Standard Model Effective Field Theory -- The SMEFTsim package

Authors

Ilaria Brivio, Yun Jiang and Micheal Trott

ilaria.brivio@nbi.ku.dk, yunjiang@nbi.ku.dk, michael.trott@cern.ch

NBIA and Discovery Center, Niels Bohr Institute, University of Copenhagen

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The model description

The Standard Model Effective Field Theory (SMEFT) is constructed out of a series of SU(3)_C × SU(2)_L × U(1)_Y invariant higher dimensional operators L₆, L₇, ... built out of the SM fields.
The SMEFTsim package provides a complete implementation of the lepton and baryon number conserving dimension-6 Lagrangian adopting the Warsaw basis ​arXiv:1008.4884

The SM Lagrangian is included and extended with the SM loop-induced Higgs couplings to gg, γγ and Zγ.

The SMEFTsim package provides implementations for 3 different flavor assumptions and 2 input scheme choices, for a total of 6 different models.

The flavor assumptions adopted are (see ​arXiv:1709.xxxxx for a detailed description)

• The flavour general case
• The U(3)⁵ flavor symmetric case, with possible non-SM CP-violating phases
• A linear Minimal flavor violation (MFV) ansatz ​arXiv:0207036, in which non-SM CP-violating effects are neglected, but linear flavor-violating spurion insertions are allowed in quark currents

For each model it is possible to choose between two input parameters sets for the electroweak sector, namely:

• α scheme: {α_em, m_Z , G_f}
• m_W scheme: {m_W, m_Z , G_f}

Importantly, field rotations required to have canonically normalized kinetic terms and parameter redefinitions following from the choice of an input parameters set are automatically applied in the Lagrangian.

Two independent models sets (A and B) are supplied. Each set contains a main file, a number of subroutines and restriction files. The two sets differ in the structure and in the technical implementation of L₆, but they produce consistent results. The use of both sets is recommended for debugging and validation of the numerical results.
Pre-exported UFO files to be interfaced with MadGraph5_aMC@NLO can also be downloaded from this page (see Table below).

We would appreciate if you could report to us any inconsistency or bugs.

Usage recommendations

The SMEFTsim package is designed to enable numerical studies of the LO interference of the SMEFT with the SM, while neglecting NLO corrections. In this spirit, it has not been optimized for loop calculations in the SM or in the SMEFT. In particular:

• the Lagrangian assumes unitary gauge. Using it in R_xi or Feynman gauge may lead to inconsistent results, as the ghost Lagrangian have not been modified to account for L_{6 corrections.}

• the UFO files are not suitable for NLO evaluation in MadGraph5_aMC@NLO

Change log

v1.0 (17.09.2017) The first version released

References

• I. Brivio, Y. Jiang and M. Trott, The SMEFTsim package, theory and tools, ​arXiv:1709.xxxxx

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Model Set A

• SMEFTsim-setA.zip​ This archive contains all the FeynRules files.
• SMEFTsim-setA.nb​ Example of a Mathematica® notebook loading the model

Model Set B

In the master code two flags: Scheme and Flavor are established, which are used to identify the input scheme and flavor symmetry being adopted in loading the model.

• SMEFTsim-setB.zip​ This archive contains all the model files. Should be expanded in the FR model directory.
• SMEFTsim-setB.nb​ Example of a Mathematica® notebook loading the model

(left with putting arXiv number in the main code *)

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Pre-exported UFO files (include restriction cards)

	Set A		Set B
	α scheme	mW scheme	α scheme	mW scheme
Flavor general SMEFT	SMEFTsim_A_general_alphaScheme_UFO.tar.gz​	SMEFTsim_A_general_MwScheme_UFO.tar.gz​	SMEFT_alpha_UFO.zip​	SMEFT_mW_UFO.zip​
MFV SMEFT	SMEFTsim_A_MFV_alphaScheme_UFO.tar.gz​	SMEFTsim_A_MFV_MwScheme_UFO.tar.gz​	SMEFT_alpha_MFV_UFO.zip​	SMEFT_mW_MFV_UFO.zip​
U(3)5 SMEFT	SMEFTsim_A_U35_alphaScheme_UFO.tar.gz​	SMEFTsim_A_U35_MwScheme_UFO.tar.gz​	SMEFT_alpha_FLU_UFO.zip​	SMEFT_mW_FLU_UFO.zip​