# Quark Size

1. Nov 21, 2009

### cbd1

I know that we (believe) we have found the mass of the 6 quarks. But, I have not been able to find anywhere if we have any idea of their various sizes. I would gesture that the heavier quarks would be larger. Does anyone know if there is any data on this?

2. Nov 21, 2009

### cbd1

I think we have thought quarks and electrons are about the same size, but it seems to me this is mostly weak theoretical argument..

3. Nov 21, 2009

### f95toli

Electrons are point particles, I guess you could say they have "zero size".
As far as I know the same is true for quarks, although the concept of size is even less well defined since there is no such thing as a free quark.

4. Nov 25, 2009

### loreak

That sounds pretty accurate to me, there are proposed sizes for electrons and quarks but the nature of the quantum world makes such measurements somewhat vague since each particle is a wave of probability.

Couldn't you make a fairly accurate estimate using degenerate matter's maximum density to approximate their minimum size since they are on the edge of failing the pauli exclusion principle? I guess you could really only get the minimum size of neutrons, but when matter is that dense does the physical size of the neutron also get compressed?

5. Nov 25, 2009

### ansgar

No you can't, you are trying to mix classical and quantum mechanics here, finite extended objects are not compatible with QM. What you can measure is the charge density distrubution (aka the Form factor) and as far as we know, the charge density function for electrons is a delta function.

6. Nov 25, 2009

### daschaich

All "elementary particles" (quarks, leptons, gauge bosons) are point particles (with "zero size") as far as we can determine experimentally. [Edit to add that the standard model and its usual extensions treat elementary particles as exactly pointlike, in agreement with experiment.] There have been (and will be at the LHC) interesting searches for quark and lepton substructure, which would be the first sign that they are actually composite (non-elementary) objects with non-zero size.

So far, the tightest upper bound on the electron radius that I'm aware of is $$r_e < 10^{-22}$$ meters, from this paper. For quarks, high-energy collider experiments have probed down to $$r \sim 10^{-18}$$ meters (which the LHC will improve), at which distance quarks and leptons still look pointlike. See also this thread.

If you try to make models where elementary particles have non-zero size, you generally enter the Realm of String Theory.

7. Nov 25, 2009

### arivero

Or not. I am not sure if we have some calculation for the size of a elementary string in each of the four sectors (RR, RNS etc). I believe that early calculations by Susskind hit some kind of problem.

Besides, are we sure that it is possible to get a "size" for elementary fermions? Yes, protons and neutrons have a size, but it comes from the boson glue, not from the fermions. There is some kind of paradoxic clash between having a size and not having classical limit.

8. Nov 25, 2009

### daschaich

The size of hadrons comes from compositeness, plain and simple. I don't see any need to worry about spin & statistics here.

I am not a string theorist, so please correct my misconceptions. I was merely parroting the popular wisdom that in string theory "the fundamental constituents of reality are strings of the Planck length (about $$10^{-33}$$ cm)", which I just copied-and-pasted from http://en.wikipedia.org/wiki/Superstring_theory#Basic_idea".

Last edited by a moderator: Apr 24, 2017
9. Nov 25, 2009

### ansgar

Last edited by a moderator: Apr 24, 2017
10. Nov 25, 2009

### humanino

Form factors are observables. They can be linked, without any approximation, to the distributions of charges in the transverse plane when the hadron is on the light-cone. The "no approximation" comes from the galilean subgroup of transverse boosts (please request references if you want). The Sachs formalism, relying on non-relativistic approximation, is in the hadron rest frame. The distributions in the rest frame and on the light cone are not supposed to be the same anyway. There are attempts to make it rigorous in the rest frame, but it's not necessarily very useful.

11. Nov 25, 2009

### arivero

Sorry I am not string theorist neither I had expected the form factor for scattering of a probe string against a "R-NS" fundamental state to be calculated somewhere in the textbooks and then its graph plotted and a size of the order of the square root of the string tension to be shown. Very dialectical, I would hope. Perhaps too trivial for a string theory textbook?

Last edited by a moderator: Apr 24, 2017
12. Nov 25, 2009

### daschaich

humanino's response is probably best, but if you're after something more qualitative and hand-wavy, think of the volume within which the hadron's (valence) quarks are confined. Quantum mechanics makes this fuzzy.

In my own field of lattice QCD, we tend to use the Compton wavelength to quantify the "size" of mesons, $$r_C \sim 1 / m_C$$ in units where $$c = \hbar = 1$$.