Changes between Version 11 and Version 12 of HeavyN


Ignore:
Timestamp:
Nov 19, 2015, 7:23:51 PM (9 years ago)
Author:
Richard Ruiz
Comment:

Updated validation remarks.

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  • HeavyN

    v11 v12  
    77
    88=== Model Description ===
    9 The Type I Seesaw Model extends the Standard Model (SM) field content by introducing three right-handed (RH) neutrinos, which are singlets under the SM gauge symmetry (no color, weak isospin, or weak hypercharge charges), as well as one RH Majorana mass for each RH neutrino. After electroweak symmetry breaking, the effective Type I Seesaw Lagrangian with three heavy Majorana neutrinos ''N''i (with i=1,2,3) is given by [ [#Atre 1] ]
     9The Type I Seesaw Model extends the Standard Model (SM) field content by introducing three right-handed (RH) neutrinos, which are singlets under the SM gauge symmetry (no color, weak isospin, or weak hypercharge charges), with each RH neutrino possessing one RH Majorana mass. After electroweak symmetry breaking, the effective Type I Seesaw Lagrangian with three heavy Majorana neutrinos ''N''i (for i=1,2,3) is given by [ [#Atre 1] ]
    1010{{{
    1111#!latex
    12 $\mathcal{L}_{\rm Type~I} = \mathcal{L}_{\rm SM} + \mathcal{L}_{N} + \mathcal{L}_{N~\text{Int.}} $,
     12\begin{equation}
     13\mathcal{L}_{\rm Type~I} = \mathcal{L}_{\rm SM} + \mathcal{L}_{N} + \mathcal{L}_{N~\text{Int.}}.
     14\end{equation}
    1315}}}
    14 where the first term is the Standard Model Lagrangian; in the mass basis, the heavy Majorana neutrinos' kinetic and mass terms are
     16The first term is the Standard Model Lagrangian. In the mass basis, i.e., after mixing with active neutrinos, the heavy Majorana neutrinos' kinetic and mass terms are
    1517{{{
    1618#!latex
    17 $\mathcal{L}_{N} = \frac{1}{2}\overline{N_k} i\!\not\!\partial N_k - \frac{1}{2}m_{N_k} \overline{N_k}N_k, \quad k=1,\dots,3$;
     19\begin{equation}
     20\mathcal{L}_{N} = \frac{1}{2}\overline{N_k} i\!\not\!\partial N_k - \frac{1}{2}m_{N_k} \overline{N_k}N_k, \quad k=1,\dots,3.
     21\end{equation}
    1822}}}
    19 and its interactions with the Weak gauge and Higgs bosons in the mass eigenbasis, i.e., after mixing with active neutrinos, are given by
     23
     24and its interactions with the Weak gauge and Higgs bosons are given by
    2025{{{
    2126#!latex
    … …  
    3237\end{eqnarray}
    3338}}}
    34 The mixing matrix elements V''lk'' parametrize the mixing between the (active) lepton flavor eigenstate ''l'' and the heavy mass eigenstate corresponding to the mass eigenvalue mNk.
     39The mixing matrix elements V''lk'' parametrize the mixing between the (active) lepton flavor eigenstate ''l'' and the heavy mass eigenstate ''N''k with the corresponding mass mNk.
    3540
    3641=== Model Files ===
     42 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/typeIseesaw/heavyN.fr heavyN.fr]:  Main model file. Relies on sm.fr (default FR model file) being declared elsewhere.
    3743
    38  * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/typeIseesaw/heavyN.fr heavyN.fr]:  Main model file. Relies on sm.fr (default FR model file) being declared elsewhere.
    39  * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/typeIseesaw/heavyN.nb heavyN.nb]:  Mathematica notebook file that loads FR and model. Allows user to run quick sanity checks (optional) and outputs UFO file.
