How hard have they banged on quarks, electrons, etc.?

[HomesliceMMA]

I think there are so far as we can tell particles of mass that are made up of quarks and leptons (electrons and what not). So far as we know those the fundamental particles of matter.

Question - how hard have we banged on quarks/leptons to see if we can blow those up into smaller units? I just ask because I understand the plank length is many, many, MANY times smaller than even an electron. So theoretically you could have a particle (or whatever else you want to call it, something with mass I guess) the size of like one plank length in length, width and height.

It just seems a bit strange to me that the most basic particles of mass as we know them are so many orders of magnitude bigger than the smallest size they could potentially be.

So how hard have we tried to bust them up to see if there is indeed nothing smaller?

Thanks!

 

[malawi_glenn]

Read
https://pdg.lbl.gov/2020/reviews/rpp2020-rev-searches-quark-lep-compositeness.pdf
and
https://pdg.lbl.gov/2018/listings/rpp2018-list-quark-lepton-compositeness.pdf

These hypothetical subparticles of quarks and leptons are often called "preons" https://en.wikipedia.org/wiki/Preon

What do you mean by "hard"? You ask what energies, or how "hard" people have tried?

 

[phinds]

how hard have we banged on quarks

What would you suggest we use as the hammer?

 

[berkeman]

What would you suggest we use as the hammer?

https://www.decalsextremeonline.com/The-Flintstones-Bam-Bam-Decal-Sticker-4-Sizes-_p_291.html

 

[malawi_glenn]

What would you suggest we use as the hammer?

We already had Large Head Collider in this thread

LHC : Large Head Collider

 

[mfb]

It's easy to make a heavier particle out of lighter particles:
* Atoms are made out of light electrons and the nucleus which is a bit lighter than the atom.
* Nuclei are made out of nucleons which are lighter than the nucleus.
* Nucleons are made out of quarks and gluons which are lighter than the nucleons. You can argue that the ~300 MeV scale of QCD is a better metric than quark masses but that's still lighter than nucleons.

Can this trend continue, quarks being made out of even lighter particles? No. Our accelerators would have enough energy to break this apart, create excited states and so on.

In principle you can create a light particle as bound state of two or more much heavier particles if the coupling has just the right binding energy to almost cancel the masses and at the same time reproduce all the values we expect for elementary particles, but that doesn't look like a very likely scenario.

There could be many new particles between the ones we know and the Planck scale. Doesn't mean that they have to be part of matter. We already know heavier particles that are not part of everyday matter, especially the whole second and third generation of quarks and leptons.

 

[Vanadium 50]

How hard have we banged? That's hard to answer. If I said "eleven" or even "eleven kabangeroos: what would that tell you?

A nucleus is 100,000 smaller than an atom. If there are subcomponents to the electron, they are at least 10,000,000 smaller. If you want to say these numbers aren't very different, no, they're not. They are what they are.

 

[vanhees71]

It's easy to make a heavier particle out of lighter particles:
* Atoms are made out of light electrons and the nucleus which is a bit lighter than the atom.
* Nuclei are made out of nucleons which are lighter than the nucleus.
* Nucleons are made out of quarks and gluons which are lighter than the nucleons. You can argue that the ~300 MeV scale of QCD is a better metric than quark masses but that's still lighter than nucleons.

Can this trend continue, quarks being made out of even lighter particles? No. Our accelerators would have enough energy to break this apart, create excited states and so on.

In principle you can create a light particle as bound state of two or more much heavier particles if the coupling has just the right binding energy to almost cancel the masses and at the same time reproduce all the values we expect for elementary particles, but that doesn't look like a very likely scenario.

There could be many new particles between the ones we know and the Planck scale. Doesn't mean that they have to be part of matter. We already know heavier particles that are not part of everyday matter, especially the whole second and third generation of quarks and leptons.

Unfortunately it's a bit more complicated than that, and the question, where the masses of particles come from is among the most complicated questions.

