Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2009-04-23
Phys.Rev.D80:096001,2009
Physics
High Energy Physics
High Energy Physics - Phenomenology
13 pages, revtex4. Same physics, shortened; version accepted for publication in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.80.096001
Although gauge-boson propagators in asymptotically-free gauge theories satisfy a dispersion relation, they do not satisfy the K\"allen-Lehmann (KL) representation because the spectral function changes sign. We argue that this is a simple consequence of asymptotic freedom. On the basis of the QED-like Ward identities of the pinch technique (PT) we claim that the product of the coupling $g^2$ and the scalar part $\hat{d}(q^2)$ of the PT propagator, which is both gauge invariant and renormalization-group invariant, can be factored into the product of the running charge $\bar{g}^2(q^2)$ and a term $\hat{H}(q^2)$ both of which satisfy the KL representation although their product does not. We show that this behavior is consistent with some simple analytic models that mimic the gauge-invariant PT Schwinger-Dyson equations (SDE) provided that the dynamic gauge boson mass is sufficiently large. The PT SDEs do not depend directly on the PT propagator through $\hat{D}$ but only through $\hat{H}$.
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