22 | | * Phys. Rev. D 71, 051901 (2005) [http://arxiv.org/abs/hep-ph/0405209] - F. Sannino and K. Tuominen, ''Orientifold Theory Dynamics and Symmetry Breaking''. Note that the original name was ''Techniorientifold'' |
23 | | * Phys. Lett. B597:89-93,2004 [http://arxiv.org/abs/hep-ph/0406200] - Deog Ki Hong, Stephen D.H. Hsu, F. Sannino, ''Composite Higgs from higher representations'' |
24 | | * Phys. Rev. D72:055001, 2005 [http://arxiv.org/abs/hep-ph/0505059] - D.D. Dietrich, F. Sannino, K. Tuominen ''Light composite Higgs from higher representations versus electroweak precision measurements: Predictions for CERN LHC'' |
25 | | * Phys. Rev. D 75, 085018 (2007) [http://arxiv.org/abs/hep-ph/0611341] - D. D. Dietrich and F. Sannino, ''Conformal window of SU(N) gauge theories with fermions in higher dimensional representations''. Note that the original name was “Walking in the SU(N)” |
26 | | * Phys. Rev. D 76, 055005 ( 2007) [http://arxiv.org/abs/0706.1696] - R. Foadi, M.T. Frandsen, T. A. Ryttov, F. Sannino, ''Minimal Walking Technicolor: Set Up for Collider Physics'' |
27 | | * Phys. Rev. D 79, 035006 (2009) [http://arxiv.org/abs/0809.0793] – A. Belyaev, R. Foadi, M.T. Frandsen, M. Jarvinen, A. Pukhov, F. Sannino, ''Technicolor Walks at the LHC'' |
28 | | * For the construction at the Lagrangian level of the terms involving the space-time epsilon tensor – representing the correct generalization of the Wess-Zumino-Witten topological term – involving massive spin one fields see Acta Phys. Polon. B40:3533-3743, 2009 [http://arxiv.org/abs/0911.0931] – F. Sannino, ''Conformal Dynamics for TeV Physics and Cosmology'' |
| 30 | The most relevant references for this model implementation are: |
| 31 | * Phys. Rev. D 71, 051901 (2005) [http://arxiv.org/abs/hep-ph/0405209] - F. Sannino and K. Tuominen, ''Orientifold Theory Dynamics and Symmetry Breaking''. Note that the original name was ''Techniorientifold''. |
| 32 | * Phys. Rev. D 76, 055005 ( 2007) [http://arxiv.org/abs/0706.1696] - R. Foadi, M.T. Frandsen, T. A. Ryttov, F. Sannino, ''Minimal Walking Technicolor: Set Up for Collider Physics''. This article derives the |
| 33 | effective theory for MWT. |
| 34 | * Phys. Rev. D 79, 035006 (2009) [http://arxiv.org/abs/0809.0793] – A. Belyaev, R. Foadi, M.T. Frandsen, M. Jarvinen, A. Pukhov, F. Sannino, ''Technicolor Walks at the LHC''. This article presents the Lagrangian used |
| 35 | in this implementation, and analyses LHC phenomenology by using the earlier LanHEP implementation. |
| 37 | See also: |
| 38 | * Phys. Lett. B597:89-93,2004 [http://arxiv.org/abs/hep-ph/0406200] - Deog Ki Hong, Stephen D.H. Hsu, F. Sannino, ''Composite Higgs from higher representations''. |
| 39 | * Phys. Rev. D72:055001, 2005 [http://arxiv.org/abs/hep-ph/0505059] - D.D. Dietrich, F. Sannino, K. Tuominen ''Light composite Higgs from higher representations versus electroweak precision measurements: Predictions for CERN LHC''. |
| 40 | * Phys. Rev. D 75, 085018 (2007) [http://arxiv.org/abs/hep-ph/0611341] - D. D. Dietrich and F. Sannino, ''Conformal window of SU(N) gauge theories with fermions in higher dimensional representations''. Note that the original name was ''Walking in the SU(N)''. |
| 41 | * For the construction at the Lagrangian level of the terms involving the space-time epsilon tensor – representing the correct generalization of the Wess-Zumino-Witten topological term – involving massive spin one fields see Acta Phys. Polon. B40:3533-3743, 2009. |
| 42 | * [http://arxiv.org/abs/0911.0931] – F. Sannino, ''Conformal Dynamics for TeV Physics and Cosmology''. |
31 | | 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. |
32 | | |
33 | | 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). |
34 | | |
35 | | * [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''. |
36 | | * [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.'' |
37 | | * [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.'' |
38 | | * [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.'' |
39 | | * [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'' ''.'' |
40 | | * [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.'' |
45 | | '''The MSSM implementation:''' |
46 | | * Main !FeynRules files: [/attachment/wiki/MSSM/susy1.0.1.tgz susy1.0.1.tgz (05.07.09)]. |
47 | | * Example of parameter file: [/attachment/wiki/MSSM/FRT_paramcard.dat SPS 1a], with the corresponding [/attachment/wiki/MSSM/sps1a.rst restriction file]. |
48 | | * Parameter file translator, SLHA format-!FeynRules format: [/attachment/wiki/MSSM/translator1.1.8.tgz Translator1.1.8]. |
49 | | * Example of a Mathematica® notebook loading the model and the parameters: [/attachment/wiki/MSSM/SUSY.nb SUSY.nb]. |
