Changes between Version 11 and Version 12 of HeavyN
 Timestamp:
 Nov 19, 2015 7:23:51 PM (3 years ago)
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HeavyN
v11 v12 7 7 8 8 === Model Description === 9 The Type I Seesaw Model extends the Standard Model (SM) field content by introducing three righthanded (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 (withi=1,2,3) is given by [ [#Atre 1] ]9 The Type I Seesaw Model extends the Standard Model (SM) field content by introducing three righthanded (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] ] 10 10 {{{ 11 11 #!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} 13 15 }}} 14 where the first term is the Standard Model Lagrangian; in the mass basis, the heavy Majorana neutrinos' kinetic and mass terms are16 The 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 15 17 {{{ 16 18 #!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} 18 22 }}} 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 24 and its interactions with the Weak gauge and Higgs bosons are given by 20 25 {{{ 21 26 #!latex … … 32 37 \end{eqnarray} 33 38 }}} 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 eigenvaluemNk.39 The 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. 35 40 36 41 === 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. 37 43 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 40 46 * [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). 41 47 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 t op 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). 43 49 44 50 * [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. … … 58 64 ~/Path $ tar zxvf Seesaw_TypeI_WithUFO.tgz 59 65 60 * In addition to the SM parameters, this model contains 15 free parameters:66 * This model contains 15 free parameters: 61 67 * Three masses: mN1, mN2, mN3. Defaults are 300 GeV, 500 GeV, and 1 TeV, respectively. 62 68 * 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. 64 70 * '''Note''': VlN are restricted to be real in the model file. 71 * '''Note''': Default parameters are set so "outofthebox" comparisons can be performed with Ref [ [#Alva 2] ]. 65 72 66 73 67 74 === 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 }}} 69 86 70 87 === List of analyses that have used the model file ===