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TY  - THES
AU  - Schaaf, Magnus Cornelius
TI  - Systematic construction of explicit operator bases for generic effective field theories automated to any mass dimension
PB  - RWTH Aachen University
VL  - Dissertation
CY  - Aachen
M1  - RWTH-2024-11713
SP  - 1 Online-Ressource : Illustrationen
PY  - 2024
N1  - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2025
N1  - Dissertation, RWTH Aachen University, 2024
AB  - In phenomenological studies involving effective field theories, it is required to work with a complete and independent set of parameters, which are to be determined by physical observables. These parameters directly correspond to the operators of an effective field theory, and it is, therefore, necessary to obtain a basis of operators. Generally, this so-called bottom-up construction of an effective field theory is remarkably challenging. On the one hand, identifying all relevant operators can be highly nontrivial already for the leading contributions in the effective field theory expansion due to their potentially large number. Furthermore, the number of operators increases approximately exponentially at each subsequent order in the expansion. On the other hand, there are complex kinematic and algebraic relations, rendering distinct operators redundant. This thesis is dedicated to the algorithmic construction of operator bases for generic effective field theories at any order in the respective expansion. The algorithm employed here is based on on-shell techniques and concepts from the representation theory of Lie groups and the symmetric group. It allows for the construction of nonredundant operator bases for a given low-energy theory with general field content and symmetries. In particular, the obtained operator bases are, by construction, free of any redundancies induced by integration by parts identities, equations of motion, algebraic relations, or permutation symmetries. Based on this algorithm, an open-source program is developed to enable the automated construction of effective field theory operator bases. This implementation is applied to various low-energy scenarios, particularly to the Standard Model and its extension by gravitational interactions. As a result, the complete operator bases for the Standard Model effective field theory at mass dimensions 10, 11, and 12 are constructed for the first time.
LB  - PUB:(DE-HGF)11
DO  - DOI:10.18154/RWTH-2024-11713
UR  - https://publications.rwth-aachen.de/record/998889
ER  -