Re: Up & Down Quark Mass or Charge Problem?

From: Matthew Nobes (nobes_at_lns61.lns.cornell.edu)
Date: 08/29/04 

Date: Sun, 29 Aug 2004 17:55:25 +0000 (UTC)

On Sat, 28 Aug 2004, Jamie Vicary wrote:

> Quarks are buggers because they can't exist by themselves, only in
> tightly bound pairs. This means that the mass of the particles which
> quarks comprise -- called the hadrons -- is *less* than the mass of the
> isolated quarks. What does it mean to talk about an "isolated" quark?
> Not very much, as it is possible that an isolated quark can never occur
> in reality, even "in principle"; "isolated" here meaning that
> measurements can be made upon it to determine its mass, the outcome of
> which is only a function of the state of the quark under investigation.

Well, that's correct at low energies/temperatures. However, in the very
early universe the temperature was high enough that quarks and gluons
existed in a deconfined "quark-gluon plasma" phase. The RHIC experiment
at Brookhaven is probing this phase of matter.

In this phase quarks and gluons behave like weakly interacting
free particles. So it is possibly to talk about what happens to
a single quark.

> Nobody even knows if quarks /have/ a "defined" mass, because nobody
> really knows what mass is, however much they tell you that they do.

Mass is a parameter in a Lagrangian. It's hard to define a quark mass
because you have to infer it from properties of Hadrons. But in principle
it's no more difficult than infering the mass of an electron from the
properties of positronium.

> This is really at the edge of science.
> As to how we know "which is which" between the bottom and top quarks -
> which is really what you're asking - I'm not so sure, given that the
> difference between the possible masses of the up and down quarks is
> vastly less than the uncertainties in the masses of each of the heavier
> quarks. I suspect looking at pairs of mesons such as (up anti-strange)
> and (strange anti-down) would shed some light, as the strange mass
> cancels out in such comparisons. A bit of theoretical waffling could
> give an argument as to what the coulomb repulsion in each of the two
> configurations is, and after cancelling that out, the only difference in
> the meson masses would be the difference between the up and the down.

There are papers by Winberg from the 60s which address these questions.
You can use chiral perturbation theory to assign quarks to masses. 

-- 
Matthew Nobes
Newman Lab, Cornell Univesity, Ithaca, NY  14853
http://www.lepp.cornell.edu/~nobes

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