Periodic Reporting for period 1 - EFT-NLO (Two-loop renormalization of the SMEFT and the WET)
Reporting period: 2024-10-01 to 2026-09-30
Summary of the context and overall objectives of the project
The search for physics beyond the Standard Model (BSM) has become one of the central goals of contemporary particle physics. While the Standard Model (SM) has been extraordinarily successful in describing a wide range of experimental results, it leaves key questions unresolved, such as the origin of dark matter, the matter–antimatter asymmetry, and the nature of neutrino masses. In the absence of direct discoveries of new particles at current collider experiments, indirect probes—through precise measurements and theoretical predictions—have emerged as one of the most powerful tools to uncover signs of new physics.
The Standard Model Effective Field Theory (SMEFT) and the Weak Effective Theory (WET) provide a systematic framework to parameterize such potential effects of new physics in a model-independent way. They allow us to connect high-energy scales, where new physics may reside, with measurable low-energy observables. However, to achieve the precision necessary to match the experimental accuracy, the theoretical description must be extended beyond leading order. Recent work has established the one-loop matching between SMEFT and WET, but this result still suffers from unphysical scheme dependences that limit its applicability for robust phenomenological studies.
This project directly addresses this need by advancing the theoretical toolkit to the next level of precision. The first objective is to compute the two-loop renormalization of the WET Wilson coefficients, which is necessary to eliminate the unphysical scheme dependence of the existing one-loop matching. This will be implemented in the public code Dsixtools, ensuring immediate accessibility and usability for the wider community. The second objective is to extend this precision program to SMEFT itself, by performing the full two-loop renormalization of its parameters. Central to this effort is the calculation of the Anomalous Dimension Matrix (ADM), which governs the scale dependence of the SMEFT Wilson coefficients. At this level, a significantly larger set of operators becomes phenomenologically relevant, thereby greatly enhancing the reach of precision studies in constraining new physics.
The pathway to impact of this project lies in enabling the first consistent, fully general next-to-leading order (NLO) analysis of SMEFT parameters. Once the one-loop matching from general BSM theories onto SMEFT becomes available—which is expected imminently—the combination with the results of this project will allow the community to perform systematic, model-independent analyses at unprecedented precision. This will sharpen the interpretive power of experimental results from the LHC, flavor experiments, and low-energy precision measurements, thereby advancing one of the highest strategic priorities in fundamental physics: the search for new physics beyond the Standard Model.
The expected impacts are significant in scale and scope. On the scientific side, the project will provide the essential theoretical foundation for precision frontier studies worldwide, directly supporting the physics programs of major experimental collaborations. On the broader strategic level, it will contribute to maintaining Europe’s and the international community’s leadership in precision theoretical physics, ensuring that we are fully equipped to interpret upcoming experimental data in the most general and reliable way possible. By eliminating key theoretical limitations and opening the door to consistent global analyses, the project aims to substantially strengthen the global effort to uncover the fundamental laws of nature.
The Standard Model Effective Field Theory (SMEFT) and the Weak Effective Theory (WET) provide a systematic framework to parameterize such potential effects of new physics in a model-independent way. They allow us to connect high-energy scales, where new physics may reside, with measurable low-energy observables. However, to achieve the precision necessary to match the experimental accuracy, the theoretical description must be extended beyond leading order. Recent work has established the one-loop matching between SMEFT and WET, but this result still suffers from unphysical scheme dependences that limit its applicability for robust phenomenological studies.
This project directly addresses this need by advancing the theoretical toolkit to the next level of precision. The first objective is to compute the two-loop renormalization of the WET Wilson coefficients, which is necessary to eliminate the unphysical scheme dependence of the existing one-loop matching. This will be implemented in the public code Dsixtools, ensuring immediate accessibility and usability for the wider community. The second objective is to extend this precision program to SMEFT itself, by performing the full two-loop renormalization of its parameters. Central to this effort is the calculation of the Anomalous Dimension Matrix (ADM), which governs the scale dependence of the SMEFT Wilson coefficients. At this level, a significantly larger set of operators becomes phenomenologically relevant, thereby greatly enhancing the reach of precision studies in constraining new physics.
The pathway to impact of this project lies in enabling the first consistent, fully general next-to-leading order (NLO) analysis of SMEFT parameters. Once the one-loop matching from general BSM theories onto SMEFT becomes available—which is expected imminently—the combination with the results of this project will allow the community to perform systematic, model-independent analyses at unprecedented precision. This will sharpen the interpretive power of experimental results from the LHC, flavor experiments, and low-energy precision measurements, thereby advancing one of the highest strategic priorities in fundamental physics: the search for new physics beyond the Standard Model.
