SM + Heavy N at NLO in QCD
Contact Author
Richard Ruiz
 University of Durham (IPPP)
 richard.ruiz AT durham.ac.uk
In collaboration with Daniel Alva and Tao Han [ 1 ], and Celine Degrande, Olivier Mattelear, and Jessica Turner [ 2 ].
Model Description
This effective 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 [ 3 ]
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.
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
 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.
Notes
 To download any of the packages and unpack via the terminal, use the commands:
~/Path $ wget http://feynrules.irmp.ucl.ac.be/rawattachment/wiki/HeavyN/SM_HeavyN_NLO_UFO.tgz
~/Path $ tar zxvf SM_HeavyN_NLO_UFO.tgz
~/Path $ wget http://feynrules.irmp.ucl.ac.be/rawattachment/wiki/HeavyN/SM_HeavyN_FilesWithUFO.tgz
~/Path $ tar zxvf SM_HeavyN_FilesWithUFO.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 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 ].
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:
List of studies that have used the model file
 Please email to update this space.
 Golling, et al., Physics at a 100 TeV pp collider: beyond the Standard Model phenomena, arXiv:1606.00947
References
 Please cite [ 3 ] for the model and [ 12 ] for the FR/UFO files.
[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] A. Atre, T. Han, S. Pascoli and B. Zhang, The Search for Heavy Majorana Neutrinos, JHEP 0905, 030 (2009), arXiv:0901.3589 [hepph]
Attachments (9)

heavyN.nb
(7.6 KB) 
added by richardphysics 3 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 3 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 3 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 3 years ago.
Same content as Seesaw_TypeI.tgz with Seesaw_TypeI_UFO.tgz

heavyN_NLO.nb
(17.2 KB) 
added by richardphysics 2 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 2 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 2 years ago.
Heavy neutrino FeynRules model file in Feynman gauge.

SM_HeavyN_Files.tgz
(12.4 KB) 
added by richardphysics 2 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 2 years ago.
Combination of SM_HeavyN_Files.tgz and SM_HeavyN_NLO_UFO.tgz
Download all attachments as: .zip