Version 13 (modified by NeilChristensen, 10 years ago) (diff)


Minimal Higgsless Model or 3-Site Model

Implementation Author

  • Neil Christensen
    • Michigan State University
    • neil@…

This implementation is based on an earlier implementation done in collaboration with Alexander Belyaev which can be found here.


  • Phys.Rev.D74:075011,2006: This is the first description of the 3-Site Model.
  • Phys.Rev.D78:031701,2008 : This is a study of the LHC collider phenomenology of the 3-Site Model that uses the earlier !LanHEP version that this implementation was based on.
  • arXiv:0906.2472 : This is the 2nd FeynRules paper where this implementation was published. It contains a shortened version of the notes below.

Model Files

Model Implementation

Details about the Minimal Higgsless Model can be found in the reference above. This implementation goes beyond that reference in two ways. It uses exact formulas for all the internal parameters and wavefunctions and the Goldstone bosons and ghosts are worked out in complete detail as is necessary for Feynman gauge. Full details about this implementation can be found in:


The 3-Site Model is implemented in both Feynman and unitary gauge. A switch ' FeynmanGauge ' has been created. To switch between the two simply set FeynmanGauge = True/False inside your Mathematica notebook after loading the model but before doing any calculations with it (finding vertices for example.) FeynmanGauge is set to False by default.


We provide a basic notebook giving examples of how to run the interfaces on this model:


This model implementation is known to work with the following interfaces:


Over 200 2->2 processes were run in a variety of ways. First, each process was compared between the original !LanHEP implementation and the current FeynRules implementation. Second, each process was run across multiple monte-carlos including !CalcHEP, !CompHEP, MadGraph and Sherpa. Third, each process was run in two different gauges, namely Feynman gauge (in !CalcHEP and !CompHEP) and in unitary gauge (in !CalcHEP, MadGraph and Sherpa). The cross section was computed for each process and compared to one another. Agreement to better than 1% was found for all processes. The parameters for these calculations were taken as in the model files above. The energies and cuts for these calculations were:

Particles involvedsqrt(s)p_T
Only SM600GeV20GeV
Heavy Fermion Partners10TeV2TeV

where "Particles" refers to what particles are involved in the process. The results of these validations can be seen in the following images:

Strong Processesff->AW Processesll->ll Processes
ff->AA Processesff->ZW Processesll->qq Processes
ff->AZ Processesff->WW Processesln->ln Processes
ff->ZZ ProcessesVV->VV Processes (Charged)ln->qq Processes
VV->VV Processes (Neutral)

Each of these processes was also run at a single phase space point of the squared amplitude. In this test, only !CalcHEP in Feynman and unitary gauge and MadGraph were used. It is planned to include Sherpa at a later date. The energies were chosen as in the cross section comparison. The angle was chosen to be 73.3 degrees. Agreement to better than 0.1% was found in all cases. Here are images of the results:

[attachment:PS-strong.jpg Strong Processes]
[attachment:PS-ffAW.jpg ff→AW Processes]
[attachment:PS-llll.jpg ll→ll Processes]
[attachment:PS-ffAA.jpg ff→AA Processes]
[attachment:PS-ffZW.jpg ff→ZW Processes]
[attachment:PS-llqq.jpg ll→qq Processes]
[attachment:PS-ffAZ.jpg ff→AZ Processes]
[attachment:PS-ffWW.jpg ff→WW Processes] [attachment:PS-lnln.jpg ln→ln Processes]
[attachment:PS-ffZZ.jpg ff→ZZ Processes]
[attachment:PS-VVVV-charged.jpg ChargedVV→VVProcesses] [attachment:PS-lnqq.jpg ln→qq Processes]
[attachment:PS-VVVV-neutral.jpg Neutral VV→VV Processes]

These tests were performed with the following versions of the software:

'''Software''' '''Version'''
!MadGraph 4.4.21
Private development version

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