Standard Model Effective Field Theory -- The SMEFTsim package

Authors

Ilaria Brivio, Yun Jiang and Michael 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 L⁽⁶⁾, L⁽⁷⁾, ... 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 symmetry assumptions and 2 input scheme choices.

The flavor symmetry assumptions adopted are (see ​arXiv:1709.06492 for a detailed description)

• The flavour general case
• The U(3)⁵ flavor symmetric case, with 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 free to choose between two input parameters sets for the electroweak sector, namely:

• α scheme: {α_ew, 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 L⁽⁶⁾, 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_ξ or Feynman gauge may lead to inconsistent results, as the ghost Lagrangian has not been modified to account for L⁽⁶⁾ corrections.

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

Numerical files in the WCxf format (​https://wcxf.github.io) can be translated into a param_card for SMEFTsim using the dedicated command-line script now available in the WCxf package.

Related bugs and threads

The most recent version of SMEFTsim requires MadGraph5_aMC@NLO v2.6.1.
If still experiencing errors, please refer to the following threads or contact us.

​https://bugs.launchpad.net/mg5amcnlo/+bug/1732756
​https://answers.launchpad.net/mg5amcnlo/+question/657094

Change log

Note that the version number adopted in two model Sets is independent.

set A - v2.1 (13.03.2018)

• a mistake in the definition of dGf has been corrected in the U(3)<sup>5 an MFV models.
  
  The correct expression is δG_F=</sup>G_F(C⁽³⁾_Hl− C′_ll/ 2)

(Eq. (3.3) in the ​paper)

set A - v2.0 (07.02.2018)

• fixed bug with complex Wilson coefficient
• Wilson coefficient of the operator O_HD renamed: cHD > cHDD to avoid conflict with cHd
• SM radiative couplings of the Higgs (hgg, haa, haz) assigned the corresponding QCD, QED orders, plus a dedicated SMHLOOP=1 interaction order.
• idle parameter ceeAbs2332 removed in the flavor general models
• further restrictions for top physics added to the flavor general, alpha scheme UFO.

Set B - v1.3 (06.02.2018)

• The cutoff scale Lambda has been introduced explicitly and assigned the proper InteractionOrder with the corresponding change made for Gf and vev parameters.
• Typo in the definition of dlam is corrected.
• Minor bugs with the color structure constant appearing in the Q_G and Q_Gtilde operators fixed.

v1.2 (24.11.2017)

• set A: LSMshifted renamed into LSMlinear for consistency with set B

v1.1 (20.10.2017)

• restriction cards topEFT added to each UFO and to the FeynRules source. They assume massless light fermions and set to 0 coefficients that are not relevant for top quark physics.
• set A: bug with operators Q_Hu, Q_Hd, Q_Hud, Q_Hq¹, Q_Hq³ in the MFV UFO files fixed.
• set B: bug with operators Q_Hq⁽¹⁾ in FLU model and bugs with operators Q_Hu, Q_Hd, Q_Hq⁽¹⁾, Q_Hq⁽³⁾, Q_Hl⁽¹⁾ in MFV UFO files fixed.

v1.0 (19.09.2017)

• The first version released

References

• I. Brivio, Y. Jiang and M. Trott, The SMEFTsim package, theory and tools, JHEP 1712 (2017) 070 ​arXiv:1709.06492

• J. Aebischer, I. Brivio, A. Celis, J. Evans, Y. Jiang, J. Kumar, X. Pan, W. Porod, J. Rosiek, D. Shih, F. Staub, D. Straub, D. Dyk, A. Vicente, WCxf: an exchange format for Wilson coefficients beyond the Standard Model, ​arXiv:1712.05298

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Model Set A

• SMEFTsim-setA_v2.tar.gz​ 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 are established: Scheme and Flavor, which are used to identify the input scheme and flavor assumption being adopted in loading the model.

• SMEFTsim-setB_v13.zip​ This archive contains all the model files. Should be expanded in the FR model directory.
• SMEFTsim-setB_v13.nb​ Example of a Mathematica® notebook loading the model. Should be stored in the SMEFTsim-setB model folder.

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Pre-exported UFO files (include restriction cards)

	Set A		Set B (v 1.3)
	α scheme	mW scheme	α scheme	mW scheme
Flavor general SMEFT	SMEFTsim_A_general_alphaScheme_UFO_v2.tar.gz​	SMEFTsim_A_general_MwScheme_UFO_v2.tar.gz​	SMEFT_alpha_UFO.zip​	SMEFT_mW_UFO.zip​
MFV SMEFT	SMEFTsim_A_MFV_alphaScheme_UFO_v2.tar.gz​	SMEFTsim_A_MFV_MwScheme_UFO_v2.tar.gz​	SMEFT_alpha_MFV_UFO.zip​	SMEFT_mW_MFV_UFO.zip​
U(3)5 SMEFT	SMEFTsim_A_U35_alphaScheme_UFO_v2.tar.gz​	SMEFTsim_A_U35_MwScheme_UFO_v2.tar.gz​	SMEFT_alpha_FLU_UFO.zip​	SMEFT_mW_FLU_UFO.zip​