Author

Richard Ruiz

• University of Durham (IPPP)
• ​https://www.ippp.dur.ac.uk/~rruiz/
• richard.ruiz AT durham.ac.uk

Model Description

The Type I Seesaw Model extends the Standard Model (SM) field content by introducing three right-handed neutrinos $N^{{i}, ~i=1,\dots,3$,}

After electroweak symmetry breaking, the effective Type I Seesaw Lagrangian with one heavy Majorana neutrino $N$ is given by [ 1 ]

$\mathcal{L}_{\rm Type~I} = \mathcal{L}_{\rm SM} + \mathcal{L}_{N} + \mathcal{L}_{N~\text{Int.}} $,

where { #!latex $\mathcal{L}_{\rm SM}$ } is the Standard Model Lagrangian, the heavy Majorana neutrino's kinetic and mass terms are

$\mathcal{L}_{N} = \frac{1}{2}\overline{N} i\!\not\!\partial N - \frac{1}{2}M_N \overline{N}N$,

and its interactions with the Weak gauge and Higgs bosons in the mass eigenbasis, i.e., after mixing with active neutrinos, are given by

\begin{eqnarray}
\mathcal{L}_{N~\text{Int}} = 
&-&\frac{g}{\sqrt{2}} W_{\mu}^{+}\sum_{\ell=e}^{\tau} \overline{N}V_{\ell N}^{*}\gamma^{\mu}P_{L}\ell^{-}
+{\rm H.c.}
\\
&-&\frac{g}{2\cos\theta_W}Z_{\mu}\sum_{\ell=e}^{\tau} \overline{N}V_{\ell N}^{*}\gamma^{\mu}P_{L}\nu_\ell
+{\rm H.c.}
\\
&-&\frac{g m_N}{2 M_W}         h \sum_{\ell=e}^{\tau} \overline{N}V_{\ell N}^{*}P_{L}\nu_\ell
+{\rm H.c.}
\end{eqnarray}

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. 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). To download and unpack, use the commands:

~/home/$ wget ​https://feynrules.irmp.ucl.ac.be/attachment/wiki/typeIseesaw/Seesaw_TypeI.tgz

~/home/$ tar -zxvf Seesaw_TypeI.tgz

• ​Seesaw_TypeI_withUFO.tgz: Same as Seesaw_TypeI.tgz but with UFO folder generated using restrictions massless.rst (only massive fermions are top quark and Majorana neutrino) and diagonalCKM.rst (CKM matrix set to unity).

• ​Seesaw_TypeI_UFO.tgz: Standalone UFO folder as packaged in Seesaw_TypeI_withUFO.tgz.

Notes:

• The model contains five free parameters in addition to SM parameters: heavy neutrino mass mN, heavy neutrino with WN, and mixing matrix elements VeN, VmuN, and VtaN that parameterize the mixing between lepton flavor eigenstates (\nu_e, \nu_mu, \nu_tau) and heavy mass eigenstate N. Note: VlN are restricted to be real in the model file.

Validation

• The model file was implemented in Ref. [ 2 ] using FeynRules v2.0.6 and MG5_aMC@NLO (MG5) v2.1.0. See Tables 2 and 5 for further validation checks; note that mixing matrices have been factored out/normalized in tabulated results.

List of analyses that have used the model file

• Please email me to update this space.

References

[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] 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]