# What are the shape of nucleons and quarks?

1. Jan 11, 2007

### eehiram

When one of the quarks was discovered, I was in high school, and I said quarks are not spherical balls of mass. How could nucleons also be spheres if 3 quarks make up a nucleon?! I said atomic and subatomic particles have a poorly defined shape and something of a lack of material substance.

However, for beginners, the quarks and nucleons are pictured as little spherical balls.

Was I right?

o| Hiram

2. Jan 11, 2007

### humanino

Hi,

quarks are definitely pointlike particles. No spatial extension for quarks has been seen at the resolutions we can achieve. This is not in contradiction with the fact that protons (or nucleons, or hadrons) have a finite size. Consider for instance atoms. Their size is given by the size of their electron cloud. This cloud is made up of electrons, and electrons are pointlike.

In both cases, the pointlike particles have spatial distributions corresponding to the shapes of the bound-states they form.

3. Jan 11, 2007

### CarlB

Bravo for using "pointlike" instead of "point".

4. Jan 11, 2007

### eehiram

I'm familiar with your comparison to atoms and electron clouds

but I would like to read something specifically about quarks. How do they form spherical nucleons from trios of quarks? Thank you in advance for your patience with me; I don't expect a book long answer, as I know I would need to read about quarks in a book to get a full response.

o| Hiram

5. Jan 12, 2007

### mjsd

Interesting.... so is photon a particle or a wave? what about for an electron? Your question seems innocent enough, simple and perhaps intuitive.... however, your question may not be the 'right' question to ask about quarks (?)

We know that there are THREE quarks for baryons (and TWO for mesons), not because we directly "see" three/two things in experiments, but we can infer that from the effects the target proton causes in an high energy collision experiments (if our experiments were correct, and we believe in the physics as we know it) OK, to cut a long story short (which I am not qualify to tell anyway), it turns out that things are only consistent in these scattering experiments if we assume nucleons are made up of 3 "things" which we called quarks. Now, the accelerators we have today (or even the LHC) do not produce collision with high enough energy that can break quarks down further and hence we believe they are fundamental and perhaps infinitestimally small, ... err.. structureless is probably the better word for it. By the way, there is also a experimental upper bound on their radius, which is very tiny as you may guess.... hence we like to refer to them as point-like.

A related issue is of course coming from QM and about the "fuzziness" nature of stuff. like the good old electron cloud. In that spirit alone, it may render your question meaningless.

perhaps, it is our nature to prefer a nice geometric description of things that brings about the concepts of
the Earth is a perfect sphere, NH_3 molecules form exact tetrahedrons,

at the end of the day though they are approximations. If the approximation is very close to being exact, that's great! But there is no guarantee that the same concepts will prevail at the sub-atomic level. We can have a "mathematical" description of them to aid our analysis and perhaps to formalise them. But it is often difficult to visualise them (although more experimental data will help).

The moral of all these is that (and to answer your question) don't take that picture of spherical quarks/nucleans too seriously. As fas as we know and what we can infer, quarks are extremely small, so small that it is meaningless to talk about its shape. As for nucleons, they certainly are composite objects with an effective radius. Now, you may ask how can three infinitestimally small objects combine to give an "extended" object? Hehehehee...
well, to be honest I don't really know the correct answer to that, but I would say, if you have three dots closely packed together but not overlapping in such a way that you only see one dot all the time when you are close-by, then if you move away from it, it looks like one "big" dot.... your nucleon.
(perhaps someone can correct or add to this, also not sure whether gluons play a role in this for we know that energy and mass are the essentially the same at relativistic energy)

Anyway, should the nucleon then regarded as spherical? triangular? tetrahedral? oval? I guess the natural choice would be spherical for symmetry reasons and perhaps easier to model its scattering behaviors (ie. billard balls analogy) But then of course nucleons also have different spin/excited states which are modelled by "the Shell model", now I am not sure whether under those situation "the effective shape" of the nucleon can change (like the way the electron cloud changes)... . but then again, we are quite comfortable with the idea of atoms being "spherical" despite the fact that electron orbitals can take on different "shapes".

6. Jan 12, 2007

### humanino

In classical textbooks you will read that nucleons are spherical. This is a natural (first) hypothesis, and it turns out that most of the data is consistent with it. Only recently do we have theoretical arsenal powerful enough to explore more complicated hypothesis. Over the past decade, new (quantum) operators have been intensively studied, corresponding to "generalized parton distributions". Those objects allow us to measure the actual shapes of hadrons, starting from the fundamental degrees of freedom (quarks and gluons). However, the experimental side is very challenging, and data constraining the theory begins to appear right now. This was the subject of my PhD, which I recently completed.

To come back to your question "how pointlike object can bound into a finite size state ?" : we must be careful with classical analogies. Making rigourous mathematical statements is a delicate matter. Mechanical models, with three (valence) quarks bounds by (gluons) spring are too simplistic. The wavefunction of the nucleon is a tower of many multiparticle states. It so happens that gluons can split into quark-antiquark pairs. In hadronic degrees of freedom, those constitute the mesonic content of baryons (like pions for instance, pairs of u and d-like (anti)quarks). All these animals are extremely relativistic in the hadronic bound state. They move at very high speeds (on the light cone), and what you see depends on the scale of your observation. Overall, one describes this fauna by the distributions one observes. If those distributions are spherical, they make-up a spherical object.

