We study the infrared renormalon in the gluon condensate in the SU(N) gauge theory with nW-flavor adjoint Weyl fermions (QCD(adj.)) on ℝ3× S1 with the ℤN twisted boundary conditions. We rely on the so-called large-β0 approximation as a conventional tool to analyze the renormalon, in which only Feynman diagrams that dominate in the large-nW limit are considered, while the coefficient of the vacuum polarization is set by hand to the one-loop beta function β0 = 11/3 2nW/3. In the large N limit within the large-β0 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 R3 × S1 possesses the renormalon ambiguity identical to that in the uncompactified space ℝ4. We also discuss the subtle issue that the location of the Borel singularity can change depending on the order of two necessary operations.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)