Re: Up & Down Quark Mass or Charge Problem?

From: Matthew Nobes (nobes_at_lns61.lns.cornell.edu)
Date: 08/30/04 

Date: 30 Aug 2004 08:54:38 -0400

On 30 Aug 2004, Arnold Neumaier wrote:

> Matthew Nobes wrote:
> > On Sat, 28 Aug 2004, Jamie Vicary wrote:
> >
> >>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.
>
> No. The parameters in the Lagrangian all diverge under renormalization.

Well, if we want to be picky, you can set up the Lagrangian in terms
of the renormalized mass (which is finite), and a counterterm.

> The mass is described by a pole in the Green's function,

That's only one definition of the quark mass. Since a free quark cannot
be isolated, the pole in the quark propagator does not have a direct
relationship to a hadron mass.

> or in terms of decay constants of correlations (in lattice gauge theory).

Those masses are typically bound state masses.

> In nonrelativistic quark models, however, the (effective) mass is a
> parameter in an effective Hamiltonian.

Usually this is choosen to be the pole mass in matching calculations.

> http://pdg.lbl.gov/2004/reviews/contents_sports.html#partpropetc
> contains online documents by the particle data group, among others one
> on 'Quark Masses'. This is the yearly updated official consensus of
> the physics community.

That's a usful read, since it makes it clear how hard it is to define
an unambigous quark mass.

                                    Matt 

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

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