The expected impacts are significant in scale and scope. On the scientific side, the project will provide the essential theoretical foundation for precision frontier studies worldwide, directly supporting the physics programs of major experimental collaborations. On the broader strategic level, it will contribute to maintaining Europe’s and the international community’s leadership in precision theoretical physics, ensuring that we are fully equipped to interpret upcoming experimental data in the most general and reliable way possible. By eliminating key theoretical limitations and opening the door to consistent global analyses, the project aims to substantially strengthen the global effort to uncover the fundamental laws of nature.
Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far
During the reporting period, significant technical progress was achieved in the field of Effective Field Theories, with particular emphasis on the Standard Model Effective Field Theory (SMEFT) and its low-energy extensions.
A central outcome was the completion of a comprehensive review article on the SMEFT [1], which systematizes the theoretical framework, available computational tools, and its broad phenomenological applications. Several original research works advanced the state of the art in precision theory: new strategies were developed for rare flavor processes, including a study of the time-dependent measurement of Bs→ϕμ+μ− at FCC-ee [2], as well as a detailed perspective on Kaon physics as a sensitive probe of new interactions [4].
On the methodological side, major progress was made in renormalization group techniques. This includes the derivation of anomalous dimensions in general gauge theories at the one-loop level [5], the calculation of two-loop anomalous dimensions in the Low Energy Effective Field Theory (LEFT) [6], and the release of a computational package enabling renormalization group running in SMEFT with sterile neutrinos [7]. Together, these results provide essential theoretical ingredients for precision tests of the Standard Model at both low- and high-energy experiments.
In addition to research outputs, technical expertise was applied in professional service, including the peer review of eight journal articles for the journals JHEP and EPJC and the evaluation of competitive research project for the Austrian Science Fund programme.
Overall, the reporting period was characterized by substantial scientific progress in theoretical particle physics, delivering new results of direct relevance for upcoming precision experiments and consolidating the role of SMEFT and related frameworks as indispensable tools for exploring physics beyond the Standard Model.
References
[1] J. Aebischer, A. J. Buras, and J. Kumar, SMEFT ATLAS: The Landscape Beyond the Standard Model, arXiv:2507.05926.
[2] T. H. Kwok, Z. Polonsky, V. Lukashenko, J. Aebischer, and B. Kilminster, Time-Dependent Precision Measurement of Bs0 → ϕµ+ µ− Decay at FCC-ee, arXiv:2506.08089.
[3] J. Aebischer, A. Ali, T. Becher, L. Born, F. Borzumati, A. Crivellin, J. Eicher, M. Fael, A. Ferroglia, T. Hurth, A. Lenz, M. Misiak, M. Steinhauser, J. Virto, and D. Wyler, Christoph greub’s impact and legacy, Eur. Phys. J. Spec. Top. (2025).
[4] J. Aebischer et al., Kaon Physics: A Cornerstone for Future Discoveries, arXiv:2503.22256.
[5] J. Aebischer, L. C. Bresciani, and N. Selimovic, Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector, arXiv:2502.14030.
[6] J. Aebischer, P. Morell, M. Pesut, and J. Virto, Two-Loop Anomalous Dimensions in the LEFT:
Dimension-Six Four-Fermion Operators in NDR, arXiv:2501.08384.
[7] J. Aebischer, T. Kapoor, and J. Kumar, A package for renormalization group running in the SMEFT with sterile neutrinos, Eur. Phys. J. C 85 (2025), no. 5 501, [arXiv:2411.07220].
A central outcome was the completion of a comprehensive review article on the SMEFT [1], which systematizes the theoretical framework, available computational tools, and its broad phenomenological applications. Several original research works advanced the state of the art in precision theory: new strategies were developed for rare flavor processes, including a study of the time-dependent measurement of Bs→ϕμ+μ− at FCC-ee [2], as well as a detailed perspective on Kaon physics as a sensitive probe of new interactions [4].
On the methodological side, major progress was made in renormalization group techniques. This includes the derivation of anomalous dimensions in general gauge theories at the one-loop level [5], the calculation of two-loop anomalous dimensions in the Low Energy Effective Field Theory (LEFT) [6], and the release of a computational package enabling renormalization group running in SMEFT with sterile neutrinos [7]. Together, these results provide essential theoretical ingredients for precision tests of the Standard Model at both low- and high-energy experiments.
In addition to research outputs, technical expertise was applied in professional service, including the peer review of eight journal articles for the journals JHEP and EPJC and the evaluation of competitive research project for the Austrian Science Fund programme.
Overall, the reporting period was characterized by substantial scientific progress in theoretical particle physics, delivering new results of direct relevance for upcoming precision experiments and consolidating the role of SMEFT and related frameworks as indispensable tools for exploring physics beyond the Standard Model.
References
[1] J. Aebischer, A. J. Buras, and J. Kumar, SMEFT ATLAS: The Landscape Beyond the Standard Model, arXiv:2507.05926.
