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The QCD beta-function from global solutions to Dyson-Schwinger equations

Guillaume van Baalen
(
- Boston U.
)
,
Dirk Kreimer
(
- IHES, Bures-sur-Yvette and
- Boston U.
)
,
David Uminsky
(
- Boston U.
)
,
Karen Yeats
(
- Boston U.
)

Jun, 2009

34 pages

Published in:

Annals Phys. 325 (2010) 300-324

e-Print:

0906.1754 [hep-th]

DOI:

10.1016/j.aop.2009.10.011

View in:

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Abstract: (arXiv)

We study quantum chromodynamics from the viewpoint of untruncated Dyson-Schwinger equations turned to an ordinary differential equation for the gluon anomalous dimension. This nonlinear equation is parameterized by a function P(x) which is unknown beyond perturbation theory. Still, very mild assumptions on P(x) lead to stringent restrictions for possible solutions to Dyson-Schwinger equations. We establish that the theory must have asymptotic freedom beyond perturbation theory and also investigate the low energy regime and the possibility for a mass gap in the asymptotically free theory.

Note:

34 pages, 4 figures

Dyson-Schwinger equations
QCD
Beta-function
mass: gap
Dyson-Schwinger equation: solution
quantum chromodynamics
perturbation theory: higher-order
anomalous dimension
asymptotic freedom
renormalization group: beta function

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