[Gdh_lowq2] Stupid question: non-zero GDH for electron?

[Alexandre Deur]

Hello Krishna,

It's actually a very good question. The GDH sum rule for an electron should be zero (in the standard model). A simple way to see this is as following: There is only inelastic reactions that contribute to the GDH sum, but there is no inelastic part in electron scattering spectrum. So the sum rule should be GDH=0. Any deviation from that would be a sign of physics beyond the standard model (e.g. a finite electron size). 

The reason why it should be 0, in spite of the finite anomalous moment, is the following: The GDH sum is an expression extracted at second order in alpha, the electromagnetic coupling constant. The electron anomalous moment starts at 3rd order in alpha. So the sum rule must be 0 for any particle for which the anomalous moment comes from quantum radiative effects.  

I recall that the GDH sum on lepton was discussed in a Ph. D thesis by Pantforder (see my Ph.D thesis for the reference, it should be there).

Best regards,

Alexandre

----- Original Message -----
> From: adhikari at jlab.org
> To: "gdh lowq2" <gdh_lowq2 at jlab.org>
> Sent: Sunday, October 27, 2013 12:32:47 AM
> Subject: [Gdh_lowq2] Stupid question:   non-zero GDH for electron?
> 
> Dear GDH followers,
> Can we say an electron also has a non-zero GDH sum?
> 
> It's now known that an electron or a muon also have anomalous
> magnetic
> moment due to quantum/radiative effects.
> (https://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_moment)
> 
> That means, the anomalies in magnetic moments have either of the
> following
> two distinct origins:
> 
> 1) Due to a substructure (i.e., due to being a composite object made
> up of
> other particles) giving rise to huge anomalies such as that of a
> proton, a
> neutron or a nucleus.
> 2) Due to quantum/radiative effects, giving rise to small anomaly
> (such as
> that of an electron or a muon)
> 
> Because I have not heard or read anyone talking about GDH for an
> electron
> or for any other similar particle, my hunch is that GDH sum rule
> perhaps
> is associated only with the first part/kind of anomalous moment and
> not
> with the other kind because the sum would have to be done over the
> excited
> states which doesn’t exist in the latter case (no excited state of
> electrons because it has no intrinsic structure of its own? Or can we
> assume it to have some structure and finite size (form factor) due to
> the
> virtual photon cloud that it may have as a result of the
> radiative/quantum
> effects). But I have no idea if the sum rule is applicable for any
> non-zero anomalous moment, no matter how the anomaly originated.
> 
> What would you think? Can we say that an electron should also have a
> non
> zero GDH sum because it has a small but non-zero anomalous moment? It
> would be great if somebody enlightens me on this.
> 
> Thank you.
> Krishna
> 
> 
> 
> 
> 
> 
> 
> 
> 
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