Open Access

UV stability of one-loop radiative corrections in higher-derivative scalar field theory

Yugo Abe¹, Takeo Inami^2,3, and Keisuke Izumi ^4,5

¹Department of Pure and Applied Physics, Kansai University, Suita 564-8680, Japan
²iTHEMS Program, RIKEN, Wako 351-0198, Japan
³Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
⁴Department of Mathematics, Nagoya University, Nagoya 464-8602, Japan
⁵Kobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602, Japan

Phys. Rev. D 113, 016020 – Published 20 January, 2026

DOI: https://doi.org/10.1103/6gb9-35zv

Abstract

We consider the theory of a higher-derivative (HD) real scalar field $ϕ$ coupled to a complex scalar $σ$ , the coupling of the $ϕ$ and $σ$ being given by two types, $λ_{σ ϕ} σ^{†} σ ϕ^{2}$ and $ξ_{σ ϕ} σ^{†} σ {(\partial_{μ} ϕ)}^{2}$ . We evaluate $ϕ$ one-loop corrections $δ V (σ)$ to the effective potential of $σ$ , both the contribution from the positive norm part of $ϕ$ and that from the negative norm part (ghost). We show that $δ V (σ_{cl})$ at $σ_{cl} \to \infty$ , where $σ_{cl}$ is a classical value of $σ$ , is positive, implying the stability of $δ V (σ_{cl})$ by the HD one-loop radiative corrections at high energy.

Physics Subject Headings (PhySH)

Article Text

References (29)

Y. Hamada, H. Kawai, and K.-y. Oda, Phys. Rev. D 87, 053009 (2013); 89, 059901(E) (2014).
F. Bezrukov, M. Y. Kalmykov, B. A. Kniehl, and M. Shaposhnikov, J. High Energy Phys. 10 (2012) 140.
G. Degrassi, S. Di Vita, J. Elias-Miro, J. R. Espinosa, G. F. Giudice, G. Isidori, and A. Strumia, J. High Energy Phys. 08 (2012) 098.
L. Smolin, Phys. Lett. 93B, 95 (1980).
S. Bhattacharjee and P. Majumdar, Nucl. Phys. B885, 481 (2014).
N. Haba, K. Kaneta, R. Takahashi, and Y. Yamaguchi, Phys. Rev. D 91, 016004 (2015).
F. Loebbert and J. Plefka, Mod. Phys. Lett. A 30, 1550189 (2015).
Y. Abe, M. Horikoshi, and T. Inami, Commun. Phys. 26, 229 (2017).
C. Álvarez-Luna, S. de la Calle-Leal, J. A. R. Cembranos, and J. J. Sanz-Cillero, J. High Energy Phys. 02 (2023) 232.
K. S. Stelle, Phys. Rev. D 16, 953 (1977).
A. Salvio, Front. Phys. 6, 77 (2018).
M. Ostrogradsky, Mem. Acad. St. Petersbourg 6, 385 (1850).
A. Pais and G. E. Uhlenbeck, Phys. Rev. 79, 145 (1950).
R. P. Woodard, Scholarpedia 10, 32243 (2015).
T. D. Lee and G. C. Wick, Nucl. Phys. B9, 209 (1969).
T. D. Lee and G. C. Wick, Phys. Rev. D 2, 1033 (1970).
J. Kubo and T. Kugo, Prog. Theor. Exp. Phys. 2023, 123B02 (2023).
J. Kubo and T. Kugo, Prog. Theor. Exp. Phys. 2024, 053B01 (2024).
S. W. Hawking and T. Hertog, Phys. Rev. D 65, 103515 (2002).
Y. Abe, T. Inami, K. Izumi, T. Kitamura, and T. Noumi, Prog. Theor. Exp. Phys. 2019, 083B06 (2019).
B. Holdom, Phys. Lett. B 843, 138023 (2023).
J. F. Donoghue and G. Menezes, J. High Energy Phys. 09 (2025) 062.
S. R. Coleman and E. J. Weinberg, Phys. Rev. D 7, 1888 (1973).
T. Fujimori, T. Inami, K. Izumi, and T. Kitamura, Prog. Theor. Exp. Phys. 2016, 013B08 (2016).
M. Laine and A. Vuorinen, Lect. Notes Phys. 925, 1 (2016).
Y. Makeenko, J. High Energy Phys. 05 (2023) 085.
Y. Makeenko, Nucl. Phys. B967, 115398 (2021).
Y. Nakayama, Lett. Math. Phys. 109, 2255 (2019).
W. Bialek and A. Zee, Phys. Rev. Lett. 61, 1512 (1988).

Phys. Rev. D 113, 016020– Published 20 January, 2026

Vol. 113, Iss. 1 — 1 January 2026

Received 13 August 2024
Accepted 2 January 2026

DOI: https://doi.org/10.1103/6gb9-35zv

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physical Review D

Reuse & Permissions

Export citation

Export citation

UV stability of one-loop radiative corrections in higher-derivative scalar field theory

Abstract

Physics Subject Headings (PhySH)

Article Text

References (29)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation