Positivity issues for the pinch-technique gluon propagator and their resolution
- Department of Physics and Astronomy, University of California, Los Angeles California 90095 (United States)
Although gauge-boson propagators in asymptotically-free gauge theories satisfy a dispersion relation, they do not satisfy the Kaellen-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{sup 2} and the scalar part d-circumflex(q{sup 2}) of the PT propagator, which is both gauge invariant and renormalization-group invariant, can be factored into the product of the running charge g{sup 2}(q{sup 2}) and a term H-circumflex(q{sup 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 d-circumflex but only through H-circumflex.
- OSTI ID:
- 21325510
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 80, Issue 9; Other Information: DOI: 10.1103/PhysRevD.80.096001; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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