== 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 [https://feynrules.irmp.ucl.ac.be 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 [https://cp3.irmp.ucl.ac.be/projects/madgraph/ MadGraph_aMC@NLO] and [http://www.feynarts.de FeynArts] are included.

=== Publication ===
We published a description of this project and the resulting Feynman rules for scalar leptoquarks in [https://arxiv.org/abs/2105.04844 ArXiv:2105.04844]. Please cite this article ([https://inspirehep.net/literature/1862806 Crivellin:2021tmz]) when using any of the contents provided here. 

=== Model files ===
-  [https://feynrules.irmp.ucl.ac.be/attachment/wiki/SLQrules/SLQrules.fr SLQrules.fr]: This is the main model file. It contains the scalar LQ parameters, field definitions as well as the complete Lagrangian. 
-  [https://feynrules.irmp.ucl.ac.be/attachment/wiki/SLQrules/SM.fr SM.fr]: This is the [https://feynrules.irmp.ucl.ac.be FeynRules] SM model file. It is needed to determine the interactions between the LQs and the SM particles. 
-  [https://feynrules.irmp.ucl.ac.be/attachment/wiki/SLQrules/SLQrules.nb SLQrules.nb]: This is an example Mathematica notebook that loads and calculates the Feynman rules and can be used to export the model files. 
-  [https://feynrules.irmp.ucl.ac.be/attachment/wiki/SLQrules/UFO.zip UFO.zip]: This archive contains the model files for [https://cp3.irmp.ucl.ac.be/projects/madgraph/ MadGraph_aMC@NLO] phenomenology studies. 
-  [https://feynrules.irmp.ucl.ac.be/attachment/wiki/SLQrules/FeynArts.zip FeynArts.zip]: This archive contains the model files for [http://www.feynarts.de 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.