The Standard Model

Authors

• Claude Duhr
  • ETH, Zurich
  • duhrc@…
• Neil Christensen
  • Michigan State University
  • neil@…
• Benjamin Fuks
  • IPHC Strasbourg / University of Strasbourg
  • benjamin.fuks@…
• Celine Degrande
  • IPPP University of Durham
  • celine.degrande@…

Model Files

• SM.fr : This is the new main file (FeynRules versions >= v1.6.2).
• SM_old.fr : This is the older implementation (FeynRules versions < v1.6.2).

Model Restrictions

• Massless.rst: Only the top, bottom and charm quarks, and the tau lepton are massive.
• DiagonalCKM.rst: The CKM maktrix is diagonal.
• Cabibbo.rst: 3rd generation mixing is off.

Instructions

The Standard Model (SM) is implemented in both Feynman and unitary gauge. A switch FeynmanGauge has been created. To switch between the two simply set FeynmanGauge = True/False inside your mathematica notebook after loading the model but before doing any calculations with it (finding vertices for example.) FeynmanGauge is set to False by default. The NLO counterterms have been computed and can be found in the SMQCD.nlo. They can be exported in the UFO format to Madgraph5/aMCatNLO.

Examples

• SM.nb: This is an example Mathematica® notebook that loads SM.fr and calculates Feynman rules.

Validation

The SM implementation was extensively tested on various 2-to-2 processes. A selection is shown in this table. (Note that the discrepancy with MG stock simply comes from the fact that MG stock has the 4 higgs vertex not implemented). The counterterms analytic expressions have been checked with the literature and the UFO compared with the built in version of SM in Madgraph5/aMCatNLO.

Interfaces

This model implementation is known to work with the following interfaces:

• FeynArts Interface
• MadGraph Interface
• CalcHEP/CompHEP
• Sherpa

UFO models

• SM_NLO.nlo UFO model with QCD corrections with the top and bottom yukawa renormalised in the on-shell scheme
• SM5F_NLO.nlo UFO model with QCD corrections in the 5 flavour scheme (massless b but non-vanishing bottom yukawa renormalised in the MSbar)
• SM4F_NLO.nlo UFO model with QCD corrections in the 4 flavour scheme (massive b but bottom yukawa renormalised in the MSbar)