== The SMEFT in the Background Field Method. ==


Author: Tyler Corbett

{{{
corbett.t.s@gmail
}}}

Niels Bohr International Academy, Niels Bohr Institute


== Description ==
Following [https://arxiv.org/abs/1803.08001 arXiv:1803.08001] we implement the Standard Model Effective Field Theory (SMEFT) dimension six operators gauge fixed using the background field method (see e.g. [https://inspirehep.net/literature/166273 Abbott, Introduction to the Background Field Method]). The implementation of the model is elaborated in an upcoming publication, arXiv:2011:XXXXX, and is verified in both this paper and [https://arxiv.org/abs/2010.08451 arXiv:2010.08451] where the one-loop Ward identities are checked for UV divergent two-point functions and the Tadpole. 


The model includes all SMEFT operators at dimension six as well as dimension-eight operators of Classes 2, 3, and 4. Fermionic operators are introduced with no assumptions on flavor and the Yukawa operators and class 5 operators are diagonalized using standard rotations of the Left and Right-handed fermionic fields, resulting in meaningful goldstone-fermion couplings which also incorporate the CKM matrix for charged goldstone interactions. Another appeal of the model is that it incorporates field and mass redefinitions coming from the SMEFT to order 1/Lambda^4, this is to the authors knowledge the only package incorporating these effects. As order 1/Lambda^4 effects are frequently included in the literature without incorporating these redefinitions this tool provides an excellent opportunity to study the implications of incomplete calculations. This is discussed in the paper outlining the implementation, arxiv:2011:XXXXX.



== Usage ==
This model may be used to derive the Feynman rules in the Feynrules interface as well as for obtaining a model file for usage with Formcalc and Feynarts. The ancillary files demonstrate usage in Feynrules and in the Feynarts/Formcalc workflow in order to obtain the two-point and tadpole amplitudes.

This model is not designed for use with simulation packages such as MadGraph, and usage of the the UFO output of Feynrules is not recommended.


== Change Log ==
v1.0 29 Nov 2020: The first version.

== References ==
T. Corbett, The Feynman Rules for the SMEFT in the Background Field Gauge, arXiv:2011:XXXXX.
Paper introducing the model and its implementation as well as verifying the SMEFT Class 2, 3, and 4 operator squared contributions to the SMEFT Ward Identities.

T. Corbett, M. Trott, One loop verification of SMEFT Ward Identities, [https://arxiv.org/abs/2010.08451 arXiv:2010.08451]
Paper verifying SMEFT dimension-six Ward Identities.