I Pole Masses of Light Quarks

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1. Jul 26, 2016

ohwilleke

The pole masses of the heavy quarks (c, b and t) are relatively well defined in QCD (i.e. the solution of m²(p²) = p² extrapolated using the beta function and the available data from other values of µ usually obtained based upon model dependent decompositions of hadron masses that include these heavy quarks).

Generally speaking, when we talk about the masses of the light quarks (u, d, and s) we use the masses at µ corresponding to 1 GeV or 2 GeV in an MS renormalization scheme (or some similar alternative) and those are the masses referenced by the particle data group.

Naively extrapolating light quark masses to lower energy scales gives much larger hypothetical pole masses for these particles (approaching constituent quark approximation masses), but it isn't obvious that these pole masses are meaningful because confinement implies that light quarks are always present in hadrons, and there are no hadrons lighter than the pion (ca. 140 MeV) and the protons (a bit under 1 GeV). So, perhaps pole masses for these particles are simply "non-physical".

The discussion of the issue in one paper (http://arxiv.org/pdf/hep-ph/9712201v2.pdf) states:
Is there a non-perturbative way to determine the light quark pole masses below µ ∼ 1 GeV? Is it simply too hard to calculate but well defined? Or, are these quantities ill defined or truly non-physical?

Last edited: Jul 26, 2016
2. Jul 27, 2016

vanhees71

3. Jul 27, 2016

ohwilleke

Thanks for the reference, although the pdg review dances around the subject rather than really attacking it head on.

4. Jul 28, 2016

vanhees71

I don't understand what you mean. It explains, how the mass values they quote are determined. As I said, it's a tricky business since quarks are not observable as "asymptotic free states".

5. Jul 28, 2016

ohwilleke

The crux of the issue is whether determining these values is simply difficult, or whether the concept of quarks have a well defined mass at a scale far less than the smallest hadron masses of hadrons that contain them is itself is in some respect unsound.