, it's also completely possible that muons might turn out to be non-elementary, because in science it's impossible to ever prove a negative! At the moment, this possibility is not under active investigation. But it's not heresy either. If sufficiently strange experimental results appeared in the future, scientists could be right back to tinkering with composite electrons and muons, trying their best to understand the results, and the universe.

• "we have no indications of a fifth force now" - phys.org/news/2016-08-physicists-discovery-nature.html – John Dvorak Aug 18 '16 at 8:40
• @JanDvorak That purported force is unrelated to this question, though. It wouldn't bind neutrinos to electrons. – knzhou Aug 18 '16 at 8:42
• This is the only answer that gives the actual reasons for the choice, rather than saying that "it is true because Authority says it is true". – Martin Kochanski Aug 18 '16 at 11:20
• @JanDvorak the timing of that UCI 5th force article couldn't have been better. Now we know, it's the protophobic X boson that binds the neutrinos to the electron inside a muon! =) – Brad Cooper - Purpose Nation Aug 19 '16 at 13:09
• @knzhou thanks, appreciate you translating into plain language the high-level criteria we might use to evaluate the "fundamental-ness" of a particle and whether it meets a definition of "elementary" and/or inclusion into the Standard Model. Perhaps the Standard Model authorities would post a similar criteria overview that laypeople like myself would understand =) – Brad Cooper - Purpose Nation Aug 19 '16 at 13:58

That a particle decays into other particles is completely disjoint from it having substructure/being fundamental or composite.

Some examples: A highly energetic photon may "decay" into an electron and a positron in the presence of another object that takes the excess momentum. That doesn't mean a photon is a composite of electron and positron. A free neutron decays into a proton, an electron and an electron anti-neutrino with an average lifetime of 10 minutes, yet it is a composite state of three quarks.

Being constituted of other particles means being a bound state of these particles. Quantum field theoretic processes have no problem turning one kind of particles into other kinds of particles (subject to certain rules, of course), but this sort of process does not imply that the results actually constituted the input. In no meaningful way is a photon a bound state of electron and positron, in no meaningful way is a neutron a bound state of proton and electron, and in no meaningful way is a muon a bound state of an electron and neutrinos.

• the photon example seems to be different case, where a boson hits or interacts w/many other particles & transitions into other particles vs. a pure "decay" w/o interactions from other outside particles. In the neutron example, seems to be just another case of a composite decaying into constituents? With your "bound state," this sounds like you are introducing a new definition of "elementary" different than the one referenced. If the referenced definition of "elementary" is wrong, that is fine. But most would not think of "bound state of the particles" to define "constituent" – Brad Cooper - Purpose Nation Aug 17 '16 at 13:45
• @PurposeNation A neutron is not composed of a proton and an electron. We know it is composed of three quarks. Just as a proton is composed of three quarks. A particle decay is not the same as nuclear fission. It is not simply the case that a particle breaks up into smaller chunks. Often you can find the mass of the result is much greater than the mass of the initial particle. It's more like a decay destroys one particle and puts the energy into a more stable particle state (usually) – Jim Aug 17 '16 at 13:51
• @ACouriousMind: Also it appears the wikipedia article on free neutrons introduces another definition of a composite vs. elementary particle: "The finite size of the neutron and its magnetic moment indicate the neutron is a composite, rather than elementary, particle." Does the size of the particle and its magnetic moment define the elementary vs. composite nature? If so, seems like the first wikipedia definition really needs a lot of additional clarification? – Brad Cooper - Purpose Nation Aug 17 '16 at 13:53
• @PurposeNation We look for substructure by scattering other particle off of the target. The "scattering patterns" (so to speak) can be used to determine if there is anything inside. This is done all the time in crystallography: scatter X-rays from a solid, and infer from the scattering the arrangement of atoms in the solid. Scattering involving muons indicate no substructure. Scattering from neutrons indicate three similar internal entities (quarks), not two dissimilar entities (electron and proton). – garyp Aug 17 '16 at 14:45
• I don't think this answer is as satisfying as it could be. You're basically just repeating what we consider to be composite in the Standard Model now. This doesn't tell the OP why we concluded those particles were composite, which is essential to knowing why we haven't concluded muons are composite. – knzhou Aug 17 '16 at 19:56

The best place to seek evidence that decay doesn't equal compositness is in particle creation. Because if decay meant compositeness, then creation would require you to get the constituents together.

