EFTs and bases
New EFTs and bases can be defined by placing the definition files into the public repository (http://github.com/wcxf/wcxf-bases). This page lists the currently defined EFTs and bases. For each basis, a PDF file listing all the operators is linked.
EFT SMEFT
Standard Model Effective Field Theory with linearly realized electroweak symmetry breaking.
Basis Higgs-Warsaw up
This is a mixture between the Higgs basis as defined e.g. in arXiv:1610.07922 and the Warsaw up basis. All bosonic operators involving at least one Higgs field as well as the operators of type $\psi^2 \phi^2 D$ are taken from the Higgs basis (with dimensionful Wilson coefficients rather than normalizing by $1/v^2$), while all other operators (in particular $\psi^2\phi^3$ and four-fermion operators) are defined as in the Warsaw up basis.
Basis SMEFTsim_MFV
Basis used in the SMEFTsim_MFV UFO models, version 3.0.0 or later. Implements Warsaw basis with $U(3)$ flavor symmetry for all fermions and includes up to 1 lepton Yukawa and 3 quark Yukawa insertions. BSM CP violation is forbidden. $q,u,d$ are the left- and right-handed quark fields. $\ell, e$ are left- and right-handed lepton fields. $Y_l,Y_u,Y_d$ are the 3x3 yukawa matrices for leptons, up- and down-quarks, defined by $L_{SM} \supset \bar d Y_d H^\dagger q$ and analogously for the others. Quark fields are in the up-aligned basis: $Y_l,Y_u$ are assumed diagonal at the scale of evaluation, while $Y_d = Y_d^{diag} V_{CKM}^\dagger$. Flavor indices are indicated with $p,r,s,t$ with Einstein conventions on repeated indices. They run over 1,2,3 for all fields. This basis definition corresponds to a fixed LambdaSMEFT=1e+3 in the UFO models. Notation and conventions can vary compared to the Warsaw basis paper, see arXiv:2012.11343 for all definitions.
Basis SMEFTsim_U35
Basis used in the SMEFTsim_U35 UFO models, version 3.0.0 or later. Implements Warsaw basis with $U(3)$ flavor symmetry for all fermions. For each operator, only the lowest-order flavor structure is kept. $q,u,d$ are the left- and right-handed quark fields. $\ell, e$ are left- and right-handed lepton fields. $Y_l,Y_u,Y_d$ are the 3x3 yukawa matrices for leptons, up- and down-quarks, defined by $L_{SM} \supset \bar d Y_d H^\dagger q$ and analogously for the others. Quark fields are in the up-aligned basis: $Y_l,Y_u$ are assumed diagonal at the scale of evaluation, while $Y_d = Y_d^{diag} V_{CKM}^\dagger$. Flavor indices are indicated with $p,r,s,t$ with Einstein conventions on repeated indices. They run over 1,2,3 for all fields. This basis definition corresponds to a fixed LambdaSMEFT=1e+3 in the UFO models. Notation and conventions can vary compared to the Warsaw basis paper, see arXiv:2012.11343 for all definitions.
Basis SMEFTsim_general
Basis used in the SMEFTsim_general UFO models, version 3.0.0 or later. Implements Warsaw basis with generic flavor indices for all fermions. $q,u,d$ are the left- and right-handed quark fields. $\ell, e$ are left- and right-handed lepton fields. Quark fields are in the up-aligned basis. This basis definition corresponds to a fixed LambdaSMEFT=1e+3 in the UFO models. Notation and conventions can vary compared to the Warsaw basis paper, see arXiv:2012.11343 for all definitions.
Basis SMEFTsim_top
Basis used in the SMEFTsim_top UFO models, version 3.0.0 or later. Implements Warsaw basis with $U(2)^3$ flavor symmetry in the quarks sector and $U(1)^3$ in the leptons sector. $Q,t,b$ are left- and right-handed 3rd gen quarks, $q,u,d$ are the left- and right-handed quark fields containing only the first two generations, and transforming as $U(2)$-flavor doublets. $\ell, e$ are left- and right-handed lepton fields. $Y_u,Y_d$ are the 2x2 Yukawas of up and down quarks in the first two generations, defined by $L_{SM} \supset \bar d Y_d H^\dagger q$ and analogously for the others. Spurions connecting the first two generations with the 3rd are absent. In the UFO models, both $Y_u$ and $Y_d$ are assumed diagonal at the scale of evaluation, and the CKM is taken to be the unit matrix. Flavor indices are indicated with $p,r,s,t$ with Einstein conventions on repeated indices. They run over 1,2 for quarks. This basis definition corresponds to a fixed LambdaSMEFT=1e+3 in the UFO models. Notation and conventions can vary compared to the Warsaw basis paper, see arXiv:2012.11343 for all definitions.
