== Vector-leptoquark model ==

=== Authors ===

Heavy vector boson implementation:

   * Michael J. Baker
      * University of Melbourne
      * michael.baker AT unimelb.edu.au
   * Javier Fuentes-Martín
      * Universidad de Grandada
      * javier.fuentes AT ugr.de
   * Gino Isidori
      * UZH, Zurich
      * isidori AT physik.uzh.ch
   * Matthias König
      * Technische Universität München
      * matthias.koenig AT tum.de

Extension with vector-like fermions:

   * Darius A. Faroughy
      * Universty of Zürich
      * faroughy AT physik.uzh.ch

   * Javier Fuentes-Martín
      * Universidad de Grandada
      * javier.fuentes AT ugr.de

=== Description of the model ===

This model is an extension of the SM featuring a vector leptoquark (''U,,1,,~('''3''','''1'''),,2/3,,''), a colored vector (''G'~('''8''','''1'''),,0,,''), and a SM singlet (''Z'~('''1''','''1'''),,0,,'') as new heavy mediators. An extension of the model including vector-like fermions coupling to the new heavy gauge bosons is included. [[BR]][[BR]]
The implementation of the heavy vector bosons is based on ''"High-p,,T,, Signatures in Vector-Leptoquark Models''" (arXiv:1901.10480). The extension of the model including vector-like fermions is based on ''"Maximal Flavour Violation: a Cabibbo mechanism for leptoquarks''" (arXiv:1808.00942) and ''"Reading the footprints of the B-meson flavor anomalies''" (arXiv:2103.16558). If you use our model file please cite these references.

=== Model Files ===

[/attachment/wiki/LeptoQuark/vector_LQ.fr  vector_LQ.fr]: This is the Feynrules model file for the vector leptoquark. [[BR]]
[/attachment/wiki/LeptoQuark/coloron.fr  coloron.fr]: This is the Feynrules model file for the vector color-octet.[[BR]]
[/attachment/wiki/LeptoQuark/Zprime.fr  Zprime.fr]: This is the Feynrules model file for the vector singlet.[[BR]]
[/attachment/wiki/LeptoQuark/VLferm.fr  VLferm.fr]: This is the Feynrules model file for the vector-like fermions.

=== Model Restrictions ===

[/attachment/wiki/LeptoQuark/Massless.rst  Massless.rst]: This restriction file sets all the masses and Yukawas to zero, except for the ones of the top quark (necessary to work in the 5 flavor scheme).

=== Instructions ===

The model is loaded by merging the model files {{{SM.fr}}} (in StandardModel), {{{vector_LQ.fr}}}, {{{coloron.fr}}}, {{{Zprime.fr}}} and {{{VLferm.fr}}}. Alternatively, one can exclude the model files {{{coloron.fr}}}, {{{Zprime.fr}}} and/or  {{{VLferm.fr}}} if the user is not interested in any of these particles.  [[BR]][[BR]]
The implementation allows for the use of the Feynman and unitary gauge in the SM. The switch between the two gauges is achieved via {{{FeynmanGauge = True/False}}} (see StandardModel). [[BR]]
The NP interaction order has been set to 1, the same as QCD.

=== Examples ===

[/attachment/wiki/LeptoQuark/model_gen.nb  model_gen.nb]: This is an example Mathematica® notebook that loads the Feynrules model files and calculates the UFO model.  [[BR]]
[/attachment/wiki/LeptoQuark/widths.nb  widths.nb]: This is an example Mathematica® notebook that loads the Feynrules model files and calculates the Feynman rules and widths of the new vectors. 

=== Interfaces ===
This model implementation is known to work with the following interfaces:
   * [wiki:FeynArtsInterface FeynArts Interface] 
   * [wiki:MadGraphInterface MadGraph Interface] 

=== Validation ===

An alternative  Feynrules implementation for the vector leptoquark model alone (but with interactions to left-handed third-generation SM fermions only) is available in https://lqnlo.hepforge.org. We have cross-checked our leptoquark implementation (with ''β,,R,,^33^ = 0'') against this one, finding a perfect agreement between the two.

=== UFO model ===

[/attachment/wiki/LeptoQuark/vector_LQ_UFO.tar  vector_LQ_UFO.tar]: UFO model including the ''U,,1,,'', ''G' '' and ''Z' '', and one family of vector-like quarks and leptons with the same quantum numbers as the SM left-handed fermions.