I'm not sure you'll be satisfied by those arguments. I'll think about it, and hope somebody can help in finding a more sound one.

7. Jan 12, 2007

### CarlB

If a nucleon has a spin axis, one supposes that it's not likely to be as symmetrical as a sphere.

But ignoring that, I don't think that there's anything barring a nucleon made up of three quarks from being spherical. I'm guessing that the original poser's intuition was based on the assumption of a Pauli exclusion principle preventing the three quarks from being in the same position. However, the three quarks have different color, so the PEP doesn't apply. So there should be an "S" state available:

$$\psi(r_R,r_G,r_B) = e^{-(r_R+r_G+r_B)}$$

8. Jan 12, 2007

### humanino

Indeed, it is very interesting to see the distributions of (polarized) quarks in a (polarized) nucleon. Details can be found for instance in GPD's and Ssa's.

9. Jan 12, 2007

### Staff: Mentor

They are quantum-mechanical objects that have both particle-like and wave-like characteristics. This applies to both electrons and photons.

10. Jan 12, 2007

### eehiram

thanks, people

Your replies definitely cleared things up, especially humanino's, whose was the most interesting and difficult.

Back when the last quark was discovered, I had a big argument with my classmates about how quarks were not just little balls that "somehow" summed up to a larger ball. I guess I win, partially, in retrospect, although I could not tell them what quarks and nucleons actually looked like either; hence the merely partial victory.

o| Hiram

11. Dec 16, 2007

### Godzilla29

As another related question. We know that two fermions cannot be in the same place at the same time. Apart from this, is there any difference between two fermions in their geometric "shape", or are they indistinguishable?

12. Dec 16, 2007

### malawi_glenn

Not all fermions, identical fermions (i.e of same kind) cant occupy the same STATE. i.e not place, but quantum state. Further, there are many kinds of fermions, you cant apply the pauli principle to electrons and muons, but only between electrons and electrons etc.
Also fermions of each kind is indistinguishable from each other plus that elementary fermions (leptons and quarks) dont have a geometric structure at all. Composite fermions like nucleons, have some kind of structure altough, but you cant say "hey, thats my proton#2 and that one is proton #4".

13. Dec 20, 2007

### Smoochie

Hello,

My first post here. Cheers all.

Regarding the shape of the nucleons / quarks - I think the best way to describe them would be by distributions. Clouds of energy that dissipate exponentially in space - which also tell us the probability of finding these particles in space. Thus, when you have a number of them together, they form a complex distribution seeking a minimum energy state allowed by the exclusion principle, coloumb attraction etc.

As to the fermions, two fermions of the same kind are indistinguishable.

Smoochie

14. Dec 20, 2007

### Riogho

Just because something is indiscernible does not mean it is identical.

15. Dec 20, 2007

### malawi_glenn

explain furter. You dont agree that identical particles exists?

16. Dec 20, 2007

### Riogho

Leibniz's Principle of the Identity of Indiscernibles which, expressed crudely, insists that two things which are indiscernible, must be, in fact, identical.

I have a problem with that based on three properties of his principle, a few of which can be countered easily:

A) states that it is not possible for two individuals to possess all properties and relations in common; the next strongest

B) excludes spatio-temporal properties from this description; and the strongest form

C) includes only monadic, non-relational properties.

For example C is the claim that no two individuals can possess all the same monadic properties.

Both, B and C are clearly violated in 'classical' physics. where distinct particles of the same kind are typically regarded as indistinguishable in the sense of possessing all intrinsic properties in common and such properties are regarded as non-relational in general and non-spatio-temporal in particular.

However, A is not violated classically, since classical statistical mechanics typically assumes that such particles are impenetrable, in precisely the sense that their spatio-temporal trajectories cannot overlap. Hence they can be individuated via their spatio-temporal properties, as indicated above.

The situation appears to be very different in quantum mechanics, however. If the particles are taken to possess both their intrinsic and state-dependent properties in common, as suggested above, then there is a sense in which even the weakest form of the Principle, A fails.
On this understanding, the Principle of Identity of Indiscernibles is actually false. Hence it cannot be used to effectively guarantee individuation via the state-dependent properties by analogy with the classical case. If one wishes to maintain that quantum particles are individuals, then their individuality will have to be taken as conferred by Lockean substance, primitive thisness or, in general, some form of non-qualitative haecceistic difference.

17. Dec 21, 2007

### malawi_glenn

Philosophical arguments does not belong when discussing modern physics kid. Sorry to say this, but you should know that the language and logic of physics is mathemathics.

Also perhaps look at the definition of identical particles in QM, and you'll see that these concepts arises from the formalism of QM and and has been proven correct.

18. Jan 19, 2008

### basePARTICLE

Wasn't that between bound particles, that Pauli's exclusion can be applied and re-applied. Correct me if I am mistaken!

19. Jan 19, 2008

### basePARTICLE

I thought that was very well summarized - paths of 2 pi times r need not be circular. Funny thing is you hardly ever find rounded molecules in nature, and nothing ever shears off with its edges rounded, believing one would find things taking their paths of least resistance, but physicists hardly ever find that bizzare!. Gold nuggets anyone?

20. Jan 19, 2008

### malawi_glenn

I dont know what you are protesting about, he only said that the Pauli principle is for identical fermions, i.e only bewteen electrons and electrons, muons and muons etc.