The question "how hard have they banged" is a pretty clever one. Not only that you need higher and higher energies to produce more and more massive instable particles but also to resolve smaller and smaller details. That's why in the history of particle and nuclear physics the resolution got finer and finer the higher the energies of collisions got with which we probe the constituents of matter.

At low energies what looks like "fundamental constituents of matter" seem to be protons, neutrons, and electrons. The protons and neutrons bind together to atomic nuclei with positive charges $Z e$, where $Z$ is the number of protons within a nucleus and $e$ is the elementary charge. The positive nuclei bind together with the negatively charged electrons to form electrically neutral atoms. The nucleus in an atom comes with a mass $m_{\text{Nuc}}$, which is given by the sum of the masses of protons and neutrons minus $E_B/c^2$. The nucleus binds together with $Z$ electrons via the electromagnetic (Coulomb) force. Again the mass of the atom is $m_{\text{atom}}=m_{\text{Nuc}}-E_B'/c^2$, where $E_B'$ is the electromagnetic binding energy between electrons and the nucleus.

With higher and higher energies more and more details about these particles could be revealed. By bombarding protons or atomic nuclei with high-energetic electrons in the 1960ies it turned out that the protons and neutrons themselves look like bound states of constituents, which were called "partons" in the beginning and then turned out to be the "quarks" of Gell-Mann's and Zweig's ordering scheme of hadrons (of which besides the proton and the neutron several more had been found in collision experiments too).

As could then be clarified in the early 1970ies concerning the strong interactions the elementary building blocks of the hadrons (coming as bound states of a quark-antiquark pair, the socalled mesons, which are bosons and bound states of three quarks, which are fermions) are quarks, carrying a so-called color charge. In analogy to the then well-known theory of the electromagnetic interactions, quantum electrodynamics, where electric charges are bound together by a massless vector field, the electromagnetic field, which in quantized version has the photons as elementary particle-like excitations, there were also vector fields binding together the quarks with color charges. The corresponding particle-like quanta were called gluons. The important difference between gluons and photons is that the gluons themselves also carry color charges, i.e., they are kinds of color-anticolor dipoles, and this makes a profound qualitative difference between the electromagnetic and the strong interaction: The coupling constant between color charges, parametrizing the interaction strength, gets larger and larger the smaller the energy in collisions of these color charges gets, and this leads to what's called "confinement", i.e., according to this theory of the strong interaction (Quantum Chromo Dynamics, QCD) it's impossible to ever observe objects carrying a non-zero net-color charge, and indeed there's never been seen a free quark, anti-quark or gluon yet. All we can find are a plethora of hadrons, which are all bound states of colored quarks and gluons, which have a net-color charge of zero.

Finally there's also the weak interaction. It has manifested itself first in terms of the $\beta$ decay of neutrons and corresponding decays of neutrons within radioactive nuclei. The weak interaction is pretty special too. In the mid 1960ies it came out that also the weak interaction is described by a quite similar theory as QED and QCD (so-called gauge theories), but again with somewhat different manifestations. It turned out that the vector fields which are analogous to the photons and gluons ("force carriers") in QED and QCD should correspond to massive particle-like quanta, and this was a big trouble for the theorists trying to describe the weak interaction, because when just writing down equations for such "massive gauge bosons" destroyed the entire mathematics of the model, i.e., it became meaningless and inconsistent. Famously Higgs (and some more physicists) around 1964 figured out how to get out of this dilemma: They evented a scheme, where the underlying mathematics (the socalled symmetries of the equations describing the fields and their interactions) was obeyed but the gauge bosons could get massive by coupling all the fields to another socalled scalar field, which should have a non-zero value even if no particles are present. The same mathematics also ruled that this socalled Higgs field "vacuum expectation value" must also be repsonsible for the masses of all the elementary particles in the so formed Standard Model (SM) of particle physics. As any field to the Higgs field there must be elementary particle-like excitations, and this is the famous Higgs boson, which was the last particle to be discoved in 2012 at the LHC at CERN.