Basis SMEFTsim_topU3l
Basis used in the SMEFTsim_topU3l UFO models, version 3.0.0 or later. Implements Warsaw basis with $U(2)^3$ flavor symmetry in the quarks sector and $U(3)^2$ in the leptons sector. $Q,t,b$ are left- and right-handed 3rd gen quarks, $q,u,d$ are the left- and right-handed quark fields containing only the first two generations, and transforming as $U(2)$-flavor doublets. $\ell, e$ are left- and right-handed lepton fields. $Y_u,Y_d$ are the 2x2 Yukawas of up and down quarks in the first two generations. $Y_l$ is the 3x3 lepton Yukawa. Yukawas defined by $L_{SM} \supset \bar d Y_d H^\dagger q$ and analogously for the others. Spurions connecting the first two generations with the 3rd are absent. In the UFO models, both $Y_u$ and $Y_d$ are assumed diagonal at the scale of evaluation, and the CKM is taken to be the unit matrix.. Flavor indices are indicated with $p,r,s,t$ with Einstein conventions on repeated indices. They run over 1,2 for quarks ans 1,2,3 for leptons. This basis definition corresponds to a fixed LambdaSMEFT=1e+3 in the UFO models. Notation and conventions can vary compared to the Warsaw basis paper, see arXiv:2012.11343 for all definitions.
Basis Warsaw
Basis suggested by Grzadkowski, Iskrzyński, Misiak, and Rosiek (arXiv:1008.4884v3). At variance with their definition, the Wilson coefficients are defined to be dimensionful, such that $\mathcal L=\sum _i C_i O_i$. The set of redundant operators coincides with the choice of DSixTools (arXiv:1704.04504). The weak basis for the fermion fields is chosen such that the running dimension-6 mass matrices of charged leptons and down-type quarks are diagonal at the scale where the coefficient values are specified, while up-type quark singlet field is rotated to diagonalise the running dimension-6 up-type quark mass matrix “from the right”.
Basis Warsaw mass
Variant of the Warsaw basis where all fermion fields are rotated such as to make their mass matrices diagonal. This rotation breaks $SU(2)_L$ invariance and is ambiguous for some operators. We adhere to the choice of arXiv:1704.03888 by Dedes, Materkowska, Paraskevas, Rosiek, and Suxho, which coincides with the “tilded” basis in arXiv:1512.02830 by Aebischer, Crivellin, Fael, and Greub.
Basis Warsaw up
Variant of the Warsaw basis where the up-type quark mass matrix (rather than the down-type quark) is diagonal.
EFT WET
Weak effective theory below the electroweak scale with five dynamical quark flavours.
Basis Bern
Basis suggested by Aebischer, Fael, Grueb, and Virto (arXiv:1704.06639). Neutrinos are in the flavor basis.
Basis EOS
Basis used by the EOS software as of version 0.4 or later. Neutrinos are in the flavour basis.
Basis FlavorKit
Basis used by the FlavorKit and SPheno packages
Basis JMS
Basis suggested by Jenkins, Manohar, and Stoffer (arXiv:1709.04486). Currently only includes baryon and lepton number conserving operators. Neutrinos are in the flavour basis.
Basis flavio
Basis used by the flavio package. Neutrinos are in the flavour basis.
Basis formflavor
Basis used by the FormFlavor package
EFT WET-2
Weak effective theory with dynamical up and down quark and electron, valid below the stange quark mass scale.
Basis JMS
Variant of the basis suggested by Jenkins, Manohar, and Stoffer (arXiv:1709.04486) with only two dynamical quark flavors.
EFT WET-3
Weak effective theory with three dynamical quark flavours and two charged lepton flavours valid between the strange and charm quark mass scales.
Basis Bern
Basis JMS
Variant of the basis suggested by Jenkins, Manohar, and Stoffer (arXiv:1709.04486) with only three dynamical quark flavors.
Basis flavio
EFT WET-4
Weak effective theory with four dynamical quark flavours valid between the charm and bottom quark mass scales.
Basis Bern
Basis JMS
Variant of the basis suggested by Jenkins, Manohar, and Stoffer (arXiv:1709.04486) with only four dynamical quark flavors.