Changes between Version 2 and Version 3 of EffLRSM


Ignore:
Timestamp:
Oct 25, 2016, 4:08:26 PM (8 years ago)
Author:
Richard Ruiz
Comment:

Dev Update

Legend:

Unmodified
Added
Removed
Modified

  • EffLRSM

    v2 v3  
    1 Hello World
     1Hello World - In Dev -
     2
     3= SM + ... at NLO in QCD =
     4
     5=== Contact Author ===
     6Richard Ruiz
     7* University of Durham (IPPP)
     8* richard.ruiz AT durham.ac.uk
     9
     10In collaboration with
     11Daniel Alva and Tao Han [ [#Alva 1] ], and Celine Degrande, Olivier Mattelear, and Jessica Turner [ [#Degrande 2] ].
     12
     13
     14== Model Description ==
     15This effective 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). Each RH neutrino possesses one RH Majorana mass. After electroweak symmetry breaking, the Lagrangian with three heavy Majorana neutrinos ''N''i (for i=1,2,3) is given by [ [#Atre 3] ]
     16{{{
     17#!latex
     18\begin{equation}
     19\mathcal{L} = \mathcal{L}_{\rm SM} + \mathcal{L}_{N} + \mathcal{L}_{N~\text{Int.}}
     20\end{equation}
     21}}}
     22The 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
     23{{{
     24#!latex
     25\begin{equation}
     26\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,
     27\end{equation}
     28}}}
     29
     30and its interactions with the Weak gauge and Higgs bosons are given by
     31{{{
     32#!latex
     33\begin{eqnarray}
     34\mathcal{L}_{N~\text{Int}} =
     35&-&\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^{-}
     36+{\rm H.c.}
     37\\
     38&-&\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
     39+{\rm H.c.}
     40\\
     41&-&\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
     42+{\rm H.c.}
     43\end{eqnarray}
     44}}}
     45Neutrino masses (mNk) and mixing parameters (Vlk) between heavy mass eigenstate and (active) flavor eigenstates are taken to be independent, phenomenological parameters. This allows for maximum flexibility and model independence when calculating rates. Therefore, some care is required by the user.
     46The lepton number- and flavor-violating interactions of the Lagrangian allow for modeling of the Type I, Inverse, and Linear seesaw mechanisms at both lepton, hadron, and lepto-hadron colliders.
     47
     48== QCD Corrections ==
     49The above Lagrangian with Goldstone boson couplings and in the Feynman Gauge was implemented into FeynRules  2.3.10. QCD renormalization and R2 rational counter terms were determined using NLOCT 1.02 and FeynArts 3.8. Feynman rules were collected into a single UFO, available below.
     50In the UFO file, five massless quarks are assumed as are zero off-diagonal CKM matrix entries.
     51For additional details, see [ [#Degrande 2] ] and references therein.
     52These additions permit tree-level calculations at LO and NLO in QCD and loop-induced calculations at LO in QCD using MadGraph_aMC@NLO.
     53
     54
     55== Model Files ==
     56 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/HeavyN/SM_HeavyN_NLO_UFO.tgz SM_HeavyN_NLO_UFO.tgz]: Standalone UFO folder.
     57
     58 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/HeavyN/heavyN.fr heavyN.fr]: Main model file. Relies on sm.fr (default FR model file) being declared elsewhere.
     59
     60 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/HeavyN/heavyN_NLO.nb heavyN_NLO.nb]: Mathematica notebook file that generates UFO file from FeynRules model files. Allows user to also run quick sanity checks (optional) on model.
     61
     62 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/HeavyN/SM_HeavyN_Files.tgz SM_HeavyN_Files.tgz]: Standalone package containing heavyN.fr, heavyN_NLO.nb, massless.rst (default FR file), diagonalCKM.rst (default FR file), and sm.fr (default FR file).
     63
     64 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/HeavyN/SM_HeavyN_FilesWithUFO.tgz SM_HeavyN_FilesWithUFO.tgz]: Combination of SM_HeavyN_NLO_UFO.tgz and SM_HeavyN_Files.tgz.
     65
     66
     67
     68== Notes ==
     69 * To download any of the packages and unpack via the terminal, use the commands:
     70
     71~/Path $ wget http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_NLO_UFO.tgz
     72
     73~/Path $ tar -zxvf SM_HeavyN_NLO_UFO.tgz
     74
     75~/Path $ wget http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_FilesWithUFO.tgz
     76
     77~/Path $ tar -zxvf SM_HeavyN_FilesWithUFO.tgz
     78
     79 * This model contains 15 free parameters:
     80  * Three masses: mN1, mN2, mN3. Defaults are 300 GeV, 500 GeV, and 1 TeV, respectively.
     81  * Three widths: WN1, WN2, WN3. Defaults are 0.303 GeV, 1.50 GeV, and 12.3 GeV, respectively.
     82  * Nine real (no CP violation) 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.
     83  * '''Note''': VlN are restricted to be real in the model file.
     84  * '''Note''': Default parameters are set so "out-of-the-box" checks can be made with [ [#Alva 1] ] and [ [#Degrande 2] ].
     85
     86
     87== Validation ==
     88* The model file was validated at LO in  [ [#Alva 1] ]; see Tables 2 and 5 for further validation checks.
     89* The model file was validated at NLO in [ [#Degrande 2] ]; see Table 1 for further validation checks.
     90* For very large masses, this model has been constructed to satisfy the Goldstone Equivalence Theorem:
     91{{{
     92#!latex
     93\begin{eqnarray}
     94\text{BR}(N_i \rightarrow W^+ \ell^-) &=& \text{BR}(N_i \rightarrow W^- \ell^+) =
     95\\
     96\text{BR}(N_i \rightarrow Z \nu_\ell + Z \overline{\nu_\ell} ) &=&
     97\text{BR}(N_i \rightarrow h \nu_\ell + h \overline{\nu_\ell} ) = 25\%.
     98\end{eqnarray}
     99}}}
     100
     101
     102=== List of analyses that have used the model file ===
     103* Please email to update this space.
     104
     105
     106== References ==
     107* Please cite [ 3 ] for the model and [ 1-2 ] for the FR/UFO files.
     108
     109[=#Alva] [1] D. Alva, T. Han, R. Ruiz, ''Heavy Majorana neutrinos from {{{$W\gamma$}}} ''fusion at hadron colliders,'' JHEP '''1502''', 072 (2015), arXiv:1411.7305 [hep-ph]
     110
     111[=#Degrande] [2] C. Degrande, O. Mattelear, R. Ruiz, J. Turner, ''Fully-Automated Precision Predictions for Heavy Neutrino Production Mechanisms at Hadron Colliders,'' arXiv:1602.06957 [hep-ph]
     112
     113[=#Atre] [3] A. Atre, T. Han, S. Pascoli and B. Zhang, ''The Search for Heavy Majorana Neutrinos,'' JHEP '''0905''', 030 (2009),  arXiv:0901.3589 [hep-ph]