TypeIISeesaw: Canonical type II Seesaw at NLO in QCD

Contact Information

Implementation author: Benjamin Fuks

• LPTHE / Sorbonne U.
• fuks@…

In collaboration with Miha Nemevšek and Richard Ruiz. See ​arXiv:1911.NNNNN [hep-ph].

Model Description and FeynRules Implementation

We extend the Standard Model by adding a scalar field lying in the adjoint representation of the weak groupe Δ with an hypercharge equals to 1. After electroweak symmetry breaking, this gives rise to one extra CP-even scalar Higgs Δ⁰, one charged scalar Δ^± and one doubly-charged scalar Δ^±± that are mostly of a triplet nature. The corresponding Lagrangian reads

\begin{equation}
  \mathcal{L} = \mathcal{L}_{\rm SM} +  {\rm Tr}\big[D_\mu \hat\Delta^\dag D^\mu\hat\Delta\big] - V_\Delta + \mathcal{L}_{{\rm Y}_\Delta}
\end{equation}

where the extra terms respectively represents the gauge-invariant kinetic terms for the triplet, the extra pieces to the scalar potential and the Yukawa interactions giving rise to neutrino masses. The above Lagrangian was implemented in the Feynman Gauge into FeynRules 2.3.35. QCD renormalization and R₂ rational counterterms were determined using MoGRe v1.1, NLOCT v1.02 and FeynArts 3.9. Feynman rules were collected into a single UFO, available below. In the UFO model, four massless quarks are assumed as are zero off-diagonal CKM matrix entries. These additions permit tree-level calculations at LO and NLO in QCD and loop-induced calculations at LO in QCD using MadGraph_aMC@NLO.

The model contains 16 free parameters (on top of the Standard Model ones):

• the mass of the first neutrino Mv1 (the other neutrino masses are internal parameters);
• the squared neutrino mass differences dmsq21 (Δm₂₁²) and dmsq31 (Δm₃₁²) collected in the LH block MNU;
• the oscillation parameters th12 (θ₁₂), th13 (θ₁₃), th23 (θ₂₃), delCP (φ_CP), phiM1 (φ₁), phiM2 (φ₂) collected in the LH block PMNS;
• the masses of the Higgs (PDG 125), Δ⁰ (PDG 44), Δ^± (PDG 38) and Δ^±± (PDG 44) fields (in the LH block MASS);
• the triplet vev v_Δ (block VEVD)
• two quartic couplings collected in the block QUARTICS

More information can be found in ​arXiv:1911.NNNNN [hep-ph].

Model Files (and more)

• type_ii.fr: The FeynRule Type II Seesaw implementation (version 1.1) to be used with a reduced SM implementation (only modified SM parts are included in type_ii.fr).
• sm_reduced.fr: Accompanying reduced SM implementation.
• MoGRe_v1.1.m: The MoGRe plugin to FeynRules (version 1.1).
• use-MoGre.nb: Illustrative Mathematica notebook using MoGRe (for NLO UFO generation and counterterm/R₂ calculations).
• typeII_4FNS_v1_1.ufo.tgz: Standalone UFO folder.