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All two-loop scalar self-energies and tadpoles in general renormalisable field theories
High Energy Physics - Phenomenology · Submitted 4 Oct 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We calculate the complete tadpoles and self-energies at the two-loop order for scalars in general renormalisable theories, a crucial component for calculating two-loop electroweak corrections to Higgs-boson masses or for any scalar beyond the Standard Model.
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The abstract, sentence by sentence
We calculate the complete tadpoles and self-energies at the two-loop order for scalars in general renormalisable theories, a crucial component for calculating two-loop electroweak corrections to Higgs-boson masses or for any scalar beyond the Standard Model. We renormalise the amplitudes using mass-independent renormalisation schemes, based on both dimensional regularisation and dimensional reduction. The results are presented here in Feynman gauge, with expressions for all 121 self-energy and 25 tadpole diagrams given in terms of scalar and tensor integrals with the complete set of rules to reduce them to a minimal basis of scalar integrals for any physical kinematic configuration. In addition, we simplify the results to a set of only 16 tadpole and 58 self-energy topologies using relations in order to substitute the ghost and Goldstone-boson couplings that we derive. To facilitate their application, we also provide our results in electronic form as a new code TLDR. We test our results by applying them to the Standard Model and compare with analytic expressions in the literature.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We calculate the complete tadpoles and self-energies at the two-loop order for scalars in general renormalisable theories, a crucial component for calculating two-loop electroweak corrections to Higgs-boson masses or for any scalar beyond the Standard Model. | contribution 0.98 | 0.96 | 0.62 | asserted 1.00 |
| s1 | We renormalise the amplitudes using mass-independent renormalisation schemes, based on both dimensional regularisation and dimensional reduction. | method 0.98 | 0.95 | 0.05 | asserted 1.00 |
| s2 | The results are presented here in Feynman gauge, with expressions for all 121 self-energy and 25 tadpole diagrams given in terms of scalar and tensor integrals with the complete set of rules to reduce them to a minimal basis of scalar integrals for any physical kinematic configuration. | result 0.66 | 0.95 | 0.21 | asserted 1.00 |
| s3 | In addition, we simplify the results to a set of only 16 tadpole and 58 self-energy topologies using relations in order to substitute the ghost and Goldstone-boson couplings that we derive. | method 0.43 | 0.96 | 0.07 | asserted 1.00 |
| s4 | To facilitate their application, we also provide our results in electronic form as a new code TLDR. | contribution 0.93 | 0.95 | 0.04 | asserted 1.00 |
| s5 | We test our results by applying them to the Standard Model and compare with analytic expressions in the literature. | method 0.79 | 0.94 | 0.07 | asserted 0.98 |
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The paper
Original abstract
We calculate the complete tadpoles and self-energies at the two-loop order for scalars in general renormalisable theories, a crucial component for calculating two-loop electroweak corrections to Higgs-boson masses or for any scalar beyond the Standard Model. We renormalise the amplitudes using mass-independent renormalisation schemes, based on both dimensional regularisation and dimensional reduction. The results are presented here in Feynman gauge, with expressions for all 121 self-energy and 25 tadpole diagrams given in terms of scalar and tensor integrals with the complete set of rules to reduce them to a minimal basis of scalar integrals for any physical kinematic configuration. In addition, we simplify the results to a set of only 16 tadpole and 58 self-energy topologies using relations in order to substitute the ghost and Goldstone-boson couplings that we derive. To facilitate their application, we also provide our results in electronic form as a new code TLDR. We test our results by applying them to the Standard Model and compare with analytic expressions in the literature.
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References
How the literature uses it
13 arXiv papers cite this in 18 sentences
Papers citing it · 9 sentences without a confident label
Uses its method or tool 2 papers
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Results at the two-loop order are derived with the help of [ref] , [ref] and [ref] .
Towards Higgs masses and decay widths satisfying the symmetries in the (N)MSSM · Introduction · 1.00
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The required Feynman diagrams are computed with the help of [ref] , [ref] , [ref] and [ref] .
