Changes between Version 12 and Version 13 of TechniColor


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Timestamp:
11/30/10 17:45:23 (10 years ago)
Author:
CP3-Origins
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  • TechniColor

    v12 v13  
    2626* Next to Minimal Walking Technicolor (NMWT) is a similar extension, but based on the gauge group SU(3) technicolor with a doublet of Dirac fermions in the two-index symmetric representation.
    2727
    28 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 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.
     28Our 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.
    2929
    3030
     
    3434The most relevant references for this model implementation are:
    3535
    36     * Phys. Rev. D 71, 051901 (2005) [http://arxiv.org/abs/hep-ph/0405209] - F. Sannino and K. Tuominen, ''Orientifold Theory Dynamics and Symmetry Breaking''. Note that the original name was ''Techniorientifold''.
     36    * Phys. Rev. D 71, 051901 (2005) [http://arxiv.org/abs/hep-ph/0405209] - F. Sannino and K. Tuominen, ''Orientifold Theory Dynamics and Symmetry Breaking''. This article introduces MWT and NMWT. Note that the original name was ''Techniorientifold''.
    3737    * Phys. Rev. D 76, 055005 ( 2007) [http://arxiv.org/abs/0706.1696] - R. Foadi, M.T. Frandsen, T. A. Ryttov, F. Sannino, ''Minimal Walking Technicolor: Set Up for Collider Physics''. This article derives the effective theory for MWT.
    38     * Phys. Rev. D 79, 035006 (2009) [http://arxiv.org/abs/0809.0793] A. Belyaev, R. Foadi, M.T. Frandsen, M. Jarvinen, A. Pukhov, F. Sannino, ''Technicolor Walks at the LHC''. This article presents the Lagrangian used in this implementation, and analyses LHC phenomenology by using the earlier LanHEP implementation.
     38    * Phys. Rev. D 79, 035006 (2009) [http://arxiv.org/abs/0809.0793] - A. Belyaev, R. Foadi, M.T. Frandsen, M. Jarvinen, A. Pukhov, F. Sannino, ''Technicolor Walks at the LHC''. This article presents the Lagrangian used in this implementation, and analyses LHC phenomenology by using the earlier LanHEP implementation.
    3939
    4040See also:
    4141
    4242    * Phys. Lett. B597:89-93,2004 [http://arxiv.org/abs/hep-ph/0406200] - Deog Ki Hong, Stephen D.H. Hsu, F. Sannino, ''Composite Higgs from higher representations''.
    43     * Phys. Rev. D72:055001, 2005 [http://arxiv.org/abs/hep-ph/0505059]  - D.D. Dietrich, F. Sannino, K. Tuominen ''Light composite Higgs from higher representations versus electroweak precision measurements: Predictions for CERN LHC''.
     43    * Phys. Rev. D72:055001, 2005 [http://arxiv.org/abs/hep-ph/0505059] - D.D. Dietrich, F. Sannino, K. Tuominen ''Light composite Higgs from higher representations versus electroweak precision measurements: Predictions for CERN LHC''.
    4444    * Phys. Rev. D 75, 085018 (2007) [http://arxiv.org/abs/hep-ph/0611341] - D. D. Dietrich and F. Sannino, ''Conformal window of SU(N) gauge theories with fermions in higher dimensional representations''. Note that the original name was ''Walking in the SU(N)''.
    45     * For the construction at the Lagrangian level of the terms involving the space-time epsilon tensor – representing the correct generalization of the Wess-Zumino-Witten topological term – involving massive spin one fields see Acta Phys. Polon. B40:3533-3743, 2009; [http://arxiv.org/abs/0911.0931] F. Sannino, ''Conformal Dynamics for TeV Physics and Cosmology''.
     45    * For the construction at the Lagrangian level of the terms involving the space-time epsilon tensor – representing the correct generalization of the Wess-Zumino-Witten topological term – involving massive spin one fields see Acta Phys. Polon. B40:3533-3743, 2009; [http://arxiv.org/abs/0911.0931] - F. Sannino, ''Conformal Dynamics for TeV Physics and Cosmology''.
    4646
    4747
     
