Version 19 (modified by 9 years ago) ( diff ) | ,
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SM + Heavy N at NLO in QCD
Implementation Author
Richard Ruiz
- University of Durham (IPPP)
- richard.ruiz AT durham.ac.uk
In collaboration with Daniel Alva and Tao Han, and Celine Degrande, Olivier Mattelear, and Jessica Turner.
Model Description
This 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 Ni (for i=1,2,3) is given by [ 1 ]
\begin{equation} \mathcal{L}_{\rm Type~I} = \mathcal{L}_{\rm SM} + \mathcal{L}_{N} + \mathcal{L}_{N~\text{Int.}} \end{equation}
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
\begin{equation} \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, \end{equation}
and its interactions with the Weak gauge and Higgs bosons are given by
\begin{eqnarray} \mathcal{L}_{N~\text{Int}} = &-&\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^{-} +{\rm H.c.} \\ &-&\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 +{\rm H.c.} \\ &-&\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 +{\rm H.c.} \end{eqnarray}
Neutrino masses (mNk) and mixing parameters (Vlk) between heavy mass eigenstate and (active) flavor eigenstates are taken to be independent, phenomenological parameters. Mixing parameters (VeNk, VmuNk, VtaNk) are taken to be real (no CP Violation). This allows for maximum flexibility and model independence when calculating rates. Therefore, some care by the user is required. The 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.
QCD Corrections
The 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. In the UFO file, five massless quarks are assumed as are zero off-diagonal CKM matrix entries. For additional details, see [ 2 ] and references within. These additions permit tree-level calculations at LO and NLO in QCD and loop-induced calculations at LO in QCD using MadGraph_aMC@NLO.
Model Files
- heavyN.fr: Main model file. Relies on sm.fr (default FR model file) being declared elsewhere.
- heavyN.nb: Mathematica notebook file that loads FR and model files. Allows user to run quick sanity checks (optional) and outputs UFO file.
- 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).
- 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).
- Seesaw_TypeI_UFO.tgz: Standalone UFO folder as packaged in Seesaw_TypeI_withUFO.tgz.
Notes
- To download any of the packages and unpack via the terminal, use the commands:
~/Path $ wget http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/typeIseesaw/Seesaw_TypeI.tgz
~/Path $ tar -zxvf Seesaw_TypeI.tgz
~/Path $ wget http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/typeIseesaw/Seesaw_TypeI_WithUFO.tgz
~/Path $ tar -zxvf Seesaw_TypeI_WithUFO.tgz
- This model contains 15 free parameters:
- Three masses: mN1, mN2, mN3. Defaults are 300 GeV, 500 GeV, and 1 TeV, respectively.
- Three widths: WN1, WN2, WN3. Defaults are 0.303 GeV, 1.50 GeV, and 12.3 GeV, respectively.
- Nine mixing parameters: Vlk for l = e, mu, tau and k = 1,2,3. Default values are Vlk = Identity(3x3), i.e., Ve1 = Vmu2 = Vta3 = 1 and all others zero.
- Note: VlN are restricted to be real in the model file.
- Note: Default parameters are set so "out-of-the-box" comparisons can be performed with [ 2 ] and 3 ].
Validation
- The model file was validated at LO in [ 2 ]; see Tables 2 and 5 for further validation checks.
- The model file was validated at NLO in [ 3 ]; see Table 1 for further validation checks.
- For very large masses, this model has been constructed to satisfy the Goldstone Equivalence Theorem:
\begin{eqnarray} \text{BR}(N_i \rightarrow W^+ \ell^-) &=& \text{BR}(N_i \rightarrow W^- \ell^+) = \\ \text{BR}(N_i \rightarrow Z \nu_\ell + Z \overline{\nu_\ell} ) &=& \text{BR}(N_i \rightarrow h \nu_\ell + h \overline{\nu_\ell} ) = 25\%. \end{eqnarray}
List of analyses that have used the model file
- Please email to update this space.
References
- Please cite [ 1 ] for model and [ 2-3 ] for the FR/UFO model files/validation.
