TypeIISeesaw: Canonical type II Seesaw at NLO in QCD

Contact Information

Implementation author: Benjamin Fuks

• LPTHE / Sorbonne U.
• fuks@…

Internal mD0 implementation/extension author: Miha Nemevšek

• IJS, Ljubljana
• miha.nemevsek@…

In collaboration with Richard Ruiz. See ​arXiv:1912.08975 [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 renormalisation 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 normal hierarchy and inverted hierarchy UFO models, 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.

In the case of a normal neutrino mass hierarchy (Mv1 < Mv2 < Mv3), 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 > 0) and dmsq31 (Δm₃₁² > 0) 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 VEVDELTA)
• two quartic couplings collected in the block QUARTICS

In the case of an inverted neutrino mass hierarchy (Mv3 < Mv1 < Mv2), the model contains 16 free parameters (on top of the Standard Model ones):

• the mass of the third neutrino Mv3 (the other neutrino masses are internal parameters);
• the squared neutrino mass differences dmsq21 (Δm₂₁² > 0) and dmsq32 (Δm₃₂² < 0) 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 VEVDELTA)
• two quartic couplings collected in the block QUARTICS

In the case of internaly computed mD0, all of the above is the same, only lamD2 is defined externally.

More information can be found in ​arXiv:1912.08975 [hep-ph].

Model Files (and more)

• MoGRe_v1.1.m: The MoGRe plugin to FeynRules (version 1.1).

• Files common for both the normal and inverted mass hierarchy cases
  • sm_reduced.fr: Accompanying reduced SM implementation.
  • Restriction file relevant for the 4FNS (4 massless quarks) and 5FNS (5 massless quarks).
  • Restriction file relevant for a diagonal CKM matrix.

• Files specific to a normal neutrino mass hierarchy (Mv1 < Mv2 < Mv3):
  • type_ii.fr: The FeynRule Type II Seesaw implementation (version 1.1) to be used with a reduced SM implementation (only the modified SM parts are included in type_ii.fr).
  • use-MoGre.nb: Illustrative Mathematica notebook using MoGRe (for NLO UFO generation and counterterm/R₂ calculations).
  • typeII_4FNS_v1_2.ufo.tgz: Standalone UFO folder.

• Files specific to an inverted neutrino mass hierarchy (Mv3 < Mv1 < Mv2):
  • type_ii_ih.fr: The FeynRule Type II Seesaw implementation (version 1.1) to be used with a reduced SM implementation (only the modified SM parts are included in type_ii_ih.fr).
  • use-MoGre_ih.nb: Illustrative Mathematica notebook using MoGRe (for NLO UFO generation and counterterm/R₂ calculations).
  • typeII_ih_4FNS_v1_1.ufo.tgz: Standalone UFO folder.

• Files specific to internally computed mD0:
  • type_ii_v1.3.fr: The FeynRule Type II Seesaw implementation (version 1.3) with externally defined lamD2 and internally computed mD0.
  • TypeIIFR_NLO_PertSafeScheme.nb: Illustrative Mathematica notebook using MoGRe (for NLO UFO generation and counterterm/R₂ calculations).