The recent theoretical progress in uncovering the phase diagram of strongly coupled theories, has lead us to identify a number of models which can dynamically break the electroweak gauge symmetry and pass the precision tests.
The simplest of these models are:
To close the gap between the theoretical community and the experimentalists working at particle colliders, we provide a public implementation of our models, to investigate their phenomenology.
Jeppe R. Andersen, Oleg Antipin and Marco Nardecchia helped in the validation.
An earlier implementation of this model on LanHEP was written by A. Belyaev, M. Frandsen, R. Foadi, and M. Järvinen.
Also see the HEPMDB database.
Our implementation makes use of the effective low-energy model containing scalars, pseudoscalars, vector mesons and other fields predicted by the models. The implemented model is the simplest one, which contains only the lightest composite states, which are expected to be the most important ones for collider phenomenology. These are the composite Higgs and the vector and axial spin-one resonances. For these states the effective theories of MWT and NMWT coincide.
The most relevant references for this model implementation are:
FeynArts and Sherpa interfaces have not been tested.
The model file is loaded as usual. The implementation supports only unitary gauge. The standard model section has only Cabibbo mixing, and the electron and the muon, as well as the up, down and strange quarks, are taken to be massless.
The calculator is needed by the MadGraph implementation in order to change the parameters of the model. The directory is provided by a README file with the instructions on the usage.
The model file implements a (linear) effective theory for the spin-zero and spin-one sectors in technicolor, with the minimal SU(2)L x SU(2)R -> SU(2)V chiral symmetry breaking pattern. The strong technicolor interactions are linked to the electroweak sector as stipulated by the electroweak gauge transformations of the techniquarks. The modifications to the effective theory due to the electroweak interactions are mostly small. The composite scalar sector contains the composite Higgs boson and a triplet of massless technipions, which are eaten by the heavy gauge boson Z and W. The Higgs is expected to be relatively light (mass less than 500 GeV). We also have vector and axial spin-one triplets, which mix with each other and with the electroweak gauge bosons.
In addition to the standard model fermions, we thus have the following new particles:
The numbering convention for the heavy spin-one states is such that R1 is always the lightest one. When the mass scale is below 1 TeV, R1 (R2) has larger component of the axial (vector) spin-one composite state than of the vector (axial) state. When masses are increased to about 2 TeV, the situation is reversed.
Using the effective theory introduces several new coupling constants. These can be constrained by linking to the underlying gauge theory via the Weinberg sum rules and the definition of the electroweak S parameter. After taking into account the Weinberg sum rules, the free parameters can be expressed in terms of:
The implementation of the following processes through the FeynRules interface was cross-checked with the already existing implementation in LanHEP (see references):
Among others, also the processes
were cross-checked between the MadGraph and CalcHEP implementations.
Standard model processes like
were checked by comparing to the standard model implementation both in CalcHEP and in MadGraph.
Furthermore, the matrix elements generated for
were checked by hand for a few phase space points.
Values of constrained parameters (e.g. rotation matrices) in CalcHEP, some randomly chosen Lagrangian terms, as well as all the partial widths for the decay of any of the composite states to any two particles, were checked against the earlier LanHEP implementation.
HiggsEffective.fr has to be loaded together with the FeynRules file for the MWT model, i.e. using the command LoadModel[HiggsEffective.fr, MWT.fr] where MWT.fr indicates the name of the MWT model file.
The value of the effective coupling is a function of the other parameters of the model, that has been calculated in full generality at the one loop order. For practical reasons though the effective coupling is declared as an external parameter. Anyway its correct value doesn’t need to be introduced in the FeynRules file but it will be computed by the modified calculator for MadGraph. Therefore this extension can be currently used only with MadGraph.
Note that the effective coupling is independent of the new dynamics because the Higgs-fermions couplings are not modified in the MWT implementation with respect to the SM.