Fluctuations about the Fubini-Lipatov instanton for false vacuum decay in classically scale invariant models
Open accessAbstract
For a scalar theory whose classical scale invariance is broken by quantum effects, we compute self-consistent bounce solutions and Green's functions. Deriving analytic expressions, we find that the latter are similar to the Green's functions in the archetypal thin-wall model for tunneling between quasidegenerate vacua. The eigenmodes and eigenspectra are, however, very different. Large infrared effects from the modes of low angular momentum $j=0$ and $j=1$, which include the approximate dilatational modes for $j=0$, are dealt with by a resummation of one-loop effects. For a parametric example, this resummation is carried out numerically.
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The solution for the τ-dependent part of the modified Green's function around the instanton can be obtained in terms of associated Legendre functions P_{μ_n/2}(u) and Q_{μ_n/2}(u).
“The solution to the equation above can be obtained in terms of associated Legendre functions P µ n 2 ( u ) and Q µ n 2 ( u ) [17, 31]. It reads [28]”
From Double-well instantons in finite volume (2024) · cites this paper as [31]
Appendix B (Eqs. B1–B2) identifies the Green-function equation in the Fubini–Lipatov background as an associated Legendre equation and writes its general solution using P and Q functions. The paper formulates this as a hyperradial Green function with indices 2 and j+1; it does not identify the solution as a τ-dependent part of a modified Green function or use the claimed μ_n/2 index. (LLM, conf=0.84)
Experimental — accuracy not yet measuredThe modified Green's function for the fluctuation operator around the static saddle points can be solved in terms of associated Legendre functions of the first and second kind P_{μ_n/0}(u) and Q_{μ_n/0}(u).
“which can be solved in terms of associated Legendre functions of the first and second kind P µ n 0 ( u ) and Q µ n 0 ( u ). See for example [31]. We have [17]”
From Double-well instantons in finite volume (2024) · cites this paper as [31]
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Cites
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Convexity, gauge-dependence and tunneling rates
Plascencia, A. D., & Tamarit, C. (2016) · Journal of High Energy Physics · doi:10.1007/jhep10(2016)099 · Cited by 64 · see citing works
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Sorted by citations
Double-well instantons in finite volume
Ai, W.-Y., Alexandre, J., Carosi, M., Garbrecht, B., & Pla, S. (2024) · Journal of High Energy Physics · doi:10.1007/jhep05(2024)099 · Cited by 6 · see citing works
- Authors
- Garbrecht, B., & Millington, P.
- Affiliations
- University of Nottingham (GB)
- ORCID
- Millington, Peter
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2018-07-02
- Volume
- 98
- Issue
- 1
- ISSN
- 2470-0010 (ISSN-L)
- 2470-0029
- OpenAlex
- W2797189794
- Cited by
- 14
- References
- 2
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 2 · 2023: 2 · 2021: 1 · 2020: 3 · 2019: 2 · 2018: 2
- FWCI
- 1.06
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Physical review. D/Physical review. D. (publishedVersion, cc-by)
- arXiv (Cornell University) (publishedVersion)
- mediaTUM (Technical University of Munich) (submittedVersion, other-oa)
- Repository@Nottingham (University of Nottingham) (submittedVersion, cc-by)
- Research Explorer (The University of Manchester) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Science and Technology Facilities Council (ST/L000393/1)
- Leverhulme Trust
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- false vacuum decay, classical scale invariance, bounce solutions, Green's function, eigenmodes, infrared effects, scalar field theory, quantum tunneling
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