== The most general Minimal Supersymmetric Standard Model ==
=== Author ===
[http://www.cern.ch/fuks 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).
* [http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+A+NILLES+AND+D+1983+and+j+phys+rept&FORMAT=www&SEQUENCE= Phys.Rept.110 (1984) 1]: H. P. Nilles, ''Supersymmetry, Supergravity and Particle Physics''.
* [http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+A+HABER+AND+A+KANE+AND+D+1984+and+j+phys+rept&FORMAT=www&SEQUENCE= Phys.Rept.117 (1985) 75]: H. E. Haber and G. L. Kane, ''The Search for Supersymmetry: Probing Physics Beyond the Standard Model.''
* [http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=a+rosiek+and+t+Complete+Set+of+Feynman+Rules&FORMAT=WWW&SEQUENCE= Phys.Rev.D41 (1990) 3464]: J. Rosiek, ''Complete Set of Feynman Rules for the Minimal Supersymmetric Extension of the Standard Model.''
* [http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=t+susy+primer&FORMAT=WWW&SEQUENCE= hep-ph/9709356]: S. P. Martin, ''A Supersymmetry primer.''
* [http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+T+SUSY+LES+HOUCHES+and+j+JHEP&FORMAT=www&SEQUENCE= JHEP 0407 (2004) 36]: P. Skands ''et al,'', ''SUSY Les Houches accord: Interfacing SUSY spectrum calculators, decay packages, and event generators'' ''.''
* [http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+T+SUSY+LES+HOUCHES+and+j+comput+phys+commun&FORMAT=www&SEQUENCE= 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): [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/susy1.0.1.tgz susy1.0.1.tgz (05.07.09)].
* Example of parameter file: [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/FRT_paramcard.dat SPS 1a], with the corresponding [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/sps1a.rst restriction file].
* Parameter file translator, SLHA format-!FeynRules format: [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/translator1.1.8.tgz Translator1.1.8].
* Example of a Mathematica® notebook loading the model and the parameters: [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/SUSY.nb 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:''' [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/tex.tgz tex.tgz (13.06.09)].
* '''FeynArts:''' [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/SUSY.mod SUSY.mod (12.06.09)].
* '''!MadGraph''': [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/mg.tgz mg.tgz (12.06.09)], [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/sps1a.mg.tgz sps1a.mg.tgz (05.07.09)].
* '''CalcHEP''': [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/ch.tgz ch.tgz (12.06.09)], [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/sps1a.ch.tgz 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:
* [http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+A+B+FUKS+AND+T+SQUARK+and+t+flavour&FORMAT=www&SEQUENCE= 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.''
* [http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+A+B+FUKS+AND+t+gauge-mediated&FORMAT=www&SEQUENCE= 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: [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/decay.tgz 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): [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/lept.tgz lept.tgz].
* Quark initial state (twice 181 channels): [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/quark.tgz quark.tgz].
* Gauge boson initial states (twice 291 channels): [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/vv.tgz vv.tgz].
* Other (twice 15 channels): [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/other.tgz other.tgz].
* '''2 to 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: [https://cp3.irmp.ucl.ac.be/projects/feynrules/attachment/wiki/MSSM/sa.tgz sa.tgz].