2021 Fiscal Year Annual Research Report
Effective field theory for sub-MeV dark matter direct detection
| Project/Area Number |
20H01896
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Melia Thomas 東京大学, カブリ数物連携宇宙研究機構, 准教授 (30814909)
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | Effective field theory / Sub-MeV dark matter |
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| Outline of Annual Research Achievements |
Developed an application of the effective field theory (EFT) construction techniques to a theory relevant for describing the canonical condensed matter Ising model - that is, phi4 theory in 4-epsilon dimensions. This involved understanding how the conformal structures that organise the operator basis impact the process of calculating quantum loop corrections, providing insight as to how the scattering elements can 'mix' into each other via these quantum effects.
The 'asymptotic handle' to study the structure of EFT was further developed. This avenue was identified as a particularly useful one to gain insight into how redundancies remove operators from an EFT: that a direct (non asymptotic) approach is prohibitively hard can be understood by the mathematical connection to the study of partition functions. Indeed, there exists no closed-form expression for even the number of integer partitions; yet, the Ramanujan asymptotic formula gives an analytic handle. A more fine-grained approach was taken, to understand more detailed analytic properties of EFT operator bases in the asymptotic limit.
The construction of EFTs is organized by symmetry. However one obstacle that was encountered in making contact with the literature was that often an organising symmetry is an outer-automorphism symmetry. These types of symmetry thus needed to be understood. This led to the observation that such symmetries could be anomalous - not preserved in the quantum theory (which is the theory of interest, including for dark matter scattering). These anomalies were investigated their nature elucidated.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
It was necessary to understand and elucidate issues surrounding outer-automorphism symmetries in organising quantum theories, which was unanticipated. This resulted in an unplanned publication on anomalies in quantum theories.
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| Strategy for Future Research Activity |
Develop the elucidation of EFT with spontaneously broken symmetry. Acknowledge that there is an important class of theories that have not been systematically studied, namely when such a symmetry is gauged. These systems are prevalent in condensed matter, and thus are an important target for the goal of this project.
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