Infrared renormalon in $SU(N)$ QCD(adj.) on $\mathbb{R}^3\times S^1$

DOI10.1093/PTEP/PTZ157zbMATH Open1477.81108arXiv1909.05489OpenAlexW3121404241MaRDI QIDQ5156501

No author found.

Publication date: 18 October 2021

Published in: PTEP. Progress of Theoretical and Experimental Physics (Search for Journal in Brave)

Abstract: We study the infrared renormalon in the gluon condensate in the

S U (N)

gauge theory with

n_{W}

-flavor adjoint Weyl fermions (QCD(adj.)) on~

m a t h b b R^{3} i m e s S^{1}

with the

m a t h b b Z_{N}

twisted boundary conditions. We rely on the so-called large-

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~

. In the large~

N

limit within the large-

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~

m a t h b b R^{3} i m e s S^{1}

possesses the renormalon ambiguity identical to that in the uncompactified space~

m a t h b b 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.

Full work available at URL: https://arxiv.org/abs/1909.05489

Mathematics Subject Classification ID

Nuclear physics (81V35) Strong interaction, including quantum chromodynamics (81V05) Feynman diagrams (81T18) Continuum limits in quantum field theory (81T27) Kaluza-Klein and other higher-dimensional theories (83E15) Boundary value problems on manifolds (58J32) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21) Casimir effect in quantum field theory (81T55) Dimensional compactification in quantum field theory (81T33)