When you bash two nucleons together at high enough energy you get a lot of junk coming out. Some of that junk is lepton particle-antiparticle pairs, and many of them arise from interactions like $$q + \bar{q} \to l^- + l^+ \,.$$ This process is called "Drell-Yan". The leptons can be electrons, muons or tauons. Getting muons is experimentally very useful, so this process is sometimes used as a probe of the structure of the nucleon sea. (When you put protons on protons, the anti-quarks have to come from the sea as the valence content is all quark.)

If you have an electron-positron machine at high energy (i.e. the decommissioned SLC or LEP) you can also do $$e^- + e^+ \to l^- + l^+ \,,$$ with similar mathematics.

Now, at energies very much over $$2m_\mu c^2$$, the rate for producing electron-pairs and that for producing muon-pairs is the same, which wouldn't be the case if one were elementary and the other composite (if the muons were composite the chance of having the right bits present would contribute to the production rate so the rate would be lower). Further the rate is in agreement with the ab initio predictions from QED for fundamental leptons. Let's take a moment to recall that QED offers the best single agreement between theory and experiment in physics (the electron's g-2).

In addition there are many other interesting predictions from QED about muons (for instance the muon g-2 which is nearly as good a theory-experiment match as that for electrons).

This is the elementary particle table of the standard model of particle physics.

Please note that it is not only the muon that decays, but also the tau and the Z , W and Higgs.

They are called elementary because they are the building blocks of the Standard Model; building up all other particles and controlling interactions in the microworld where quantum mechanics is necessary to calculate and predict the behavior of particles, using the Standard Model.

Decays are not a unique indication of the existence of a substructure. The substructure is investigated in scattering experiments fitted with the standard model functions. The elementary particles in the table are called point particles because they have no substructure as a hypothesis of the model, and the model is continuously validated, i.e. it has not been falsified.As the diagram provided by @Statics shows, there is a point vertex in the weak decay of the muon ( as also of the tau and the Z and the W). All particles in the table are considered point particles when they interact. No space for constituents.

String theories aim to extend the standard model, describe elementary particles as strings, but this is a subject of research, and still there are no constituents in the string representation of a particle.

Addition after more recall.

How was the compositeness of the nucleus of the atoms established? By the famous Rutherford experiment which showed deep inelastic scattering.

The same scattering experiments at higher energies showed deep inelastic scattering in the protons, establishing the existence of quarks and gluons.

In general scattering experiments established the Form factors of the targets, the "shape" in space and energy/momentum space of the targets, see figure 11 here. That the proton and neutron were not point particles was established long before the discovery of the quark content, and Feynman had proposed his parton model to model the data. Experiments showed deviations from the parton model which established the hard scattering on scattering centers by the so called high p_t data.

No such structure has appeared for the electron within the energy range of our experiments, its size point like within $$10^{-18}$$ meters, and its shape spherical to great accuracy ..

The symmetries in the standard model of physics are then utilized to posit a point like structure for the elementary particles in the table. At the moment the success of the standard model in describing the experimental data does not leave space for compositeness of elementary particles. If it exists, much higher energies have to be reached in our experiments to discover it.

The muon is not a composite particle. The fact that it can decay is related to weak interaction, being possible due to the existence of $$W/Z$$-bosons. The muon can decay into neutrino and electron since its rest mass is larger than that of an electron. Since there is no other charged lepton with a mass lower than that of an electron, the electron can not decay into anything itself.

From all the thousands of experiments, we know that a muon has pretty much the same properties as an electron and can thus be considered a lepton. Lepton is not composite particles of anything, they do not bind neutrinos and electrons together. There is no known force that would describe such bindings.

• How we do we know it is not made up of constituent particles? How do we know it is not a composite particle? – Brad Cooper - Purpose Nation Aug 17 '16 at 13:13
• @PurposeNation Perhaps that is the question you should have asked: How do we know the size of the muon is small, and that of hadrons is large (fermis)? The answer, is of course, [form factors] en.wikipedia.org/wiki/Form_factor_(quantum_field_theory) . Experimentally, you may establish limits on the size of particles through investigation of their form factors, and the size of leptons is always smaller than any scale probed so far, to date, but the size of hadrons is as big as a fermi-sized marshmallow--they are soft and squishy. A good QFT text explains that. – Cosmas Zachos Aug 17 '16 at 17:47