Fighting off field dependence in MSSM Higgs-mass corrections of order $\alpha_t\,\alpha_s$ and $\alpha_t^2$ · Introduction · 1.00
Cites it as support 1 paper
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However, we can expect the neglected two-loop momentum effects to be subleading, in the light of existing results for scalar mass calculations at two loops – see for instance Refs. [ref] , and therefore this setting is sufficient for investigating the possible maximal size of two-loop corrections.
Leading two-loop corrections to the Higgs boson self-couplings in models with extended scalar sectors · Computation in the scheme · 1.00
Cites it as background 5 papers
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The accuracy of the prediction for the light -even Higgs-boson mass of the MSSM has been significantly improved during the last years (see [ref] for recent works), in particular for the case where some or all of the supersymmetric (SUSY) particles are relatively heavy.
Precise prediction for the mass of the light MSSM Higgs boson for the case of a heavy gluino · Introduction · 0.87
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This results in corrections of the Higgs-boson masses and mixings (see [ref] for recent fixed-order calculations). * In the effective field theory (EFT) approach, all heavy particles are integrated out and the Higgs mass is then calculated in the low-energy EFT (see [ref] for recent EFT calculations). * While the FO approach is precise for low but not for high SUSY-breaking mass scales (leading to light or heavy superpartner particles, respectively), it is vice versa for the EFT approach.
Hybrid calculation of the MSSM Higgs boson masses using the complex THDM as EFT · Introduction · 0.86
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Recently, the KUTS initiative has stimulated substantial advances in various related directions, such as calculations at fixed order (FO) [ref] or in the context of low-energy Effective Field Theories (EFTs) [ref] , hybrid approaches combining FO and EFT results [ref] , or the development of public codes [ref] .
Fighting off field dependence in MSSM Higgs-mass corrections of order $\alpha_t\,\alpha_s$ and $\alpha_t^2$ · Introduction · 0.96
What it cites · 84 sentences without a confident label
Uses the method or tool of 5 papers
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We have derived the reduction formulas for all integrals that appear in 't Hooft–Feynman gauge with the help of , [ref] and the recurrence relations in Davydychev:1998si.
TARCER - A Mathematica program for the reduction of two-loop propagator integrals · Appendix · 0.99
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Our aim is to reduce all scalar two-loop integrals into the basis of integrals that can be evaluated numerically by the code [ref] .
TSIL: a program for the calculation of two-loop self-energy integrals · Appendix · 1.00
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Symmetry factors: Analytical results in terms of amplitudes for the genuine, generic two-loop diagrams as well as the corresponding one-loop diagrams with counterterm vertex, and the one-loop counterterm insertions are generated with the help of , [ref] and [ref] (we also make use of that is part of ).
Reduction of general two-loop self-energies to standard scalar integrals · Introduction · 1.00
Cites as background 17 papers
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The early expectation was for new coloured supersymmetric particles near the electroweak scale, and since the Minimal Supersymmetric SM (MSSM) had a tree-level upper bound on the Higgs mass equal to the mass of the $Z$ boson, a full fixed-order calculation in the MSSM at the one-loop order [ref] is vital, but the results at the two-loop order are known to contribute several GeV to the SM-like Higgs-boson mass.
The Higgs Boson Masses and Mixings of the Complex MSSM in the Feynman-Diagrammatic Approach · Introduction · 0.83
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The early expectation was for new coloured supersymmetric particles near the electroweak scale, and since the Minimal Supersymmetric SM (MSSM) had a tree-level upper bound on the Higgs mass equal to the mass of the $Z$ boson, a full fixed-order calculation in the MSSM at the one-loop order [ref] is vital, but the results at the two-loop order are known to contribute several GeV to the SM-like Higgs-boson mass.
The one-loop renormalization of the MSSM Higgs sector and its application to the neutral scalar Higgs masses · Introduction · 0.83
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The early expectation was for new coloured supersymmetric particles near the electroweak scale, and since the Minimal Supersymmetric SM (MSSM) had a tree-level upper bound on the Higgs mass equal to the mass of the $Z$ boson, a full fixed-order calculation in the MSSM at the one-loop order [ref] is vital, but the results at the two-loop order are known to contribute several GeV to the SM-like Higgs-boson mass.
Precision Corrections in the Minimal Supersymmetric Standard Model · Introduction · 0.83
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