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DR2MS

DR2MS[lag] takes the renormalizable Lagrangian lag that is renormalized in dimensional reduction using the

scheme as input and returns the version of that Lagrangian renormalized using dimensional regularization in the

scheme by incorporating the appropriate finite counterterms required for the scheme change.

Details and Options

The argument lag must be a valid Lagrangian containing only renormalizable interactions. Non-renormalizable interactions are currently not supported. In addition, the shift is only performed for Lagrangian terms that can contribute to the tree-level matching of the theory. Finite counterterms for interactions that only contribute at the loop level are not included as these appear only as a two-loop effect in the corresponding EFT.
This function then loops over all relevant Lagrangian terms and includes the finite scheme change counterterms following Martin and Vaughn (1993) [hep-ph/9308222].
The finite counterterms for the gauge couplings are immediately absorbed into a redefinition of these gauge couplings to achieve a canonical normalization of the kinetic terms of the gauge fields.

Examples

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Basic Examples (1)

Defining a SU(2) gauge group:

Defining 3 fields: a fundamental scalar, an adjoint Majorana fermion, and a fundamental Dirac fermion:

Defining a Yukawa and quartic scalar coupling:

Defining a Lagrangian with a Yukawa interaction and a scalar quartic:

Mapping from the to the scheme:

A finite scheme-change counterterm is generated for the Majorana mass term, the scalar quartic, and the Yukawa interaction. The finite counterterm for the gauge couplings is immediately absorbed by redefining the gauge coupling to retain a canonical normalization of the kinetic term of the gauge field.

Applications (1)

In the MSSM model file, the DR2MS function is called internally such that the Lagrangian is returned in the scheme but in a SUSY-preserving form:

Selecting only the finite counterterms:

The term containing c_2γ in the correction the the Higgs quartic, is obtained by the shift of the gauge coupling to retain canonical kinetic term of the gauge fields. Only terms relevant for the tree-level matching onto the SMEFT are included. For example, no counterterms for the gaugino masses are added, since these do not contribute to the tree-level matching and hence constitute a two-loop effect in the EFT.

Possible Issues (1)

The DR2MS function only works for renormalizable interaction terms, since it uses the formulas from https://arxiv.org/abs/hep-ph/9308222 for the computation of the counterterms. Higher-dimensional operators are currently not supported.