     44 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/typeIseesaw/heavyN.nb heavyN.nb]:  Mathematica notebook file that loads FR and model files. Allows user to run quick sanity checks (optional) and outputs UFO file.
     45
    4046 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/typeIseesaw/Seesaw_TypeI.tgz Seesaw_TypeI.tgz]: Standalone package containing heavyN.fr, heavyN.nb, massless.rst (default FR file), diagonalCKM.rst (default FR file), and sm.fr (default FR file).
    4147
    42  * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/typeIseesaw/Seesaw_TypeI_WithUFO.tgz Seesaw_TypeI_withUFO.tgz]: Same as Seesaw_TypeI.tgz but with UFO folder generated using restrictions massless.rst (only massive fermions are top quark and Majorana neutrino) and diagonalCKM.rst (CKM matrix set to unity).
     48 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/typeIseesaw/Seesaw_TypeI_WithUFO.tgz Seesaw_TypeI_withUFO.tgz]: Same as Seesaw_TypeI.tgz but with UFO folder generated using restrictions massless.rst (only massive fermions are the top quark and three Majorana neutrinos) and diagonalCKM.rst (CKM matrix set to unity).
    4349
    4450 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/typeIseesaw/Seesaw_TypeI_UFO.tgz Seesaw_TypeI_UFO.tgz]: Standalone UFO folder as packaged in Seesaw_TypeI_withUFO.tgz.
    … …  
    5864~/Path $ tar -zxvf Seesaw_TypeI_WithUFO.tgz
    5965
    60  * In addition to the SM parameters, this model contains 15 free parameters:
     66 * This model contains 15 free parameters:
    6167  * Three masses: mN1, mN2, mN3. Defaults are 300 GeV, 500 GeV, and 1 TeV, respectively.
    6268  * Three widths: WN1, WN2, WN3. Defaults are 0.303 GeV, 1.50 GeV, and 12.3 GeV, respectively.
    63   * Nine mixing parameters, V''lk'' for ''l'' = ''e, mu, tau'' and ''k'' = 1,2,3. Default values are V''lk'' = Identity(3x3), i.e., Ve1 = Vmu2 = Vta3 = 1 and all others zero.
     69  * Nine mixing parameters: V''lk'' for ''l'' = ''e, mu, tau'' and ''k'' = 1,2,3. Default values are V''lk'' = Identity(3x3), i.e., Ve1 = Vmu2 = Vta3 = 1 and all others zero.
    6470  * '''Note''': VlN are restricted to be real in the model file.
     71  * '''Note''': Default parameters are set so "out-of-the-box" comparisons can be performed with Ref [ [#Alva 2] ].
    6572
    6673
    6774=== Validation ===
    68 * The model file was implemented in Ref. [ [#Alva 2] ] using FeynRules v2.0.6 and MG5_aMC@NLO (MG5) v2.1.0. See Tables 2 and 5 for further validation checks; note that mixing matrices have been factored out/normalized in tabulated results.
     75* The model file was implemented in Ref. [ [#Alva 2] ] using FeynRules v2.0.6 and MG5_aMC@NLO (MG5) v2.1.0 and v2.3.2.2.  See Tables 2 and 5 of Ref. [ [#Alva 2] ] for further validation checks; note that mixing matrices have been factored out/normalized in tabulated results.
     76* For very large masses, this model has been constructed to satisfy the Goldstone Equivalence Theorem:
     77{{{
     78#!latex
     79\begin{eqnarray}
     80\text{BR}(N_i \rightarrow W^+ \ell^-) &=& \text{BR}(N_i \rightarrow W^- \ell^+) =
     81\\
     82\text{BR}(N_i \rightarrow Z \nu_\ell + Z \overline{\nu_\ell} ) &=&
     83\text{BR}(N_i \rightarrow h \nu_\ell + h \overline{\nu_\ell} ) = 25\%.
     84\end{eqnarray}
     85}}}
    6986
    7087=== List of analyses that have used the model file ===