Changes between Version 10 and Version 11 of HeavyN
 Timestamp:
 Nov 19, 2015 7:07:38 PM (3 years ago)
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HeavyN
v10 v11 2 2 Richard Ruiz 3 3 * University of Durham (IPPP) 4 * richard.ruiz AT durham.ac.uk 4 5 * https://www.ippp.dur.ac.uk/~rruiz/ 5 * richard.ruiz AT durham.ac.uk 6 6 7 7 8 === Model Description === 8 The Type I Seesaw Model extends the Standard Model (SM) field content by introducing three righthanded neutrinos $N^{i}, ~i=1,\dots,3$, 9 10 After electroweak symmetry breaking, the effective Type I Seesaw Lagrangian with one heavy Majorana neutrino $N$ 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), 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] ] 11 10 {{{ 12 11 #!latex 13 12 $\mathcal{L}_{\rm Type~I} = \mathcal{L}_{\rm SM} + \mathcal{L}_{N} + \mathcal{L}_{N~\text{Int.}} $, 14 13 }}} 15 where { #!latex $\mathcal{L}_{\rm SM}$ } is the Standard Model Lagrangian, the heavy Majorana neutrino'skinetic and mass terms are14 where the first term is the Standard Model Lagrangian; in the mass basis, the heavy Majorana neutrinos' kinetic and mass terms are 16 15 {{{ 17 16 #!latex 18 $\mathcal{L}_{N} = \frac{1}{2}\overline{N } i\!\not\!\partial N  \frac{1}{2}M_N \overline{N}N$,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 18 }}} 20 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 22 \begin{eqnarray} 24 23 \mathcal{L}_{N~\text{Int}} = 25 &&\frac{g}{\sqrt{2}} W_{\mu}^{+}\sum_{ \ell=e}^{\tau} \overline{N}V_{\ell N}^{*}\gamma^{\mu}P_{L}\ell^{}24 &&\frac{g}{\sqrt{2}} W_{\mu}^{+}\sum_{k=1}^{3}\sum_{\ell=e}^{\tau} \overline{N_k}V_{\ell k}^{*}\gamma^{\mu}P_{L}\ell^{} 26 25 +{\rm H.c.} 27 26 \\ 28 &&\frac{g}{2\cos\theta_W}Z_{\mu}\sum_{ \ell=e}^{\tau} \overline{N}V_{\ell N}^{*}\gamma^{\mu}P_{L}\nu_\ell27 &&\frac{g}{2\cos\theta_W}Z_{\mu}\sum_{k=1}^{3}\sum_{\ell=e}^{\tau} \overline{N_k}V_{\ell k}^{*}\gamma^{\mu}P_{L}\nu_\ell 29 28 +{\rm H.c.} 30 29 \\ 31 &&\frac{g m_N}{2 M_W} h \sum_{ \ell=e}^{\tau} \overline{N}V_{\ell N}^{*}P_{L}\nu_\ell30 &&\frac{g m_N}{2 M_W} h \sum_{k=1}^{3}\sum_{\ell=e}^{\tau} \overline{N_k}V_{\ell k}^{*}P_{L}\nu_\ell 32 31 +{\rm H.c.} 33 32 \end{eqnarray} 34 33 }}} 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. 35 35 36 36 === Model Files === … … 38 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 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. 40 * [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). To download and unpack, use the commands: 41 ~/home/$ wget https://feynrules.irmp.ucl.ac.be/attachment/wiki/typeIseesaw/Seesaw_TypeI.tgz 42 43 ~/home/$ tar zxvf Seesaw_TypeI.tgz 40 * [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). 44 41 45 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). 46 43 47 48 44 * [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. 49 45 46 47 48 50 49 Notes: 51 * The model contains five free parameters in addition to SM parameters: heavy neutrino mass mN, heavy neutrino with WN, and mixing matrix elements VeN, VmuN, and VtaN that parameterize the mixing between lepton flavor eigenstates (\nu_e, \nu_mu, \nu_tau) and heavy mass eigenstate N. '''Note''': VlN are restricted to be real in the model file. 50 * To download any of the packages and unpack via the terminal, use the commands: 51 52 ~/Path $ wget http://feynrules.irmp.ucl.ac.be/rawattachment/wiki/typeIseesaw/Seesaw_TypeI.tgz 53 54 ~/Path $ tar zxvf Seesaw_TypeI.tgz 55 56 ~/Path $ wget http://feynrules.irmp.ucl.ac.be/rawattachment/wiki/typeIseesaw/Seesaw_TypeI_WithUFO.tgz 57 58 ~/Path $ tar zxvf Seesaw_TypeI_WithUFO.tgz 59 60 * In addition to the SM parameters, this model contains 15 free parameters: 61 * Three masses: mN1, mN2, mN3. Defaults are 300 GeV, 500 GeV, and 1 TeV, respectively. 62 * 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. 64 * '''Note''': VlN are restricted to be real in the model file. 65 52 66 53 67 === Validation ===