Changes between Version 1 and Version 2 of SMWeinberg


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Timestamp:
Dec 15, 2020, 4:22:05 PM (4 years ago)
Author:
Richard Ruiz
Comment:

copy from HeavyN

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  • SMWeinberg

    v1 v2  
    1 Hello world!
     1= {{{SMWeinberg}}}: The Standard Model + The Dimension Five Weinberg Operator at NLO in QCD =
     2
     3=== Contact Author ===
     4Richard Ruiz
     5* Universite Catholique de Louvain
     6* richard.ruiz AT uclouvain.be
     7
     8In collaboration with
     9Benjamin Fuks, Jonas Neundorf, Krisztian Peters, and Matthias Saimpert
     10
     11
     12For additional instructions and examples on using the {{{SMWeinberg}}} UFO libraries, see B. Fuks, et al, arXiv:2012.abcde
     13
     14* If using the {{{SMWeinberg}}} UFO, please cite [ [#Fuks 1] ] along with the appropriate {{{FeynRules}}} and generator papers.
     15* For studies of lepton number violation in {{{$W^\pm W^\pm$}}} scattering, please also consider citing [ [#Fuks 2] ].
     16
     17
     18== Model Description ==
     19
     20The UFO file models the Weinberg operator for high-energy scattering and decays by exploiting the observation [ [#Fuks 1] ] that an intermediate current of massless neutrinos {{{$(\nu_\ell \nu_{\ell'}^c)$}}} can be an unphysical Majorana neutrino with mass {{{$m_{\ell \ell'}=C^{\ell\ell'}_5 v^2/\Lambda$}}}.
     21
     22
     23=== Majorana ===
     24This effective/simplified 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 5] ]
     25{{{
     26#!latex
     27\begin{equation}
     28\mathcal{L} = \mathcal{L}_{\rm SM} + \mathcal{L}_{5} + \mathcal{O}(\Lambda^{-1})
     29\end{equation}
     30}}}
     31The 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
     32{{{
     33#!latex
     34\begin{equation}
     35\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,
     36\end{equation}
     37}}}
     38
     39and its interactions with the Weak gauge and Higgs bosons are given by
     40{{{
     41#!latex
     42\begin{eqnarray}
     43\mathcal{L}_{N~\text{Int}} =
     44&-&\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^{-}
     45+{\rm H.c.}
     46\\
     47&-&\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
     48+{\rm H.c.}
     49\\
     50&-&\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
     51+{\rm H.c.}
     52\end{eqnarray}
     53}}}
     54Neutrino 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.
     55The 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.
     56
     57
     58
     59== QCD Corrections ==
     60The 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.
     61In the UFO file, five massless quarks are assumed as are zero off-diagonal CKM matrix entries.
     62For additional details, see [ [#Degrande 2] ] and references therein.
     63These additions permit tree-level calculations at LO and NLO in QCD and loop-induced calculations at LO in QCD using MadGraph_aMC@NLO.
     64
     65
     66== Model Files ==
     67'''Note:''' The only difference between NLO and LO libraries is the presence of additional (effective) O(a_s) Feynman rules. By definition the NLO libraries can compute tree-level processes at LO precision.
     68
     69 * [https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_NLO_UFO.tgz SM_HeavyN_NLO_UFO.tgz]: Standalone UFO folder. Assumes massless bottom quark and tau lepton, diagonal CKM.
     70
     71 * [https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_Gen3Mass_NLO.tgz SM_HeavyN_Gen3Mass_NLO.tgz]: Standalone UFO folder. Assumes massive bottom quark and tau lepton, diagonal CKM.
     72
     73 * [https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_CKM_AllMasses_LO.tgz SM_HeavyN_CKM_AllMasses_LO.tgz]: Standalone UFO folder. Assumes LO in QCD, with CKM elements (in radians), and all particle masses. Majorana equivalent of SM_HeavyN_Dirac_CKM_Masses_LO_UFO.
     74
     75
     76 * [https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/heavyN.fr heavyN.fr]: Main model file. Relies on sm.fr (default FR model file) being declared elsewhere.
     77
     78 * [https://feynrules.irmp.ucl.ac.be/raw-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.
     79
     80 * [https://feynrules.irmp.ucl.ac.be/raw-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).
     81
     82 * [https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_FilesWithUFO.tgz SM_HeavyN_FilesWithUFO.tgz]: Combination of SM_HeavyN_NLO_UFO.tgz and SM_HeavyN_Files.tgz.
     83
     84
     85
     86
     87
     88
     89== Download and Unpack ==
     90 * To download any of the packages and unpack via the terminal, use the commands:
     91
     92==== Majorana NLO ====
     93~/Path $ wget http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_NLO_UFO.tgz
     94
     95~/Path $ tar -zxvf SM_HeavyN_NLO_UFO.tgz
     96
     97==== Majorana LO ====
     98~/Path $ wget http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_FilesWithUFO.tgz
     99
     100~/Path $ tar -zxvf SM_HeavyN_FilesWithUFO.tgz
     101
     102==== Dirac NLO ====
     103~/Path $ wget http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_Dirac_NLO_UFO.tgz
     104
     105~/Path $ tar -zxvf SM_HeavyN_Dirac_NLO_UFO.tgz
     106
     107==== Dirac LO ====
     108~/Path $ wget http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_Dirac_LO_UFO.tgz
     109
     110~/Path $ tar -zxvf SM_HeavyN_Dirac_LO_UFO.tgz
     111
     112== Notes ==
     113 * For instructions on using the {{{SMWeinberg}}} UFO, see B. Fuks, et al, arXiv:2020.abcde
     114
     115 * This model contains seven external parameters:
     116  * One effective field theory scale: {{{Lambda}}}
     117  * Six Wilson coefficients: {{{Cee,Cem,Cet,Cmm,Cmt,Ctt}}}
     118
     119 * This model contains 15 free parameters:
     120  * One Majorana neutrino mass: {{{mN1}}} with default value 49.1 GeV
     121  * One width: {{{wN1}}} with default value zero
     122  * '''Note''': {{{Cll}}} are restricted to be real in the model file.
     123  * '''Note''': External parameters must be tuned to reproduce [ [#Fuks 1] ].
     124
     125* For Majorana file, particle identification (PID) codes for N1 follow standard HEP MCPID codes: 9900012
     126
     127
     128 
     129
     130== Validation ==
     131* The model file was validated at NLO in [ [#Fuks 1] ]; see Table 1 for validation checks
     132
     133== Studies that have used the above model files ==
     134Please email to update this space.
     135* ...
     136
     137== References ==
     138* For studies of Majorana neutrinos, please consider citing [ 5 ] for the Lagrangian and [ 1-2 ] for the Majorana FR/UFO files.
     139* For studies of heavy Dirac neutrinos, please also consider citing [ 4 ].
     140
     141
     142[=#Fuks] [1] B. Fuks, J. Neundorf, K. Peters, R. Ruiz and M. Saimpert,
     143''To Appear,'' arXiv:2012.abcde [hep-ph]
     144
     145[=#Fuks] [2] B. Fuks, J. Neundorf, K. Peters, R. Ruiz and M. Saimpert,
     146''Majorana Neutrinos in Same-Sign $W^\pm W^\pm$ Scattering at the LHC: Breaking the TeV Barrier,'' arXiv:2011.02547 [hep-ph]