[2] T. H. Kwok, Z. Polonsky, V. Lukashenko, J. Aebischer, and B. Kilminster, Time-Dependent Precision Measurement of Bs0 → ϕµ+ µ− Decay at FCC-ee, arXiv:2506.08089.
[3] J. Aebischer, A. Ali, T. Becher, L. Born, F. Borzumati, A. Crivellin, J. Eicher, M. Fael, A. Ferroglia, T. Hurth, A. Lenz, M. Misiak, M. Steinhauser, J. Virto, and D. Wyler, Christoph greub’s impact and legacy, Eur. Phys. J. Spec. Top. (2025).
[4] J. Aebischer et al., Kaon Physics: A Cornerstone for Future Discoveries, arXiv:2503.22256.
[5] J. Aebischer, L. C. Bresciani, and N. Selimovic, Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector, arXiv:2502.14030.
[6] J. Aebischer, P. Morell, M. Pesut, and J. Virto, Two-Loop Anomalous Dimensions in the LEFT:
Dimension-Six Four-Fermion Operators in NDR, arXiv:2501.08384.
[7] J. Aebischer, T. Kapoor, and J. Kumar, A package for renormalization group running in the SMEFT with sterile neutrinos, Eur. Phys. J. C 85 (2025), no. 5 501, [arXiv:2411.07220].
Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)
The project has delivered several results that go beyond the current state of the art in the field of Effective Field Theories (EFTs) and their applications to precision particle physics.
A major outcome is the completion of a large review article on the SMEFT [1], which provides the community with a systematic and authoritative reference on the theoretical framework, its computational aspects, and its phenomenological applications. This work sets the benchmark for future studies in the field and will serve as a key resource for both theorists and experimentalists.
Important original contributions were made to rare flavor processes and their potential to probe new physics, including a precision study of the time-dependent measurement of Bs0→ϕμ+μ− at the FCC-ee [2], and a comprehensive roadmap for the role of Kaon physics in future discoveries [4]. These results demonstrate how EFT methods can be applied to extract new physics sensitivity at future collider and flavor experiments, and they contribute directly to shaping the physics case for future large-scale research infrastructures.
On the methodological side, the project advanced the frontier of renormalization group techniques. Key results include the derivation of anomalous dimensions in general gauge theories [5], the computation of two-loop anomalous dimensions in the Low Energy Effective Field Theory (LEFT) [6], and the development of a public code for renormalization group running in the SMEFT with sterile neutrinos [7]. These achievements go beyond the existing state of the art by extending the precision and applicability of EFT frameworks, ensuring that theoretical predictions will match the experimental accuracy expected at next-generation facilities.
Through invited talks at major international conferences and workshops (Kaon 2025, FLASY 2025, Planck 2025, among others), as well as dedicated seminars at CERN, these scientific advances were disseminated to the broader community. The fellow also contributed to community building by organizing international scientific events, such as the HEFT 2025 conference at CERN, the SMEFT-Tools workshop at MITP, and the Christophest workshop at the University of Bern [3], which brought together leading experts to discuss precision predictions and EFT methodologies.
Professional service was provided by refereeing multiple papers for JHEP and EPJC, as well as a competitive research project for the Austrian Science Fund, ensuring the quality and impact of ongoing research in the field.
Potential impacts and key needs for further uptake
The results provide essential theoretical input for the physics case of future colliders and intensity-frontier experiments, directly supporting the European Strategy for Particle Physics. The methodologies and tools developed here will enable precise interpretation of experimental results in terms of new physics and thereby maximize the scientific return of major EU investments in research infrastructure.
To ensure full uptake and success, continued support is required for:
• further development of higher-order EFT techniques, to match the increasing precision of experimental data;
• integration and dissemination of computational tools, enabling broader use by the experimental community;
• sustained investment in training and mobility, ensuring that expertise in advanced EFT methods is passed on to the next generation of researchers.
Overall, the project has consolidated Europe’s leadership in SMEFT and EFT research, delivered concrete results that go beyond the state of the art, and provided tools and knowledge essential for the success of future experimental programs.References
References
[1] J. Aebischer, A. J. Buras, and J. Kumar, SMEFT ATLAS: The Landscape Beyond the Standard Model, arXiv:2507.05926.
[2] T. H. Kwok, Z. Polonsky, V. Lukashenko, J. Aebischer, and B. Kilminster, Time-Dependent Precision Measurement of Bs0 → ϕµ+ µ− Decay at FCC-ee, arXiv:2506.08089.
[3] J. Aebischer, A. Ali, T. Becher, L. Born, F. Borzumati, A. Crivellin, J. Eicher, M. Fael, A. Ferroglia, T. Hurth, A. Lenz, M. Misiak, M. Steinhauser, J. Virto, and D. Wyler, Christoph greub’s impact and legacy, Eur. Phys. J. Spec. Top. (2025).
