Infrared renormalon in SU(N) QCD(adj.) on R^3× S^1
Abstract
We study the infrared renormalon in the gluon condensate in the SU(N) gauge theory with n_W-flavor adjoint Weyl fermions (QCD(adj.)) on R^3× S^1 with the Z_N twisted boundary conditions. We rely on the so-called large-β_0 approximation as a conventional tool to analyze the renormalon, in which only Feynman diagrams that dominate in the large-n_W limit are considered, while the coefficient of the vacuum polarization is set by hand to the one-loop beta function β_0=11/3-2n_W/3. In the large N limit within the large-β_0 approximation, the W-boson, which acquires the twisted Kaluza-Klein momentum, produces the renormalon ambiguity corresponding to the Borel singularity at u=2. This provides an example that the system in the compactified space R^3× S^1 possesses the renormalon ambiguity identical to that in the uncompactified space R^4. We also discuss the subtle issue that the location of the Borel singularity can change depending on the order of two necessary operations.
- Publication:
-
Progress of Theoretical and Experimental Physics
- Pub Date:
- February 2020
- DOI:
- 10.1093/ptep/ptz157
- arXiv:
- arXiv:1909.05489
- Bibcode:
- 2020PTEP.2020b3B01A
- Keywords:
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- High Energy Physics - Theory;
- High Energy Physics - Lattice;
- High Energy Physics - Phenomenology
- E-Print:
- 24 pages, 1 figure, the final version to appear in PTEP