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@PHDTHESIS{Schaaf:998889,
author = {Schaaf, Magnus Cornelius},
othercontributors = {Harlander, Robert V. and Krämer, Michael},
title = {{S}ystematic construction of explicit operator bases for
generic effective field theories automated to any mass
dimension},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2024-11713},
pages = {1 Online-Ressource : Illustrationen},
year = {2024},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University 2025; Dissertation, RWTH Aachen University, 2024},
abstract = {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.},
cin = {136220 / 130000},
ddc = {530},
cid = {$I:(DE-82)136220_20140620$ / $I:(DE-82)130000_20140620$},
pnm = {GRK 2497 - GRK 2497: Physik der schwersten Teilchen am
Large Hadron Collider (400140256) / DFG project
G:(GEPRIS)396021762 - TRR 257: Phänomenologische
Elementarteilchenphysik nach der Higgs-Entdeckung
(396021762)},
pid = {G:(GEPRIS)400140256 / G:(GEPRIS)396021762},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2024-11713},
url = {https://publications.rwth-aachen.de/record/998889},
}
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