According to this SM the elementary constituents of matter are

quarks and anti-quarks, which carry electric, color, and "weak" charges (in fact QED and the electroweak interaction are somewhat more close in the mathematics, i.e., the corresponding Quantum Flavor Dynamics describes in a kind of "unification" both electromagnetic an weak interactions and on a fundamental level one has the socalled weak hyper-charge and weak isospin). The quarks come in "3 families", each of contains a pair of quarks: (up,down), (charm,strange), (top,bottom) each carrying an electric charge of $+2/3 e$ and $-1/3 e$ as well as 3 color charges ("red", "green", "blue"). The corresponding anti-quarks carry just the opposite charges and are otherwise identical with the quarks.

leptons and anti-leptons: carry only electroweak charges and come also in three families (as the quarks), i.e., a charged lepton and a corresponding neutrino: $(e,\nu_e)$, $\mu,\nu_{\mu}$, $\tau,\nu_{\tau})$ and the corresponding anti-leptons. The charged leptons carry electric charge $-e$ and the neutrinos are all uncharged. Again the anti-leptons carry the opposite charges but are otherwise identical with the leptons.

Gluons: "force carriers" of the strong interaction. They come in 8 color-charges (a color-anticolor dipole, but one of the possible 9 combinations is strictly color neutral, and doesn't occur as a gluon). They are strictly massless.

Photons: "force carriers" of the electromagnetic interaction. They are uncharged and interact with particle carrying electric charges. They are strictly massless.

W- and Z-Bosons: "force carriers" of the weak interaction: The $W$-bosons come as electrically charged carrying a positive charge $+e$ or $-e$, and the Z-bosons are electrically neutral. They are all massive due to the Higgs mechanism.

Higgs boson(s): In the most simple variant of the SM in addition there's one Higgs boson, the elementary excitation of the Higgs field, whose vacuum-expectation value also delivers all the masses of the quarks and leptons.

Now the amazing thing is that the mass of the matter around us, i.e., the atomic nuclei is almost completely due to the strong interaction and the associated phenomenon of confinement. Only about 2% of the mass of the atoms building up our everyday matter, is due to the Higgs mechanism. The vast rest is due to the binding of quarks and gluons to hadrons. The problem is that we don't have a really intuitive picture of this "confinement" phenomenon. The best argument for this conclusion from the SM is that, when simulating QCD, the theory describing the strong interactions, on computers (the socalled "lattice gauge theory"), we can predict pretty well which hadrons should be found in nature and their masses.

A qualitative picture can be given in terms of the so-called "MIT bag model". The idea is that in the "vacuum of QCD" bags are formed, within which quarks and gluons are confined. In this picture a proton consists of three (valence) quarks (2 up-quarks and 1 down-quark with a total charge of $2 \times 2/3 e +(-1/3 e)=+1 e$ as it should be for a proton) which are confined in a small spherical hole in the vacuum with a radius of about 1 fm (1 fermi=1 femto meter=$10^{-15}m$). Now if you confine particles in such a small volume according to the uncertainty principle of quantum mechanics they must have a pretty high momentum uncertainty, i.e., the momenta of the quarks fluctuate around the average zero value for a proton at rest, and the corresponding kinetic energy of this motion leads to the mass of the proton. That's why with the quite light up and down quarks with masses of a few $\text{MeV}/c^2$ you get the quite large proton mass of $938\; \text{MeV}/c^2$.

A more modern understanding is quite abstract and related to the so-called trace-anomaly of QCD and the formation of a quark condensate due to strong attractive interactions. The modern picture of the proton is also way more complicated than the simple bag model suggests: It consists not only of the 3 valence quarks but in addition also of "sea quarks and anti-quarks" as well as "gluons", i.e., of complicated field configurations of quark and gluon fields, and with ever higher energetic electrons one can try to resolve this structure of "partons" and in some sense also figure out, how the total mass and spin of the proton (and also other hadrons) are "distributed" over all these fields.

