Author

Richard Ruiz

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

Model Description

After electroweak symmetry breaking, the effective Type I Seesaw Lagrangian 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 given by

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

and its interaction terms with the Weak gauge and Higgs bosons in the mass eigenbasis, i.e., after mixing with active neutrinos, 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.
• 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 unpack, use the command:

~/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

This model file was validated using FeynRules v2.0.6 and MG5_aMC@NLO (MG5) v2.1.0. The results are reported in Ref. 2.

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]