== Minimal Dilaton Model (MDM) ==


'''Authors'''

 * Junjie Cao
   * Henan Normal University; Center for High Energy Physics, Peking University
   * junjiec@itp.ac.cn
 * Xiqing Hao
   * Henan Normal University
   * haoxq@ihep.ac.cn
 * Zhaoxia Heng
   * Henan Normal University
   * zhaoxiaheng@gmail.com
 * Liangliang Shang
   * Henan Normal University
   * shlwell1988@gmail.com
 * Yang Zhang   
   * Institute of Theoretical Physics, Academia Sinica
   * phyzhangyang@gmail.com

'''Description of the model'''

This model is an extension of the SM by introducing a linearized singlet dilaton field ''S'' and a vector-like top partner ''T'' with the same quantum number as the right-handed top quark. The low energy effective Lagrangian of the MDM is given by [1] [2] [3]: 

[[Image(the low energy effective Lagrangian of the MDM.png)]]

where ''L'',,SM,, is the part of the SM Lagrangian without the Higgs potential, ''M'' presents the scale of a certain strong dynamics in which the fields ''T'' and ''S'' are involved, ''q,,3L,,'' is the ''SU(2),,L,,'' left-handed quark doublet of the third generation, and ''M,,H,,'', ''M,,S,,'', ''λ,,S,,'', ''κ'' and ''λ,,H,,'' are all free parameters describing the new Higgs potential.

'''Model files'''
 * [attachment:MDM.fr MDM.fr ]: the main model file.
 * [attachment:MDM.nb MDM.nb]: the example of Mathematica notebook that loads the model, calculates the Feynman rules and extracts the model files within the CalcHEP output and the UFO output.
 * [attachment:Minimal-Dilaton-Model-CH.tar.gz Minimal-Dilaton-Model-CH.tar.gz]: the model files within the CalcHEP output.
 * [attachment:Minimal_Dilaton_Model_UFO.tar.gz Minimal_Dilaton_Model_UFO.tar.gz]: the model files within the UFO output.

Notes:

 * Except the free parameters in the SM, there are still five free parameters in the MDM：
   * ''f'': the vacuum expectation value of Dilaton;
   * ''θ,,L,,'': the mixing angle of top and top partner;
   * ''θ,,S,,'': the mixing angle of Higgs and Dilaton;
   * ''m,,s,,'': the mass of dilaton-boson;
   * ''m,,t^'^,,'': the mass of top partner.
 * The dilaton-boson mass and width are set using the parameters MsDM and WsDM, respectively.
 * The top partner mass and width are set using the parameters MTP and WTP, respectively.
 * The vacuum expectation value of Dilaton is given by vevf.
 * The tangent value of Higgs-Dilaton mixing angle is set by ts.
 * The sine value of top and top partner mixing angle is set by sl.

'''Validation'''

The Feynman rules were computed by hand and compared with the [http://feynrules.irmp.ucl.ac.be/ FeynRules] vertices and found to agree. Furthermore, the three main partial decay widths of top partner were calculated by hand, compared with the numerical results both in [http://theory.sinp.msu.ru/~pukhov/calchep.html/ CalcHEP] with Feynman gauge and Unitary gauge and in [http://madgraph.hep.uiuc.edu/ MadGraph] with Unitary gauge, and found to agree. We have uploaded our model file in the [http://feynrules.phys.ucl.ac.be/validation/ FeynRules validation web] and checked our model file. Moreover, the hermiticity of the Lagrangian was tested at the Feynman rules level.



'''References'''

[1] Tomohiro Abe, Ryuichiro Kitano, Yasufumi Konishi, Kin-ya Oda, Joe Sato and Shohei Sugiyama, Minimal Dilaton Model, Phys. Rev. D86 (2012) 115016, [http://arxiv.org/abs/arXiv:1209.4544/ arXiv:1209.4544] [hep-ph].

[2] Junjie Cao, Yangle He, Peiwen Wu, Mengchao Zhang and Jingya Zhu, Higgs phenomenology in the Minimal Dilaton Model after Run I of the LHC, JHEP 1401 (2014) 150, [http://arxiv.org/abs/1311.6661/ arXiv:1311.6661] [hep-ph].

[3] Junjie Cao, Zhaoxia Heng, Dongwei Li, Liangliang Shang, Peiwen Wu, Higgs-strahlung production process e^+^e^−^ → Zh at the future Higgs factory in the Minimal Dilaton Model, [http://arxiv.org/abs/arXiv:1405.4489/ arXiv:1405.4489] [hep-ph].