The most general Minimal Supersymmetric Standard Model

Author

​Benjamin Fuks

• IPHC Strasbourg / University of Strasbourg
• fuks @ cern.ch

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 the most general one in a 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. This yields thus 105 new free parameters. In order to deal in a transparent way with all of those, our implementation will follow the commonly used universal set of conventions provided by the Supersymmetry Les Houches Accord, except for some minor points (see instructions below).

• ​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 & extensions

The MSSM implementation:

• Main FeynRules files (as a tar-ball): ​susy1.0.1.tgz (05.07.09).
• Example of parameter file: ​SPS 1a, with the corresponding ​restriction file.
• Parameter file translator, SLHA format-FeynRules format: ​Translator1.1.8.
• Example of a Mathematica® notebook loading the model and the parameters: ​SUSY.nb.

Not yet public / planned extensions (can be obtained on demand):

• Other gauges, such as Feynman gauge,
• Most general R-parity violating Minimal Supersymmetric Standard Model,
• Most general next-to-Minimal Supersymmetric Standard Model.

Instructions

The MSSM is implemented in unitary gauge.

• The switch FeynmanGauge (future devlopments) must thus be set to False,
• The flag $sWScale can be set to the value "weak" or "susy", depending on the scale to which the electroweak parameters have to be evaluated,
• The flag $svevScale can be set to the value "weak" or "susy", depending on the scale to which the vev has to be evaluated,
• The flag $CKMDiag can be set to the value True or False, allowing for a CKM matrix different from the identity or not (this can also be done through a possible restriction file),
• A parameter file must be loaded before running the model, or all the parameters would have a value of -1 (ReadLHAFile[Input->"myfile"]).

Interfaces

Here are the output files obtained for SPS1a after using the various translation interfaces and the example notebook given above.The prefix sps1a in the filename means the use of a sps1a restriction file to remove all the zero elements of the mixing matrices from the vertices.

• TeX: ​tex.tgz (13.06.09).
• FeynArts: ​SUSY.mod (12.06.09).
• MadGraph: ​mg.tgz (12.06.09), ​sps1a.mg.tgz (05.07.09).
• CalcHEP: ​ch.tgz (12.06.09), ​sps1a.ch.tgz (08.07.09).
• SHERPA: not available yet.

Validation

In order to validate our implementation, we have performed the following tests.

• 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 , private communication.
• Comparison of the built-in CalcHEP (CH-ST) and MadGraph (MG-ST) model files with the FeynRules generated ones, MG-FR and CH-FR, 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.
  • 1 to 2 decay widths for all Standard Model particles and their superpartners (320 channels), for MG-FR and MG-ST: ​decay.tgz.
  • 2 to 2 cross sections related to the production of any pair of particles from a Standard Model initial state of 2x600 GeV and 2x1000 GeV, and for the four implementations CH-ST, CH-FR, MG-ST and MG-FR. CalcHEP is run in unitary gauge.
    • Leptonic initial states (twice 149 channels): ​lept.tgz.
    • Quark initial state (twice 181 channels): ​quark.tgz.
    • Gauge boson initial states (twice 291 channels): ​vv.tgz.
    • Other (twice 15 channels): ​other.tgz.
  • 2 → 3 matrix element evaluation for given phase space points: not available yet.
  • Note: we have some disagreements (red spots in the jpg-files). They are due to
    • A certain amount of bugs in the CH-ST implementation.
    • Massless propagators in t-channel diagrams leading to unreliable results for all implementations. We have tested here unintegrated matrix elements for 100 different phase space points: ​sa.tgz.