== 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): [attachment:susy1.0.1.tgz susy1.0.1.tgz (05.07.09)]. 
   * Example of parameter file: [attachment:FRT_paramcard.dat SPS 1a], with the corresponding [attachment:sps1a.rst restriction file]. 
   * Parameter file translator, SLHA format-FeynRules format: [attachment:translator1.1.8.tgz Translator1.1.8]. 
   * 
   * Example of a Mathematica® notebook loading the model and the parameters: [attachment:SUSY.nb SUSY.nb]. 

'''Not yet public / planned extensions''' (can be obtained on demand):
   * Other gauges, ''e.g.'' 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 <font color="saddlebrown" class="WYSIWYG_COLOR">FeynmanGauge</font> (future devlopments) must thus be set to <font color="saddlebrown" class="WYSIWYG_COLOR">False</font>, 
   * The flag <font color="saddlebrown" class="WYSIWYG_COLOR">$sWScale</font> can be set to the value <font color="saddlebrown" class="WYSIWYG_COLOR">"weak" </font>or <font color="saddlebrown" class="WYSIWYG_COLOR">"susy"</font>, depending on the scale to which the electroweak parameters have to be evaluated, 
   * The flag <font color="saddlebrown" class="WYSIWYG_COLOR">$svevScale</font> can be set to the value <font color="saddlebrown" class="WYSIWYG_COLOR">"weak" </font>or <font color="saddlebrown" class="WYSIWYG_COLOR">"susy"</font>, depending on the scale to which the vev has to be evaluated, 
   * The flag <font color="saddlebrown" class="WYSIWYG_COLOR">$CKMDiag</font> can be set to the value <font color="saddlebrown" class="WYSIWYG_COLOR">True </font>or <font color="saddlebrown" class="WYSIWYG_COLOR">False</font>, 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 (<font color="saddlebrown" class="WYSIWYG_COLOR">ReadLHAFile[Input->"myfile"]</font>). 
=== 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:''' [attachment:tex.tgz tex.tgz (13.06.09)]. 
   * '''FeynArts:''' [attachment:SUSY.mod SUSY.mod (12.06.09)]. 
   * '''MadGraph''': [attachment:mg.tgz mg.tgz (12.06.09)], [attachment:sps1a.mg.tgz sps1a.mg.tgz (05.07.09)]. 
   * '''CalcHEP''': [attachment:ch.tgz ch.tgz (12.06.09)], [attachment: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 <font color="saddlebrown" class="WYSIWYG_COLOR">SPS 1a</font> and set the<font color="saddlebrown" class="WYSIWYG_COLOR"> widths of the particles to zero</font> *.* 
      * '''1 &rarr; 2''' decay widths for all Standard Model particles and their superpartners (320 channels), for MG-FR and MG-ST: [attachment:decay.tgz decay.tgz]. 
      * '''2 &rarr; 2''' cross sections related to the production of any pair of particles from a Standard Model initial state of <font color="saddlebrown" class="WYSIWYG_COLOR">2x600 GeV</font> and<font color="saddlebrown" class="WYSIWYG_COLOR"> 2x1000 GeV</font>, and for the four implementations CH-ST, CH-FR, MG-ST and MG-FR. <font color="saddlebrown" class="WYSIWYG_COLOR">CalcHEP is run in unitary gauge. </font> 
         * Leptonic initial states (twice 149 channels): [attachment:ee600.jpg ee600.jpg], [attachment:ee1000.jpg ee1000.jpg], [attachment:tautau600.jpg tautau600.jpg], [attachment:tautau1000.jpg tautau1000.jpg], [attachment:enu600.jpg enu600.jpg], [attachment:enu1000.jpg enu1000.jpg], [attachment:taunu600.jpg taunu600.jpg], [attachment:taunu1000.jpg taunu1000.jpg]. 
         * Quark initial state (twice 181 channels): [attachment:uu600.jpg uu600.jpg], [attachment:uu1000.jpg uu1000.jpg], [attachment:dd600.jpg dd600.jpg], [attachment:dd1000.jpg dd1000.jpg], [attachment:bb600.jpg bb600.jpg], [attachment:bb1000.jpg bb1000.jpg], [attachment:bt600.jpg bt600.jpg], [attachment:bt1000.jpg bt1000.jpg]. 
         * Gauge boson initial states (twice 291 channels): [attachment:aa600.jpg aa600.jpg], [attachment:aa1000.jpg aa1000.jpg], [attachment:ga600.jpg ga600.jpg], [attachment:ga1000.jpg ga1000.jpg], [attachment:gg600.jpg gg600.jpg], [attachment:gg1000.jpg gg1000.jpg], [attachment:gz600.jpg gz600.jpg], [attachment:gz1000.jpg gz1000.jpg], [attachment:za600.jpg za600.jpg], [attachment:za1000.jpg za1000.jpg], [attachment:zz600.jpg zz600.jpg], [attachment:zz1000.jpg zz1000.jpg], [attachment:ww600.jpg ww600.jpg], [attachment:ww1000.jpg ww1000.jpg], [attachment:wa600.jpg wa600.jpg], [attachment:wa1000.jpg wa1000.jpg], [attachment:gw600.jpg wg600.jpg], [attachment:wg1000.jpg wg1000.jpg], [attachment:wz600.jpg wz600.jpg], [attachment:wz1000.jpg wz1000.jpg]. 
         * Other (twice 15 channels): [attachment:qg600.jpg qg600.jpg], [attachment:qg1000.jpg qg1000.jpg], [attachment:other600.jpg other600.jpg], [attachment:other1000.jpg other1000.jpg]. 
      * '''2 &rarr; 3''' matrix element evaluation for given phase space points: not available yet. 
      * Note: we have '''some disagreements''' (red spots in the jpg). They are due to 
         * A certain amount of %RED%bugs in the CH-ST implementation%ENDCOLOR%. 
         * %RED%Massless propagators in t-channel diagrams%ENDCOLOR% leading to unreliable results for all implementations. We have tested here unintegrated matrix elements for 100 different phase space points: [attachment:sa600.jpg sa600.jpg], [attachment:sa1000.jpg sa1000.jpg].