DMSimpt: A general framework for t-channel dark matter models at NLO in QCD

Contact Information

Benjamin Fuks

• LPTHE / Sorbonne U.
• fuks @ lpthe.jussieu.fr

Chiara Arina

• UC Louvain
• chiara.arina @ uclouvain.be

Luca Mantani

• UC Louvain
• luca.mantani @ uclouvain.be

See ​arXiv:2001.05024 [hep-ph].

Model Description and FeynRules Implementation

We extend the Standard Model by a dark matter candidate X and a coloured mediator Y. The model includes several spin possibilities for X and Y, the dark matter being either of a Majorana nature or not and of spin equal to 0, 1/2 or 1. The mediator is accordingly of spin 1/2 (scalar or bosonic dark matter) or 0 (fermionic dark matter). The model Lagrangian is given by

\begin{equation*}
  \mathcal{L} = \mathcal{L}_{\rm SM} + \mathcal{L}_{\rm kin} + \mathcal{L}_F(\chi) + \mathcal{L}_F(\tilde\chi) + \mathcal{L}_S(S) + \mathcal{L}_S(\tilde S)
       + \mathcal{L}_V(V)    + \mathcal{L}_V(\tilde V) \ .
\end{equation*}

The first term consists in the Standard Model Lagrangian, the second one includes gauge-invariant kinetic and mass terms for all new fields and the last ones describe the interactions of the dark matter state with the mediator and the Standard Model. The latter focus respectively on Dirac fermion, Majorana fermion, complex scalar, real scalar, complex vector and real vector dark matter, and are given by

\begin{eqnarray*}
   \mathcal{L}_F(X)& = & \Big[
           {\bf \lambda_{Q}} \bar X Q_L \varphi^\dag_{Q}
     \!+\! {\bf \lambda_{u}} \bar X u_R \varphi^\dag_{u}
     \!+\! {\bf \lambda_{d}} \bar X d_R \varphi^\dag_{d}
     \!+\! {\rm h.c.} \Big] \ ,\\
   \mathcal{L}_S(X)& = & \Big[
          {\bf \hat\lambda_{Q}} \bar\psi_{Q} Q_L X
    \!+\! {\bf \hat\lambda_{u}} \bar\psi_{u} u_R X
    \!+\! {\bf \hat\lambda_{d}} \bar\psi_{d} d_R X
    \!+\! {\rm h.c.} \Big] \ , \\
   \mathcal{L}_V(X)& = & \Big[
          {\bf \hat\lambda_{Q}} \bar\psi_{Q} \gamma^\mu X_\mu Q_L
    \!+\! {\bf \hat\lambda_{u}} \bar\psi_{u} \gamma^\mu X_\mu u_R
    \!+\! {\bf \hat\lambda_{d}} \bar\psi_{d} \gamma^\mu X_\mu d_R
    \!+\! {\rm h.c.} \Big] \ ,
\end{eqnarray*}

where φ and ψ consists in coloured scalar and fermionic mediators.

The above Lagrangian was implemented in the Feynman gauge into FeynRules 2.3.35. QCD renormalisation and R₂ rational counterterms were determined using NLOCT v1.02 and FeynArts 3.9. Feynman rules were collected into a single UFO, in which 5 flavours of massless quarks are considered, which enables tree-level calculations at LO and NLO QCD and loop-induced calculations at LO QCD using MadGraph_aMC@NLO.

The above new physics couplings can be controlled on run-time through the Les Houches blocks DMS3Q, DMS3U, DMS3D (scalar mediator interactions with the Q_L, u_R and d_R quarks), as well as DMF3Q, DMF3U, DMF3D (scalar mediator interactions with the Q_L, u_R and d_R quarks). The mass of the new particles can be modified through the usual mass blocks. The PDG codes of the new particles are:

• Dark matter: 51 (real scalar), 52 (Majorana fermion), 53 (real vector), 56 (complex scalar), 57 (Dirac fermion) and 58 (complex vector).
• Scalar mediators: 1000001 (φ_dL), 1000002 (φ_uL), 1000003 (φ_sL), 1000004 (φ_cL), 1000005 (φ_bL), 1000006 (φ_tL), 2000001 (φ_dR), 2000002 (φ_uR), 2000003 (φ_sR), 2000004 (φ_cR), 2000005 (φ_bR) and 2000006 (φ_tR).
• Fermionic mediators: 5910001 (ψ_dL), 5910002 (ψ_uL), 5910003 (ψ_sL), 5910004 (ψ_cL), 5910005 (ψ_bL), 5910006 (ψ_tL), 5920001 (ψ_dR), 5920002 (ψ_uR), 5920003 (ψ_sR), 5920004 (ψ_cR), 5920005 (ψ_bR) and 5920006 (ψ_tR).

More information can be found in ​arXiv:2001.05024 [hep-ph].

Model Files (and more)

• FeynRules model files:
  • sm.fr: Accompanying SM implementation.
  • dmsimpt_v1.2.fr: Main DMSimpt FeynRules model.
  • Restriction file relevant for the 5FNS (5 massless quarks).
  • Restriction file relevant for a diagonal CKM matrix.
  • use-DMsimpt.nb: Illustrative Mathematica notebook using the DMSimpt FeynRules model.

• UFO models
  • dmsimpt_v1.3.2.ufo.tgz: Standalone NLO UFO folder in the 5FNS, including all 18 restrictions of ​arXiv:2001.05024 [hep-ph] (v1.3.1 and 1.3.2 changes: some update in the restriction cards).
  • dmsimpt_v1.2_s3dur.ufo.tar.gz: Standalone UFO LO folder, in the S3D_uR restriction, with 6 massive quarks.
  • dmsimpt_v1.2_s3mur.ufo.tar.gz: Standalone UFO LO folder, in the S3M_uR restriction, with 6 massive quarks.
  • UFO_all_mq.zip: Standalone UFO LO folder with 6 massive quarks in the general model case.

• CalcHep models
  • dmsimpt_v1.2_s3dur.ch.tar.gz: Standalone CalcHep model files with massive quarks, in the S3D_uR restriction.
  • dmsimpt_v1.2_s3mur.ch.tar.gz: Standalone CalcHep model files with massive quarks, in the S3M_uR restriction.

Leptophilic Model Description and FeynRules Implementation

We also provide a very generic t-channel model in which the dark matter candidate couples to the SM leptons only. The dark matter can be again self-conjugate or not, and can be spin 0, spin 1/2 and spin 1. The mediator particles are non-coulored and couple the dark matter either to the right-handed charged lepton or the left-handed SU(2) leptonic doublet. Neutrinos are described as in the SM and do not have a right-handed field. The naming of the dark matter candidates and mediators is as in the coloured case, described above.

For further details and if you use this model please cite ​arXiv:2102.XXXXX [hep-ph].

Model Files for Leptophilic dark matter

• FeynRules model file:
  • dmsimpt_leptons.fr: Main DMSimpt leptohpilic FeynRules model ( to be used with the same SM fr file as above).
  • Restriction file relevant for a diagonal CKM matrix.

• UFO and CH model for MadDM and micrOMEGAs (LO, all quark massive)
  • DMSimpt_leptons_UFO.zip: Standalone UFO model files for MadDM at LO.
  • DMSimpt_leptons_CH.zip: Standalone CalcHep model files.