= {{{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.NNNNN [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 
{{{ 
#!latex 
\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 (and focus respectively on Dirac fermion, Majorana fermion, complex scalar, real scalar, complex vector and real vector dark matter. Those Lagrangians are given by
{{{ 
#!latex 
\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 R,,2,, rational counterterms were determined using NLOCT v1.02 and !FeynArts 3.9. Feynman rules were collected into a [/raw-attachment/wiki/TypeIISeesaw/dmsimpt_v1_2.ufo.tar.gz 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.NNNNN [hep-ph].


=== Model Files (and more) ===

 * !FeynRules model files:
   * [/raw-attachment/wiki/DMsimpt/sm.fr sm.fr]: Accompanying SM implementation.
   * [/raw-attachment/wiki/DMsimpt/dmsimpt_v1.2.fr dmsimpt_v1.2.fr]: Main DMSimpt !FeynRules model.
   * [/raw-attachment/wiki/DMsimpt/Massless_5f.rst Restriction file] relevant for the 5FNS (5 massless quarks).
   * [/raw-attachment/wiki/DMsimpt/DiagonalCKM.rst Restriction file] relevant for a diagonal CKM matrix.
   * [/raw-attachment/wiki/DMsimpt/use-DMsimpt.nb use-DMsimpt.nb]: Illustrative Mathematica notebook using the DMSimpt !FeynRules model.

 * UFO models
   * [/raw-attachment/wiki/DMsimpt/dmsimpt_v1_2.ufo.tar.gz dmsimpt_v1_2.ufo.tar.gz]: Standalone NLO UFO folder in the 5FNS.
   * [/raw-attachment/wiki/DMsimpt/dmsimpt_massive.ufo.tar.gz dmsimpt_v1_2.ufo.tar.gz]: Standalone LO UFO folder with 6 massive quarks.

 * !CalcHep models
   * [/raw-attachment/wiki/DMsimpt/dmsimpt_v1_2_s3d.ch.tar.gz dmsimpt_v1_2.ch.tar.gz]: Standalone !CalcHep model files with massive quarks, in the S3D restriction.
   * [/raw-attachment/wiki/DMsimpt/dmsimpt_v1_2_s3m.ch.tar.gz dmsimpt_v1_2.ch.tar.gz]: Standalone !CalcHep model files with massive quarks, in the S3M restriction.