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 SMEFT is constructed out of a series of SU(3)_C × SU(2)_L × U(1)_Y invariant (local and analytic) higher dimensional operators L₆, L₇, ... built out of the SM fields.

The SMEFTsim package provides a complete implementation of the dimension-6 Lagrangian adopting the Warsaw basis ​https://arxiv.org/abs/1008.4884 and it is designed to enable numerical studies of the LO interference of the SMEFT with the SM, while neglecting NLO corrections.

The SM Lagrangian is extended with the inclusion of the complete set of baryon-number-conserving operators of the Warsaw basis and of the SM loop-induced Higgs couplings to gg, γγ and Zγ. The code assumes unitary gauge: in particular, modifications of the ghost Lagrangian have not been included. 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.

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

The flavor symmetry assumptions adopted are (see ​https://arxiv.org/abs/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, in which non-SM CP-violating effects are neglected, but flavor-violation 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}

each set contains a main file, a number of subroutines and restriction files. Pre-exported UFO files to be interfaced with MadGraph5_aMC@NLO can also be downloaded from this page.

The SMEFTsim package is to provide a complete tool for the analysis of the tree level interference terms between the L₆ dependent amplitude and the SM amplitudes in a measured process. In this spirit, we stress that this package is neither to be employed for the extraction of accurate SM predictions nor equipped for NLO calculations in MadGraph5_aMC@NLO.

The models are built upon the default SM implementation in FeynRules, from which they inherit the SM fields, parameters and Lagrangian definitions. The original file has been extended and modified to include the complete set of L₆ baryon number conserving operators of the Warsaw basis. The loop-induced effective couplings of SM Higgs to gg, γγ and Zγ have also been included. At this stage, the ghost Lagrangian has been left in its SM form. The entire Wilson coefficient parameter space of the L₆ SMEFT and the automatic inclusion of the shifts due to the choice of an input parameters set are implemented.

Two independent sets are supplied in the SMEFTsim package. Each set contains a single master code and a number of subroutines, along with several restriction files. The model file can be loaded in FeynRules using the notebook program, with the product of the UFOs. Model files and pre-exported UFO files to be interfaced with MadGraph5_aMC@NLO can be downloaded on this page.

Note that 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. We appreciate if you could report us any inconsistency or bugs.

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.XXXX

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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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UFO generated files

	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​