Standard Model Effective Theory at Next-to-Leading-Order in QCD

Céline Degrande, Gauthier Durieux, Fabio Maltoni, Ken Mimasu, Eleni Vryonidou & Cen Zhang

A complete implementation of the SMEFT compatible with NLO QCD predictions.

The implementation is based on the Warsaw basis of operators and includes all degrees of freedom consistent with the following symmetry assumptions:

• CP-conservation.
• U(2)_Q x U(2)_u x U(3)_d x U(3)_L x U(3)_e flavor symmetry.

The CKM matrix is approximated as a unit matrix. The flavor symmetry imposes that only the top quark is massive. The model therefore implements the 5-flavor scheme for PDFs. The bosonic operators are implemented as in the Warsaw basis employing the M_Z, M_W, G_F scheme of Electroweak input parameters.

The Standard Model input parameters that need to be specified are:

M_Z, M_W, G_F, M_H, M_t, α_S(M_Z)

The fermionic degrees of freedom (2 & 4 fermion operators) are defined according to the common standards and prescriptions established by the LHC TOP WG for the EFT interpretation of top-quark measurements at the LHC (see the ​dim6top page for more information). This model has been validated at LO with the dim6top implementation.

A new coupling order, NP, is added to the model for the SMEFT interactions.

The ​definitions.pdf document specifies the operators definitions, normalisations and coefficient names in the UFO model

Usage notes

The NLO restriction card should be used when importing the model for NLO QCD generation:

 > import model SMEFTatNLO_U2_2_U3_3_cG_4F_LO_UFO-NLO

This invokes a restricted set of operators for which the required counterterms are implemented.

We recommend specifying the full QCD, QED and NP orders for process generation.

For example:

 > generate p p > t t~ QCD=2 QED=0 NP=2 [QCD]

Generated the NLO QCD top pair production process including the QCD-induced SM and the SMEFT contributions.

Model Files

• ​SMEFTatNLO_U2_2_U3_3_cG_4F_LO_UFO.tgz : archive of UFO model - 4 fermion and c_G operators at LO, U(2)² x U(3)³ flavor symmetry

Version updates

• 2018/12/20 - v.0.1: First version upload, 4F and c_G operators at LO pending validation; a few minor convention tweaks required to match dim6top exactly. decays.py missing.
• 2019/04/03 - v.0.1: Added definitions.pdf document and uploaded a new version with a fix for restrict_default.dat