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Advances in High Energy Physics
Volume 2012, Article ID 379736, 10 pages
Research Article

Soft Collinear Degeneracies in an Asymptotically Free Theory

1School of Computing and Mathematics, University of Plymouth, Plymouth PL4 8AA, UK
2Department of Physics & Engineering Physics, University of Saskatchewan, Saskatoon, SK, Canada S7N 5E2

Received 7 July 2011; Accepted 10 November 2011

Academic Editor: Anastasios Petkou

Copyright © 2012 Martin Lavelle et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In asymptotically free theories with collinear divergences it is sometimes claimed that these divergences are cancelled if one sums over initial and final state degenerate cross-sections and uses an off-shell renormalisation scheme. We show for scalar theory in six dimensions that there are further classes of soft collinear divergences and that they are not cancelled. Furthermore, they yield a nonconvergent series of terms at a fixed order of perturbation theory. Similar effects in gauge theories are also summarised.