 

[malawi_glenn]

Note to OP: that $e$ both represents the electron particle and the elementary charge $e = 1.6 \times 10^{-19}$ C.

 

[ohwilleke]

Read
https://pdg.lbl.gov/2020/reviews/rpp2020-rev-searches-quark-lep-compositeness.pdf
and
https://pdg.lbl.gov/2018/listings/rpp2018-list-quark-lepton-compositeness.pdf

This is pretty much the most direct answer and amount to the conclusion that "Recent results from the LHC, using data collected at proton-proton center-of-mass energy of √ s = 13 TeV" leading to compositeness exclusions at scales of 7-29 TeV depending upon the exact scenario considered. In other words, we've banged them as hard as the Large Hadron Collider permits us to, because that is the most powerful "atom smasher" (as they used to call particle colliders) of all time.

This gets you to a paradox where the binding energy you'd think you would need to hold a composite quark or lepton together would seem to be more than the mass of the particles studied (mass and energy, of course, can be converted using the familiar equation E=mc²).

You also have indirect measures of compositeness like the anomalous magnetic moment (g-2) of a particle which is one of a particle's observable properties describing how it behaves in magnetic fields. In particular, the measured values of electron g-2 and muon g-2 are within parts per billion of the Standard Model predictions with fundamental rather than composite particles. You similarly get tight agreement between the measured and expected values of electric dipole moments of charged leptons which is another electromagnetic property of particles that can be observed.

In contrast, when you measure g-2 for a composite particle, like a neutron, you get a value which is completely different from what you would expect from a fundamental particle with a zero electromagnetic charge.

Another reason to reject a composite model is that W boson mediated transitions between one quark flavor and another quark flavor can always run in both directions. For example, you can have both a charm quark to strange quark transition and a strange quark to charm quark transition, which is a property that greatly constrains preon theories for quark flavors.

We also have strongly suggestive evidence, even if it is not 100% conclusive, that there are exactly three generation of quarks and leptons rather than a theoretically infinite number of excitations of them of the kind that are found in some kinds of composite particles made of quarks and/or gluons and bound by the strong force called hadrons.

There have also been efforts to use the "renormalization" mathematics which are used to do Standard Model physics to determine if there is some particular fundamental renormalization scale below which the equations below up which would suggest that fundamental SM particles correspond to some non-point-like physical scale.

Renormalization is basically a process of truncating the results of calculations in a consistent manner below a standardized threshold scale (which can be conceived of as a distance scale) so that terms too close to the scale at which infinities would pop up into the calculations making them intractable are ignored. Figuring this out this mathematical trick was Richard Feynman's greatest contribution to physics.

Occasionally, there are some slight hints that maybe one renormalization scale might be better than another, but overwhelmingly, within a reasonable range, you get the same physical results and predictions no matter what renormalization scale you use to get the end results, and there is no clear indication of a preferred renormalization scale. This suggests that this mathematical trick does not flow from any physically real scale in the universe that this trick is leveraging. This also tends to disfavor compositeness and puts a cap on the maximum size of a non-point-like fundamental particle.

But it is also worth recognizing that the Standard Model concept of fundamental particles as point particles is not necessary for a particle to still not be a composite particle.

This is an observation at the heart of string theory (which suggests that are particles are excitations of non-point-like strings or loops with a finite tiny length), but it doesn't have to be confined to string theory either.

From a quantum field theory perspective, fundamental particles are just permitted kinds of excitations of fields (in other words, three dimensional waves) made up of the three Standard Model forces that are confined in a particular small location, rather than precisely point-like objects.

Experimentally, we describe particle resonances that we observe not just by their mass but also by their "width" which, while it is substantively closer to the idea of a fundamental half life of a particle than a space dimensional physical width, also hints at the idea that the point particle concept can't be pushed indefinitely. This is because, generally, in particle physics, time and space dimensions are interchangeable with the right speed of light conversion factors.

Likewise, if fundamental particles were truly point particles, then every massive fundamental particle would be a black hole in classical general relativity, which clearly breaks down at this scale and requires some sort of theory of quantum gravity or some other fix to prevent this outcome.

