HeavyN: The Standard Model + Heavy Neutrinos at NLO in QCD
Contact Author
Richard Ruiz
 Universite Catholique de Louvain
 richard.ruiz AT uclouvain.be
In collaboration with: Daniel Alva and Tao Han [ 1 ]; Celine Degrande, Olivier Mattelear, and Jessica Turner [ 2 ]; and Silvia Pascoli and Cedric Weiland [ 3, 4 ].
For detailed instructions and examples on using the HeavyN UFO libraries, see C. Degrande, et al, arXiv:1602.06957 and S. Pascoli, et al, arXiv:1812.08750
 For studies of heavy Majorana neutrinos, please consider citing [ 5 ] for the Lagrangian and [ 1, 2 ] for the Majorana FR/UFO files.
 For studies of heavy Dirac neutrinos, please consider citing [ 2, 4 ].
Model Description
Majorana
This effective/simplified 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). 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 [ 5 ]
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
and its interactions with the Weak gauge and Higgs bosons are given by
Neutrino 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. The lepton number and flavorviolating interactions of the Lagrangian allow for modeling of the Type I, Inverse, and Linear seesaw mechanisms at both lepton, hadron, and leptohadron colliders.
Dirac
The Dirac variant of the HeavyN model file contains the same interaction Lagrangian as the Majorana case. The heavy Dirac neutrinos' kinetic and mass terms are [ 4 ]
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 offdiagonal CKM matrix entries. For additional details, see [ 2 ] and references therein. These additions permit treelevel calculations at LO and NLO in QCD and loopinduced calculations at LO in QCD using MadGraph_aMC@NLO.
Model Files
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 treelevel processes at LO precision.
Majorana
 SM_HeavyN_NLO_UFO.tgz: Standalone UFO folder.
 heavyN.fr: Main model file. Relies on sm.fr (default FR model file) being declared elsewhere.
 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.
 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).
 SM_HeavyN_FilesWithUFO.tgz: Combination of SM_HeavyN_NLO_UFO.tgz and SM_HeavyN_Files.tgz.
Dirac
 SM_HeavyN_Dirac_NLO_UFO.tgz: Standalone NLO UFO libraries
 SM_HeavyN_Dirac_LO_UFO.tgz: Standalone LO UFO libraries.
 SM_HeavyN_Dirac_CKM_Masses_LO_UFO.tgz: Standalone LO UFO libraries, assuming nondiagonal CKM matrix, six quark masses, and three charged lepton masses
 heavyN_Dirac.fr: Main model file. Relies on sm.fr (default FR model file) being declared elsewhere.
Download and Unpack
 To download any of the packages and unpack via the terminal, use the commands:
Majorana NLO
~/Path $ wget http://feynrules.irmp.ucl.ac.be/rawattachment/wiki/HeavyN/SM_HeavyN_NLO_UFO.tgz
~/Path $ tar zxvf SM_HeavyN_NLO_UFO.tgz
Majorana LO
~/Path $ wget http://feynrules.irmp.ucl.ac.be/rawattachment/wiki/HeavyN/SM_HeavyN_FilesWithUFO.tgz
~/Path $ tar zxvf SM_HeavyN_FilesWithUFO.tgz
Dirac NLO
~/Path $ wget http://feynrules.irmp.ucl.ac.be/rawattachment/wiki/HeavyN/SM_HeavyN_Dirac_NLO_UFO.tgz
~/Path $ tar zxvf SM_HeavyN_Dirac_NLO_UFO.tgz
Dirac LO
~/Path $ wget http://feynrules.irmp.ucl.ac.be/rawattachment/wiki/HeavyN/SM_HeavyN_Dirac_LO_UFO.tgz
~/Path $ tar zxvf SM_HeavyN_Dirac_LO_UFO.tgz
Notes
 For instructions on using the HeavyN UFO, see C. Degrande, et al, arXiv:1602.06957 and S. Pascoli, et al, arXiv:1812.08750
 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 real (no CP violation) 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 "outofthebox" checks can be made with [ 1 ] and [ 2 ].
 For Majorana file, particle identification (PID) codes for N1,...,N3, follow standard HEP MCPID codes: 9900012, 9900014, 9900016
 For Dirac file, to avoid conflict with Pythia8, where the above PIDs are reserved for Majorana fields, the nonstandard HEP MCPID codes for N1,...,N3 are:9990012, 9990014, 9990016
Validation
 The model file was validated at LO in [ 1 ]; see Tables 2 and 5 for further validation checks.
 The model file was validated at NLO in [ 2 ]; see Table 1 for further validation checks.
 For very large masses, this model has been constructed to satisfy the Goldstone Equivalence Theorem:
Studies that have used the above model files
Please email to update this space.
 Golling, et al., Physics at a 100 TeV pp collider: beyond the Standard Model phenomena, arXiv:1606.00947
 CMS, Search for heavy neutral leptons in events with three charged leptons in protonproton collisions at 13 TeV, arXiv:1802.02965 [hepex]
 CMS, Search for heavy Majorana neutrinos in samesign dilepton channels in protonproton collisions at 13 TeV, arXiv:1806.10905 [hepex]
References
 For studies of Majorana neutrinos, please consider citing [ 5 ] for the Lagrangian and [ 12 ] for the Majorana FR/UFO files.
 For studies of Dirac neutrinos, please consider citing [ 2, 4 ].
[1] D. Alva, T. Han, R. Ruiz, Heavy Majorana neutrinos from $W\gamma$ fusion at hadron colliders, JHEP 1502, 072 (2015), arXiv:1411.7305 [hepph]
[2] C. Degrande, O. Mattelear, R. Ruiz, J. Turner, FullyAutomated Precision Predictions for Heavy Neutrino Production Mechanisms at Hadron Colliders, PRD 94, 053002 (2016), arXiv:1602.06957 [hepph]
[3] S. Pascoli, R. Ruiz and C. Weiland, Safe Jet Vetoes, PLB 786, 106 (2018), arXiv:1805.09335 [hepph]
[4] S. Pascoli, R. Ruiz and C. Weiland, Heavy Neutrinos with Dynamic Jet Vetoes: Multilepton Searches at $\sqrt{s}=$14, 27, and 100 TeV, arXiv:1812.08750 [hepph]
[5] A. Atre, T. Han, S. Pascoli and B. Zhang, The Search for Heavy Majorana Neutrinos, JHEP 0905, 030 (2009), arXiv:0901.3589 [hepph]
Attachments (13)