    5959=== Interfaces and related files ===
    6060 
    61    * '''CalcHEP''': [/attachment/wiki/TechniColor/MWT_ch.zip (12.06.09)].
    62    * '''!MadGraph''': [/attachment/wiki/TechniColor/MWT_mg.zip (12.06.09)].
     61   * '''CalcHEP''': [/attachment/wiki/TechniColor/MWT_ch.zip MWT_ch.zip].
     62   * '''!MadGraph''': [/attachment/wiki/TechniColor/MWT_mg.zip MWT_mg.zip].
    6363   * [/attachment/wiki/TechniColor/MWT_Calculator.zip MWT_Calculator.zip]: the calculator needed in !MadGraph in order to generate the param_card.dat for a different set of model parameters.
     64
     65!FeynArts and Sherpa interfaces have not been tested.
    6466
    6567
     
    6769=== Instructions and details ===
    6870
    69 The model file is loaded as usual. The attached Mathematica® notebook can be used for this task. 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.
    70 
     71The 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.
     72{{{
     73#!comment
     74The attached Mathematica® notebook can be used for this task.
     75}}}
    7176The 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.
    7277
    73 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 is 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.
     78The 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.
    7479
    7580In addition to the standard model fermions, we thus have the following new particles:
     
    8186* Charged heavy vectors R,,2,,^+^, R,,2,,^-^
    8287
    83 The numbering convention for the heavy spin-one states is such that R,,1,, is always the lighter one. When the mass scale is below 1 TeV R,,1,, (R,,2,,) 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.
     88The numbering convention for the heavy spin-one states is such that R,,1,, is always the lightest one. When the mass scale is below 1 TeV, R,,1,, (R,,2,,) 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.
    8489
    8590Using 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:
     
    8994* S: The (contribution of the lowest spin-one states to the) S parameter. Recommended values come from naive estimates of the S parameter (calculation of techniquark loops), which gives S=0.15 for MWT and S=0.3 for NMWT.
    9095* MH: The mass of the composite Higgs boson.
    91 * rs: Parametrizes the couplings of the Higgs to the composite spin-one states. Expected to be O(1).
     96* rs: Parametrizes the couplings of the Higgs to the composite spin-one states. Expected to be of order 1.
    9297
    9398
     
    95100=== Validation ===
    96101
    97 The implementation of the following MWTC processes through the FeynRules interface was cross-checked with the already existing implementation in LanHEP (see references):
     102The implementation of the following processes through the FeynRules interface was cross-checked with the already existing implementation in LanHEP (see references):
    98103
    99   * pp>jj at 1400 GeV
    100   * pp>mu+mu- at 1400 GeV
     104  * pp>jj at 14 TeV
     105  * pp>mu+mu- at 14 TeV
     106
     107Among others, also the processes
     108
     109* e+e->mu+mu- at 14 TeV
     110* uu~>hZ at 14 TeV
     111
     112were cross-checked between the !MadGraph and CalcHEP implementations.
     113
     114Standard model processes like
     115* gg>gg
     116* ug>ug
     117* ud>us
     118were checked by comparing to the standard model implementation both in CalcHEP and in !MadGraph.
    101119
    102120Furthermore, the matrix elements generated for
     
    106124* uu~>!r1>dd~
    107125* l+l->!r1>uu~g
    108 * l+vl>W->W-H and l-vl>W+>W+H
     126* l+vl>W->W-h and l-vl>W+>W+h
    109127
    110128were checked by hand for a few phase space points.
     129
     130Values 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.
    111131
    112132
     
    118138
    119139!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.
    120 The value of the effective coupling coincides with the full one loop result, and depends on the values assumed by the other parameters of the model. For practical reasons though the effective coupling is introduced as an external parameter. Anyway its value doesn't need to be introduced at the Lagrangian level (i.e. in the FeynRules file) but will be calculated by the modified calculator for MadGraph, that computes its value based on the full one loop result. Therefore this extension can be used currently 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 respect to the SM.
     140[[BR]]
     141The 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.
     142[[BR]]
     143Note 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.