[4] J. Aebischer et al., Kaon Physics: A Cornerstone for Future Discoveries, arXiv:2503.22256.
[5] J. Aebischer, L. C. Bresciani, and N. Selimovic, Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector, arXiv:2502.14030.
[6] J. Aebischer, P. Morell, M. Pesut, and J. Virto, Two-Loop Anomalous Dimensions in the LEFT:
Dimension-Six Four-Fermion Operators in NDR, arXiv:2501.08384.
[7] J. Aebischer, T. Kapoor, and J. Kumar, A package for renormalization group running in the SMEFT with sterile neutrinos, Eur. Phys. J. C 85 (2025), no. 5 501, [arXiv:2411.07220].
A major outcome is the completion of a large review article on the SMEFT [1], which provides the community with a systematic and authoritative reference on the theoretical framework, its computational aspects, and its phenomenological applications. This work sets the benchmark for future studies in the field and will serve as a key resource for both theorists and experimentalists.
Important original contributions were made to rare flavor processes and their potential to probe new physics, including a precision study of the time-dependent measurement of Bs0→ϕμ+μ− at the FCC-ee [2], and a comprehensive roadmap for the role of Kaon physics in future discoveries [4]. These results demonstrate how EFT methods can be applied to extract new physics sensitivity at future collider and flavor experiments, and they contribute directly to shaping the physics case for future large-scale research infrastructures.
On the methodological side, the project advanced the frontier of renormalization group techniques. Key results include the derivation of anomalous dimensions in general gauge theories [5], the computation of two-loop anomalous dimensions in the Low Energy Effective Field Theory (LEFT) [6], and the development of a public code for renormalization group running in the SMEFT with sterile neutrinos [7]. These achievements go beyond the existing state of the art by extending the precision and applicability of EFT frameworks, ensuring that theoretical predictions will match the experimental accuracy expected at next-generation facilities.
Through invited talks at major international conferences and workshops (Kaon 2025, FLASY 2025, Planck 2025, among others), as well as dedicated seminars at CERN, these scientific advances were disseminated to the broader community. The fellow also contributed to community building by organizing international scientific events, such as the HEFT 2025 conference at CERN, the SMEFT-Tools workshop at MITP, and the Christophest workshop at the University of Bern [3], which brought together leading experts to discuss precision predictions and EFT methodologies.
Professional service was provided by refereeing multiple papers for JHEP and EPJC, as well as a competitive research project for the Austrian Science Fund, ensuring the quality and impact of ongoing research in the field.
Potential impacts and key needs for further uptake
The results provide essential theoretical input for the physics case of future colliders and intensity-frontier experiments, directly supporting the European Strategy for Particle Physics. The methodologies and tools developed here will enable precise interpretation of experimental results in terms of new physics and thereby maximize the scientific return of major EU investments in research infrastructure.
To ensure full uptake and success, continued support is required for:
• further development of higher-order EFT techniques, to match the increasing precision of experimental data;
• integration and dissemination of computational tools, enabling broader use by the experimental community;
• sustained investment in training and mobility, ensuring that expertise in advanced EFT methods is passed on to the next generation of researchers.
Overall, the project has consolidated Europe’s leadership in SMEFT and EFT research, delivered concrete results that go beyond the state of the art, and provided tools and knowledge essential for the success of future experimental programs.References
References
[1] J. Aebischer, A. J. Buras, and J. Kumar, SMEFT ATLAS: The Landscape Beyond the Standard Model, arXiv:2507.05926.
[2] T. H. Kwok, Z. Polonsky, V. Lukashenko, J. Aebischer, and B. Kilminster, Time-Dependent Precision Measurement of Bs0 → ϕµ+ µ− Decay at FCC-ee, arXiv:2506.08089.
[3] J. Aebischer, A. Ali, T. Becher, L. Born, F. Borzumati, A. Crivellin, J. Eicher, M. Fael, A. Ferroglia, T. Hurth, A. Lenz, M. Misiak, M. Steinhauser, J. Virto, and D. Wyler, Christoph greub’s impact and legacy, Eur. Phys. J. Spec. Top. (2025).
[4] J. Aebischer et al., Kaon Physics: A Cornerstone for Future Discoveries, arXiv:2503.22256.
[5] J. Aebischer, L. C. Bresciani, and N. Selimovic, Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector, arXiv:2502.14030.
[6] J. Aebischer, P. Morell, M. Pesut, and J. Virto, Two-Loop Anomalous Dimensions in the LEFT:
Dimension-Six Four-Fermion Operators in NDR, arXiv:2501.08384.
[7] J. Aebischer, T. Kapoor, and J. Kumar, A package for renormalization group running in the SMEFT with sterile neutrinos, Eur. Phys. J. C 85 (2025), no. 5 501, [arXiv:2411.07220].