Comparing Electrons & Quarks: Mass, Charge & Size

[sidmontu]

Hi,

I am currently a student, still grasping some basic concepts of quantum mechanics. I've been reading some books, and the model on quarks intrigue me. There's something I'll like to clarify though.

Mass

Up Quark - 1.5 to 3.3 MeV/c2
Down Quark - 3.5 to 6.0 MeV/c2
Electron - 0.511 MeV/c2

Electron radius - 2.8179 x 10^-15 (classical radius)
Quark radius - unknown
Proton radius - 1.0 x 10^-15 (3 times smaller than an electron)
Hence, quark radius must be smaller than an electron's radius.
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So electrons have a charge that is 3 times stronger than a down quark, have a radius that is at least 6 times bigger than a down quark, yet they weigh about 6 to 12 times less than a down quark.

1) Am I right in saying that? Or did I get some values wrong? Because it seems quite absurd to me the way an electron's mass, size and charge compare to a down quark.

2) Also, why are there differing masses of each quark (e.g. 1.5 to 3.3 MeV/c2) whereas electrons have a fixed known mass value of 0.511 MeV/c2? Is this due to experimentation error due to the difficulty of measuring the mass of a quark?

Thanks.

 

[Meir Achuz]

The "classical radius" of the electron is just a dimensional construct and has nothing to do with the radius of the electron (although some classical physicists may have thought it did). As far as it can be measured, and in current theory, the electron is a point particle.

 

[jtbell]

The experimental upper limit for the electron radius, from scattering experiments, is something like 10^{-20} m. (This means that we haven't detected an effect that would be caused by a nonzero radius, but because of experimental uncertainty we wouldn't have been able to detect anything smaller.)

It's difficult to measure properties of individual quarks because we can't isolate them.

 

[sidmontu]

Hi, thanks for the replies.

clem: I understand that the electron is regarded as a point particle for simplicity sake in models. It makes it easier to do standard mathematical calculations if you consider it as a singularity. Am I right?

jtbell: I did notice the 10^-20 upper limit for the radius due to the scattering experiments as pointed out in a wikipedia article on electrons. But if it's the case, that makes an electron at least 5000 times smaller than a proton, and in turn about at least 2500 times smaller than a quark. Still a pretty huge number when you compare it's mass is only 6 to 12 times smaller than a down quark. That makes an electron very dense?

So theoratically, two up quarks (of first generation) should have identical masses, and the current value of mass (1.5 to 3.3 MeV/c2) is due to experimental limitations?

Thanks again.

 

[HallsofIvy]

I think it is more correct to say that at sub-atomic levels, the whole notion of "radius" or "size" in general becomes ambiguous.

 

[Meir Achuz]

clem: I understand that the electron is regarded as a point particle for simplicity sake in models. It makes it easier to do standard mathematical calculations if you consider it as a singularity. Am I right?

It is not just for simplicity. Most quantum theories of the electron really mean it is a point particle. The problem with teaching of physics is that classical physics is covered for the first two years, which makes it very hard to think like a quantum mechanic. You have to consciously disregard much of your classical training.

jtbell: I did notice the 10^-20 upper limit for the radius due to the scattering experiments as pointed out in a wikipedia article on electrons. But if it's the case, that makes an electron at least 5000 times smaller than a proton, and in turn about at least 2500 times smaller than a quark. Still a pretty huge number when you compare it's mass is only 6 to 12 times smaller than a down quark. That makes an electron very dense?

The upper limit is just an upper limit, related to experimental precision.
There is no good estimate of the size of a quark, other than it is consistent with also being a point particle. The classical concept of "density" is meaningless for a quantum point particle.

So theoretically, two up quarks (of first generation) should have identical masses, and the current value of mass (1.5 to 3.3 MeV/c2) is due to experimental limitations?

All quarks of the same flavor have the same mass. The "mass" of a quark cannot be measured as directly as the electron or proton mass. The quark mass appears as a parameter in theoretical models, and its value can different for different models.

 

[humanino]

The quark mass appears as a parameter in theoretical models, and its value can different for different models.

The current quark mass is renormalization scheme dependent at next-to-next to leading order (IIRC), the scheme usually chosen is MS-bar, and the above quoted mass is the one for instance given on the PDG web site. For light quarks, we use chiral perturbation theory which as usual requires an absolute scale to be determined otherwise. Its uncertainty is experimental. In principle one can go from one scheme to another to relate different values in different schemes.

See the review on quark masses