2, 84, 30, 993, 560, 15456, 11962, 261485, . . .: higher dimension operators in the SM EFT

An Erratum to this article was published on 03 September 2019

This article has been updated

Abstract

In a companion paper [1], we show that operator bases for general effective field theories are controlled by the conformal algebra. Equations of motion and integration by parts identities can be systematically treated by organizing operators into irreducible representations of the conformal group. In the present work, we use this result to study the standard model effective field theory (SM EFT), determining the content and number of higher dimension operators up to dimension 12, for an arbitrary number of fermion generations. We find additional operators to those that have appeared in the literature at dimension 7 (specifically in the case of more than one fermion generation) and at dimension 8. (The title sequence is the total number of independent operators in the SM EFT with one fermion generation, including hermitian conjugates, ordered in mass dimension, starting at dimension 5.)

A preprint version of the article is available at ArXiv.

Change history

  • 03 September 2019

    We fix a typographical error that occurred in copying the output of the Hilbert series of the standard model effective field theory into the unnumbered equation in section 4.2 that counts the number of independent operators as a function of the number of fermion generations, Nf, split according to baryon violation number.

  • 03 September 2019

    We fix a typographical error that occurred in copying the output of the Hilbert series of the standard model effective field theory into the unnumbered equation in section 4.2 that counts the number of independent operators as a function of the number of fermion generations, Nf, split according to baryon violation number.

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Correspondence to Tom Melia.

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ArXiv ePrint: 1512.03433

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ESM1

Mathematica notebook self-contained annotated tutorial. (NB 55 kb)

ESM2

Auxiliary Mathematica file: expressions of the form eq. (3.20) for mass dimension 5--12. (M 579 kb)

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Henning, B., Lu, X., Melia, T. et al. 2, 84, 30, 993, 560, 15456, 11962, 261485, . . .: higher dimension operators in the SM EFT. J. High Energ. Phys. 2017, 16 (2017). https://doi.org/10.1007/JHEP08(2017)016

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Keywords

  • Beyond Standard Model
  • Effective Field Theories