Basically, conventional wisdom in particle physics, although it hasn't been rigorously proven, holds that somewhere around the Planck scale (which is far smaller than we can experimentally probe for compositeness or non-point-like extent at this point), the point particle simplification used for fundamental particles in the Standard Model probably breaks down somehow.

How small is that?

The Planck length is 1.616255(18)×10⁻³⁵ meters. A typical proton, in contrast, in on the order of 10⁻¹⁵ meters. So, the Planck length is about 100,000,000,000,000,000,000 times shorter than a proton.

The ratio of the Planck length to the size of a proton is about the same as the ratio of the size of a proton to 100km.

Conventional wisdom is that significantly above the Planck length, fundamental particles are indistinguishable from point particles.

Mathematically, we describe fundamental particles with their conserved quantum numbers and their mass-energies, and the rule is that everything that is possible in terms of transformations from one particle to another, subject to those conservation laws, does happen with some predictable probability, and that everything that is not possible subject to those conservation laws never happens.

Because of these various considerations, theorists informed by our experiments to date have tended to favor distinctions between fundamental particles that are, for example, topological, at some deeper level, rather than distinctions that draw on a composite structure for seemingly fundamental particles.

 

[vanhees71]

Note to OP: that $e$ both represents the electron particle and the elementary charge $e = 1.6 \times 10^{-19}$ C.

That's of course my sloppiness. Sorry for that! The electron and all other particles should be set upright, while the elementary electric charge should be set in italics.

 

[ohwilleke]

That's of course my sloppiness. Sorry for that! The electron and all other particles should be set upright, while the elementary electric charge should be set in italics.

Who knew as younger people setting out to study subjects like physics and law that advanced typesetting would become a critical skill in these fields?

Times have changed, however. Both of my children (who are in their early 20s now) were required to write papers using LaTeX in their high school and college STEM classes.

 

[malawi_glenn]

Every time I see people writing units with italics on this forum makes me wanna
$v = 13 m/s$

 

[phinds]

Every time I see people writing units with italics on this forum makes me wanna
$v = 13 m/s$

Oh, come on now, it's not that bad

 

[Vanadium 50]

wanna

Is not a word.
(Hey, you started it!)

 

[malawi_glenn]

Is not a word.

https://dictionary.cambridge.org/dictionary/english/wanna

Spelling and grammar of "non-scientific" phrases is not of concern to me
But when it comes to units and italics, my brain becomes like a bull seeing a waving red piece of cloth.

 

[lpetrich]

This question presumably refers to how much energy has been put into these particles in an attempt to break them apart.

Entity	Energy / mass
Atoms - ionization of hydrogen (worst case)	~ 10-8
Nuclei - 1 MeV / nucleon	~ 10-3
Hadrons	~ 1

Let's now do this calculation for leptons and quarks

Particle	Mass	Energy	Energy / mass
Electron	0.511 eV	104.5 GeV (LEP)	2*105
Up, down quarks	~ 2.3, 4.8 MeV	~ 1.7 TeV (LHC)	(3.5 - 7)*105

For the LHC, the energy per quark was estimated at 1/4 the total energy of each proton that was accelerated.

• LEP: Large Electron-Positron Collider
• LHC: Large Hadron Collider

Quark mass estimates were from Quark - Wikipedia

So over 100 thousand times the particles' rest masses has gone into these particles without making any observable evidence of compositeness.

 

[vanhees71]

Who knew as younger people setting out to study subjects like physics and law that advanced typesetting would become a critical skill in these fields?

The problem is that many people don't care about such subtleties anymore. In math and physics it's a bit better than in other fields, because there LaTeX is used. In other fields, horribile dictu, they use Word, and there it's impossible to have a concise microtypography.

Times have changed, however. Both of my children (who are in their early 20s now) were required to write papers using LaTeX in their high school and college STEM classes.

Must be very good schools! In Germany they teach Microsoft Office as "IT science" :-(.