heavyN.nb
(7.6 KB) 
added by richardphysics 4 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.

Seesaw_TypeI.tgz
(9.9 KB) 
added by richardphysics 4 years ago.
Selfcontained Type I Seesaw package. Includes: sm.fr (FR default), diagonalCKM.rst (FR default), massless.rst (FR default), heavyN.fr, heavyN.nb

Seesaw_TypeI_UFO.tgz
(14.5 KB) 
added by richardphysics 4 years ago.
Standalone UFO model file: assumes top quark and heavy neutrinos are the only massive fermions + diagonal CKM.

Seesaw_TypeI_WithUFO.tgz
(24.5 KB) 
added by richardphysics 4 years ago.
Same content as Seesaw_TypeI.tgz with Seesaw_TypeI_UFO.tgz

heavyN_NLO.nb
(17.2 KB) 
added by richardphysics 4 years ago.
Mathematica notebook to generate UFO files from heavy neutrino FeynRules model file.

SM_HeavyN_NLO_UFO.tgz
(23.0 KB) 
added by richardphysics 4 years ago.
Standalone UFO model file: assumes top quark and heavy neutrinos are the only massive fermions + diagonal CKM.

heavyN.fr
(8.9 KB) 
added by richardphysics 4 years ago.
Heavy neutrino FeynRules model file in Feynman gauge.

SM_HeavyN_Files.tgz
(12.4 KB) 
added by richardphysics 4 years ago.
Selfcontained Heavy N at NLO package. Includes: sm.fr (FR default), diagonalCKM.rst (FR default), massless.rst (FR default), heavyN.fr, heavyN_NLO.nb

SM_HeavyN_FilesWithUFO.tgz
(35.4 KB) 
added by richardphysics 4 years ago.
Combination of SM_HeavyN_Files.tgz and SM_HeavyN_NLO_UFO.tgz

SM_HeavyN_Dirac_LO_UFO.tgz
(17.5 KB) 
added by richardphysics 17 months ago.
UFO for LO SM_HeavyN_Dirac

SM_HeavyN_Dirac_NLO_UFO.tgz
(24.5 KB) 
added by richardphysics 17 months ago.
UFO for NLO SM_HeavyN_Dirac

heavyN_Dirac.fr
(9.0 KB) 
added by richardphysics 17 months ago.
Model flie for HeavyN_Dirac

SM_HeavyN_Dirac_CKM_Masses_LO_UFO.tgz
(21.8 KB) 
added by richardphysics 17 months ago.
UFO for HeavyN Dirac model, at LO in QCD, with CKM element, and all particle masses
Download all attachments as: .zip