Abstract

We present the universal one-loop effective action for all operators of dimension up to six obtained by integrating out massive, non-degenerate multiplets. Our general expression may be applied to loops of heavy fermions or bosons, and has been checked against partial results available in the literature. The broad applicability of this approach simplifies one-loop matching from an ultraviolet model to a lower-energy effective field theory (EFT), a procedure which is now reduced to the evaluation of a combination of matrices in our universal expression, without any loop integrals to evaluate. We illustrate the relationship of our results to the Standard Model (SM) EFT, using as an example the supersymmetric stop and sbottom squark Lagrangian and extracting from our universal expression the Wilson coefficients of dimension-six operators composed of SM fields.

Highlights

  • Property enabled them to obtain a one-loop effective action that applies quite generally, albeit under the restrictive condition that the particles in the UV theory are degenerate in mass [5]

  • The broad applicability of this approach simplifies one-loop matching from an ultraviolet model to a lower-energy effective field theory (EFT), a procedure which is reduced to the evaluation of a combination of matrices in our universal expression, without any loop integrals to evaluate

  • We illustrate the relationship of our results to the Standard Model (SM) EFT, using as an example the supersymmetric stop and sbottom squark Lagrangian and extracting from our universal expression the Wilson coefficients of dimension-six operators composed of SM fields

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Summary

The covariant derivative expansion

As discussed in the previous section, the reader who wishes to compute one-loop Wilson coefficients for operators of dimension up to six can start directly with (2.3) and need not worry about the details of the CDE method that we used to derive the universal one-loop effective Lagrangian. The reader who wishes to compute one-loop Wilson coefficients for operators of dimension up to six can start directly with (2.3) and need not worry about the details of the CDE method that we used to derive the universal one-loop effective Lagrangian. There are many other cases where one may wish to use the path integral, so we briefly summarise the CDE here. This was first introduced in the 1980s by Gaillard [3] and Cheyette [4]. We refer to the extensive review in ref. [5] for a clear and detailed description We refer to the extensive review in ref. [5] for a clear and detailed description

The CDE method for integrating out fields
Integrating out non-degenerate fields
Discussion
B Master integrals
C Mass dependences of the universal coefficients
D Application: integrating out squarks
E Covariant derivative expansion for fermionic fields
Full Text
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