# 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 `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 package. 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.