The Minimal Supersymmetric Standard Model

Author

​Benjamin Fuks

• IPHC Strasbourg / University of Strasbourg
• fuks@…

Description of the model & references

One popular Beyond the Standard Model theory is the Minimal Supersymmetric Standard Model (MSSM). Its main features are to link bosons with fermions and unify internal and external symmetries. Moreover, it allows for a stabilization of the gap between the Planck and the electroweak scale and for gauge coupling unification at high energies, provides a dark matter candidate as the lightest supersymmetric particle and appears naturally in string theories. However, since supersymmetric particles have not yet been discovered, supersymmetry must be broken at low energies, which makes the superpartners massive in comparison to their Standard Model counterparts.

Our MSSM implementation in FeynRules is general in the sense that it is keeping all the flavour-violating and helicity-mixing terms in the Lagrangian and also all the possible additional CP-violating phases. In order to deal in a transparent way with all the free parameters of the model, our implementation follows the commonly used universal set of conventions provided by the Supersymmetry Les Houches Accord.

The current version of the model, compatible with FeynRules v1.6.0 and below used the ​superspace module of FeynRules.

• ​Phys.Rept.110 (1984) 1: H. P. Nilles, Supersymmetry, Supergravity and Particle Physics.
• ​Phys.Rept.117 (1985) 75: H. E. Haber and G. L. Kane, The Search for Supersymmetry: Probing Physics Beyond the Standard Model.
• ​Phys.Rev.D41 (1990) 3464: J. Rosiek, Complete Set of Feynman Rules for the Minimal Supersymmetric Extension of the Standard Model.
• ​hep-ph/9709356: S. P. Martin, A Supersymmetry primer.
• ​JHEP 0407 (2004) 36: P. Skands et al, SUSY Les Houches accord: Interfacing SUSY spectrum calculators, decay packages, and event generators .
• ​Comput.Phys.Commun.180 (2009) 8: B. C. Allanach et al, SUSY Les Houches Accord 2.

Model files

• mssm.fr: MSSM implementation using the superspace module (compatible with FeynRules 1.6.x)
• sps1a: parameter file to be read, associated to the sps1a scenario. In the case of the Whizard interface, this parameter file must be used instead.
• MSSM.nb: Example of a Mathematica® notebook loading the model and the parameters.

• susy1.0.1.tgz (05.07.09): Old MSSM implementation (compatible with FeynRules 1.4.x), with the corresponding parameter file for the sps1a benchmark point, and the old example notebook.

Specific instructions

• Both Feynman and unitarity gauges are supported.
• The flags $CKMDiag and $MNSDiag, being set to True or False, allow for CKM and PMNS matrices different from the identity or not.
• A parameter file must be loaded before running the model, or all the parameters would have a value of -1 (ReadLHAFile[Input->"myfile"]).

Optimized matrix element generator models for sps1a (removal of all zero terms in the vertices) and TeX interface output

sps1a_ch.tgz	The model files for CalcHep.
sps1a_fa.tgz	The model files for FeynArts.
sps1a_mg.tgz	The model files for MadGraph 4.
sps1a_ufo.tgz	The model files in UFO format (e.g. for MadGraph 5).
sps1a_wo.tgz	The model files for Whizard.
sps1a_tex.tgz	LaTeX output.

The Sherpa interface is not supported.

Validation

• The MSSM-superspace model has been validated against the first MSSM implementation in FeynRules. We calculate the Feynman rules associated to the difference of the old and the new Lagrangian, and obtains an empty set of rules.
• The old MSSM implementation has been validated as follow:
  • FeynArts model file generated by FeynRules: recalculation of the helicity amplitudes related to the hadroproduction of a pair of supersymmetric particles and comparison with the three references:
    • ​Nucl. Phys. B787 (2007) 1: G. Bozzi, B. Fuks, B. Herrmann and M. Klasen, Squark and gaugino hadroproduction and decays in non-minimal flavour violating supersymmetry.
    • ​Nucl. Phys. B810 (2009) 266: B. Fuks, B. Herrmann and M. Klasen, Flavour Violation in Gauge-Mediated Supersymmetry Breaking Models: Experimental Constraints and Phenomenology at the LHC.
    • B. Fuks, B. Herrmann and M. Klasen, in preperation.
  • Comparison of the built-in Monte Carlo model files with the FeynRules generated ones (CalcHep, MadGraph, !Whizard and !Sherpa) through the calculation of various quantities. For each implementation, we have fixed all the parameters to those of SPS 1a and set the widths of the particles to zero. We have calculated 2 to 2 cross sections related to the production of any pair of particles from a Standard Model initial state of 2x600 GeV, in unitarity gauge.The results are available here validation.tgz. We have some disagreements (red spots in the jpg-files). They are due to
    • A certain amount of bugs in the CH-ST implementation.
    • Incompatibilities within the Sherpa interface.
    • Massless propagators in t-channel diagrams leading to unreliable results for all implementations.