Infrared renormalon in SU(N) QCD(adj.) on ℝ3 × S1

Masahiro Ashie; Okuto Morikawa; Hiroshi Suzuki; Hiromasa Takaura; Kengo Takeuchi

doi:10.1093/ptep/ptz157

Infrared renormalon in SU(N) QCD(adj.) on ℝ³ × S¹

Masahiro Ashie, Okuto Morikawa, Hiroshi Suzuki, Hiromasa Takaura, Kengo Takeuchi

Experimental Particle Physics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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 ℝ³× S¹ with the ℤ_N 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-n_W limit are considered, while the coefficient of the vacuum polarization is set by hand to the one-loop beta function β₀ = 11/3 2n_W/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.

Original language	English
Article number	023B01
Journal	Progress of Theoretical and Experimental Physics
Volume	2020
Issue number	2
DOIs	https://doi.org/10.1093/ptep/ptz157
Publication status	Published - Feb 28 2020

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Physics and Astronomy(all)

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title = "Infrared renormalon in SU(N) QCD(adj.) on ℝ3 × S1",

abstract = "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.",

author = "Masahiro Ashie and Okuto Morikawa and Hiroshi Suzuki and Hiromasa Takaura and Kengo Takeuchi",

note = "Funding Information: H.S. would like to thank the Theoretical Physics Department of CERN, where part of this work was carried out, for kind hospitality. We are grateful to Mohamed M. Anber, Aleksey Cherman, and Mithat {\"U}nsal for valuable comments. This work was supported by Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research numbers JP18J20935 (O.M.), JP16H03982 (H.S.), and JP19K14711 (H.T.). Publisher Copyright: {\textcopyright} 2020 The Author(s).",

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AU - Morikawa, Okuto

AU - Suzuki, Hiroshi

AU - Takaura, Hiromasa

AU - Takeuchi, Kengo

N1 - Funding Information: H.S. would like to thank the Theoretical Physics Department of CERN, where part of this work was carried out, for kind hospitality. We are grateful to Mohamed M. Anber, Aleksey Cherman, and Mithat Ünsal for valuable comments. This work was supported by Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research numbers JP18J20935 (O.M.), JP16H03982 (H.S.), and JP19K14711 (H.T.). Publisher Copyright: © 2020 The Author(s).

PY - 2020/2/28

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N2 - 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.

AB - 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.

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Infrared renormalon in SU(N) QCD(adj.) on ℝ³ × S¹

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