SLQrules

Author

• Luc Schnell (luschnel_at_student.ethz.ch)
  • LPTHE, Sorbonne Université et CNRS
  • ETH Zürich
  • École Polytechnique de Paris

Description

This project contains the complete set of Feynman rules for all five scalar leptoquarks, implemented in ​FeynRules. We include the LQ-LQ-Higgs(-Higgs) interactions and the resulting LQ mass eigenstates, the couplings to the SM gauge bosons and fermions as well as the LQ-LQ-LQ(-Higgs) and LQ-LQ-LQ-LQ interactions. The Mathematica notebook to determine and export the Feynman rules as well as the model files for ​MadGraph_aMC@NLO and ​FeynArts are included.

Publication

We published a description of this project and the resulting Feynman rules for scalar leptoquarks in ​ArXiv:2105.04844. Please cite this article (​Crivellin:2021tmz) when using any of the contents provided here.

Model files

• ​SLQrules.fr: This is the main model file. It contains the scalar LQ parameters, field definitions as well as the complete Lagrangian.
• ​SM.fr: This is the ​FeynRules SM model file. It is needed to determine the interactions between the LQs and the SM particles.
• ​SLQrules.nb: This is an example Mathematica notebook that loads and calculates the Feynman rules and can be used to export the model files.
• ​UFO.zip: This archive contains the model files for ​MadGraph_aMC@NLO phenomenology studies.
• ​FeynArts.zip: This archive contains the model files for ​FeynArts phenomenology studies.

Instructions

The notebook [SLQrules.nb](SLQrules.nb) is used to display and export the Feynman rules. Having loaded the model files in [SLQrules](SLQrules), the different parts of the Lagrangian can be accessed via the FeynRules variable names

| Lagrangian: Latex name | Lagrangian: Code name | Description | | ------ | ------ | ------ | | $\mathcal{L}^{\text{LQ}}$ | LQall | Entire leptoquark Lagrangian. | | $\mathcal{L}_{2\Phi}$ | LQ2Phi | LQ masses and LQ-LQ-Higgs(-Higgs) interactions. | | $\mathcal{L}_{kin}$ | LQkin | Kinetic terms and couplings to gauge bosons. | | $\mathcal{L}_{f}$ | LQf | Couplings to SM fermions. | | $\mathcal{L}_{3\Phi}$ | LQ3Phi | LQ-LQ-LQ(-Higgs) interactions. | | $\mathcal{L}_{4\Phi}$ | LQ4Phi | LQ-LQ-LQ-LQ interactions. |

The command `mathematica FeynmanRules[LQall]; ` is used to derive the Feynman rules, here for the entire Lagrangian $\mathcal{L}^{\text{LQ}}$. The Feynman rules can be exported as UFO files to be used in MadGraph. This is done via the command `mathematica FeynmanGauge = False; WriteUFO[LSM + LQall, Output -> "SLQrules-UFO"]; ` The boolean FeynmanGauge on the first line is used to switch between Feynman and unitary gauge. The files are exported to SLQrules/SLQrules-UFO in your FeynRules directory. We also provide ready-to-use UFO files for $\mathcal{L}^{\text{LQ}}$, these can be found under [UFO/SLQrules-UFO](UFO/SLQrules-UFO). Similarly, the export to FeynArts is carried out using `mathematica FeynmanGauge = False; WriteFeynArtsOutput[LSM + LQall, Output -> "SLQrules-FA"]; ` We provide prefabricated FeynArts files under [FeynArts/SLQrules-FA](FeynArts/SLQrules-FA). Additionally, the export to MadGraph with the counterterms needed for NLO computations as well as Sherpa, CalcHep or Whizard is possible. The corresponding commands can be found in [SLQrules.nb](SLQrules.nb), but we opt not to include prefabricated files for these applications.