Changes between Version 10 and Version 11 of HeavyN


Ignore:
Timestamp:
Nov 19, 2015, 7:07:38 PM (9 years ago)
Author:
Richard Ruiz
Comment:

Updates Model File text and notes. Readying for publication.

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  • HeavyN

    v10 v11  
    22Richard Ruiz
    33* University of Durham (IPPP)
     4* richard.ruiz AT durham.ac.uk
    45* https://www.ippp.dur.ac.uk/~rruiz/
    5 * richard.ruiz AT durham.ac.uk
     6
    67
    78=== Model Description ===
    8 The Type I Seesaw Model extends the Standard Model (SM) field content by introducing three right-handed 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] ]
     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), 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] ]
    1110{{{
    1211#!latex
    1312$\mathcal{L}_{\rm Type~I} = \mathcal{L}_{\rm SM} + \mathcal{L}_{N} + \mathcal{L}_{N~\text{Int.}} $,
    1413}}}
    15 where { #!latex $\mathcal{L}_{\rm SM}$ } is the Standard Model Lagrangian, the heavy Majorana neutrino's kinetic and mass terms are
     14where the first term is the Standard Model Lagrangian; in the mass basis, the heavy Majorana neutrinos' kinetic and mass terms are
    1615{{{
    1716#!latex
    18 $\mathcal{L}_{N} = \frac{1}{2}\overline{N} i\!\not\!\partial N - \frac{1}{2}M_N \overline{N}N$,
     17$\mathcal{L}_{N} = \frac{1}{2}\overline{N_k} i\!\not\!\partial N_k - \frac{1}{2}m_{N_k} \overline{N_k}N_k, \quad k=1,\dots,3$;
    1918}}}
    2019and its interactions with the Weak gauge and Higgs bosons in the mass eigenbasis, i.e., after mixing with active neutrinos, are given by
    … …  
    2322\begin{eqnarray}
    2423\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^{-}
    2625+{\rm H.c.}
    2726\\
    28 &-&\frac{g}{2\cos\theta_W}Z_{\mu}\sum_{\ell=e}^{\tau} \overline{N}V_{\ell N}^{*}\gamma^{\mu}P_{L}\nu_\ell
     27&-&\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
    2928+{\rm H.c.}
    3029\\
    31 &-&\frac{g m_N}{2 M_W}         h \sum_{\ell=e}^{\tau} \overline{N}V_{\ell N}^{*}P_{L}\nu_\ell
     30&-&\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
    3231+{\rm H.c.}
    3332\end{eqnarray}
    3433}}}
     34The 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.
    3535
    3636=== Model Files ===
    … …  
    3838 * [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.
    3939 * [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).
    4441
    4542 * [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).
    4643
    47 
    4844 * [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.
    4945
     46
     47
     48
    5049Notes:
    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/raw-attachment/wiki/typeIseesaw/Seesaw_TypeI.tgz
     53
     54~/Path $ tar -zxvf Seesaw_TypeI.tgz
     55
     56~/Path $ wget http://feynrules.irmp.ucl.ac.be/raw-attachment/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
    5266
    5367=== Validation ===