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

By L. Lehman, Adam Martin. 2015

153 citations recorded by the source corpus.

A bstractIn 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 Nf = 1 operators.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/32e31ebfab9da7927bd8a797b16483cd6f41f82e

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In Nuclear and High Energy Physics

1. T. You
2. John Ellis
3. J. Quevillon
4. A. Drozd
5. Veronica Sanz
6. Cms Collaboration

In Statistical and Nonlinear Physics

1. J. Quevillon
2. John Ellis
3. T. You
4. A. Drozd

Citations in the corpus

• Operator bases, S-matrices, and their partition functions (2017, unknown): “They were adapted in the two papers [40, 43] to deal with the problem of finding Lorentz invariant operators involving multiple types of field, but only for the subset of the operator basis where no more than one derivative appears in an operator.”
• The universal one-loop effective action (2015, background): “There is however nothing limiting the extension of our universal results to operators of dimension seven [48] and higher [117, 118].”