[1] A. Atre, T. Han, S. Pascoli and B. Zhang, The Search for Heavy Majorana Neutrinos, JHEP 0905, 030 (2009) arXiv:0901.3589 [hep-ph]
[2] C. Degrande, O. Mattelear, R. Ruiz, J. Turner, arXiv:1602.00000 [hep-ph]
[3] D. Alva, T. Han, R. Ruiz, Heavy Majorana neutrinos from #!latex $W\gamma$
fusion at hadron colliders, JHEP 1502, 072 (2015), arXiv:1411.7305 [hep-ph]
Attachments (18)
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heavyN.nb
(7.6 KB
) - added by 9 years ago.
Type I Seesaw Model FR mathematica notebook that loads model file, performs basic sanity checks, and outputs to desired format, e.g., UFO.
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Seesaw_TypeI.tgz
(9.9 KB
) - added by 9 years ago.
Self-contained Type I Seesaw package. Includes: sm.fr (FR default), diagonalCKM.rst (FR default), massless.rst (FR default), heavyN.fr, heavyN.nb
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Seesaw_TypeI_UFO.tgz
(14.5 KB
) - added by 9 years ago.
Stand-alone UFO model file: assumes top quark and heavy neutrinos are the only massive fermions + diagonal CKM.
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Seesaw_TypeI_WithUFO.tgz
(24.5 KB
) - added by 9 years ago.
Same content as Seesaw_TypeI.tgz with Seesaw_TypeI_UFO.tgz
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heavyN_NLO.nb
(17.2 KB
) - added by 9 years ago.
Mathematica notebook to generate UFO files from heavy neutrino FeynRules model file.
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SM_HeavyN_NLO_UFO.tgz
(23.0 KB
) - added by 8 years ago.
Stand-alone UFO model file: assumes top quark and heavy neutrinos are the only massive fermions + diagonal CKM.
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heavyN.fr
(8.9 KB
) - added by 8 years ago.
Heavy neutrino FeynRules model file in Feynman gauge.
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SM_HeavyN_Files.tgz
(12.4 KB
) - added by 8 years ago.
Self-contained Heavy N at NLO package. Includes: sm.fr (FR default), diagonalCKM.rst (FR default), massless.rst (FR default), heavyN.fr, heavyN_NLO.nb
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SM_HeavyN_FilesWithUFO.tgz
(35.4 KB
) - added by 8 years ago.
Combination of SM_HeavyN_Files.tgz and SM_HeavyN_NLO_UFO.tgz
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SM_HeavyN_Dirac_LO_UFO.tgz
(17.5 KB
) - added by 6 years ago.
UFO for LO SM_HeavyN_Dirac
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SM_HeavyN_Dirac_NLO_UFO.tgz
(24.5 KB
) - added by 6 years ago.
UFO for NLO SM_HeavyN_Dirac
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heavyN_Dirac.fr
(9.0 KB
) - added by 6 years ago.
Model flie for HeavyN_Dirac
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SM_HeavyN_Dirac_CKM_Masses_LO_UFO.tgz
(21.8 KB
) - added by 6 years ago.
UFO for HeavyN Dirac model, at LO in QCD, with CKM element, and all particle masses
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SM_HeavyN_CKM_AllMasses_LO.tgz
(23.0 KB
) - added by 4 years ago.
UFO for HeavyN Majorana model, at LO in QCD, with CKM element, and all particle masses (updated 2020_0813: remove double counting of FeynRules))
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heavyN_vSMEFTdim6.fr
(15.6 KB
) - added by 3 years ago.
.fr file for SM_HeavyN_vSMEFTdim6 (updated to include arXiv info)
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SM_HeavyN_vSMEFTdim6_NLO.tgz
(24.7 KB
) - added by 3 years ago.
Stand-alone NLO UFO for SM_HeavyN_vSMEFTdim6 (updated to include arXiv info)
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SM_HeavyN_vSMEFTdim6_XLO.tgz
(19.2 KB
) - added by 3 years ago.
Stand-alone LO UFO for SM_HeavyN_vSMEFTdim6 (updated to include arXiv info)
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SM_HeavyN_Gen3Mass_NLO.tgz
(24.9 KB
) - added by 3 years ago.
Stand-alone NLO UFO model file: assumes Gen III (t,b,tau) and heavy neutrinos are massive + diagonal CKM + tau width
Download all attachments as: .zip