Low-derivative operators of the Standard Model effective field theory via Hilbert series methods

A bstract In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we conjecture an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of m...

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Bibliographic Details
Published in:The journal of high energy physics 2016-02, Vol.2016 (2), p.1-31, Article 81
Main Authors: Lehman, Landon, Martin, Adam
Format: Article
Language:English
Subjects:
Accounting
Algorithms
Classical and Quantum Gravitation
Derivatives
Elementary Particles
Equations of motion
Field theory
Invariants
Operators
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Redundancy
Regular Article - Theoretical Physics
Relativity Theory
String Theory
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Summary:A bstract In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we conjecture an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts. Specifically, the conjectured technique can be applied whenever there is only one Lorentz invariant for a given partitioning of derivatives among the fields. At higher numbers of derivatives, equation of motion redundancies can be removed, but the increased number of Lorentz contractions spoils the subtraction of integration by parts redundancies. While restricted, this technique is sufficient to automatically recreate the complete set of invariant operators of the Standard Model effective field theory for dimensions 6 and 7 (for arbitrary numbers of flavors). At dimension 8, the algorithm does not automatically generate the complete operator set; however, it suffices for all but five classes of operators. For these remaining classes, there is a well defined procedure to manually determine the number of invariants. Assuming our method is correct, we derive a set of 535 dimension-8 N f = 1 operators.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP02(2016)081