50 | | |
51 | | '''Not yet public / planned extensions''' (can be obtained on demand): |
52 | | * Other gauges, such as Feynman gauge, |
53 | | * Most general R-parity violating Minimal Supersymmetric Standard Model, |
54 | | * Most general next-to-Minimal Supersymmetric Standard Model. |
| 48 | * AAAAAAAAA.fr is the main !FeynRules file. |
| 49 | * BBBBBBBBB.nb is a Mathematica® notebook that can be used to load the MWT FeynRules model. |
| 50 | * CCCCCCCCC.fr is an extension introducing the effective coupling HGG (Higgs + two non-abelian gauge bosons) raising at loop level. |
59 | | The MSSM is implemented in '''unitary gauge'''. |
60 | | * The switch __FeynmanGauge__ (future devlopments) must thus be set to __False__, |
61 | | * The flag __$sWScale__ can be set to the value __"weak"__ or __"susy"__, depending on the scale to which the electroweak parameters have to be evaluated, |
62 | | * The flag __$svevScale__ can be set to the value __"weak"__ or __"susy"__, depending on the scale to which the vev has to be evaluated, |
63 | | * 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), |
64 | | * A parameter file __must__ be loaded before running the model, or all the parameters would have a value of -1 (__ReadLHAFile[Input->"myfile"]__). |
| 54 | === Interfaces and related files === |
| 55 | |
| 56 | * '''CalcHEP''': [/attachment/wiki/MSSM/ch.tgz ch.tgz (12.06.09)], [/attachment/wiki/MSSM/sps1a.ch.tgz sps1a.ch.tgz (08.07.09)]. |
| 57 | * '''!MadGraph''': [/attachment/wiki/MSSM/mg.tgz mg.tgz (12.06.09)], [/attachment/wiki/MSSM/sps1a.mg.tgz sps1a.mg.tgz (05.07.09)]. |
| 58 | * the calculator needed in !MadGraph in order to generate the param_card.dat for a different set of model parameters. |
67 | | === Interfaces === |
68 | | 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. |
69 | | * '''TeX:''' [/attachment/wiki/MSSM/tex.tgz tex.tgz (13.06.09)]. |
70 | | * '''FeynArts:''' [/attachment/wiki/MSSM/SUSY.mod SUSY.mod (12.06.09)]. |
71 | | * '''!MadGraph''': [/attachment/wiki/MSSM/mg.tgz mg.tgz (12.06.09)], [/attachment/wiki/MSSM/sps1a.mg.tgz sps1a.mg.tgz (05.07.09)]. |
72 | | * '''CalcHEP''': [/attachment/wiki/MSSM/ch.tgz ch.tgz (12.06.09)], [/attachment/wiki/MSSM/sps1a.ch.tgz sps1a.ch.tgz (08.07.09)]. |
73 | | * '''SHERPA''': not available yet. |
| 61 | |
| 62 | === Instructions and details === |
| 63 | |
| 64 | The model file is loaded as usual. The attached Mathematica® notebook can be used for this task.***** |
| 65 | |
| 66 | The calculator is needed by the MadGraph implementation in order to change the parameters of the model. The directory is provided by a README file with the instructions on the usage. |
| 67 | '''...Say something about Tuomas HGG''' |
| 68 | |
| 69 | The model file implements a (linear) effective theory for the spin-zero and spin-one sectors in technicolor, with the minimal SU(2),,L,, x SU(2),,R,, -> SU(2),,V,, chiral symmetry breaking pattern. The strong technicolor interactions is linked to the electroweak sector as stipulated by the electroweak gauge transformations of the techniquarks. The modifications to the effective theory due to the electroweak interactions are mostly small. The composite scalar sector contains the composite Higgs boson and a triplet of massless technipions, which are eaten by the heavy gauge boson Z and W. The Higgs is expected to be relatively light (mass less than 500 GeV). We also have vector and axial spin-one triplets, which mix with each other and with the electroweak gauge bosons. |
| 70 | |
| 71 | In addition to the standard model fermions, we thus have the following new particles: |
| 72 | * Composite Higgs scalar H |
| 73 | * Neutral heavy vector R_1^0^ |
| 74 | * Charged heavy vector R,,1,,^+^, R,,1,,^-^ |
| 75 | * Neutral heavy vector R,,2,,^0^ |
| 76 | * Charged heavy vector R,,2,,^+^, R,,2,,^-^ |
| 77 | |
| 78 | The numbering convention for the heavy spin-one states is such that R,,1,, is always the lighter one. When the mass scale is below 1 TeV R,,1,, (R,,2,,) has larger component of the axial (vector) spin-one composite state than of the vector (axial) state. When masses are increased to about 2 TeV, the situation is reversed. |
| 79 | |
| 80 | Using the effective theory introduces several new coupling constants. These can be constrained by linking to the underlying gauge theory via the Weinberg sum rules and the definition of the electroweak S parameter. After taking into account the Weinberg sum rules, the free parameters can be expressed in terms of: |
| 81 | * MA: The spin-one mass scale. More precisely, the mass of the axial spin-one state in the limit where the electroweak interactions are turned off. Allowed range is from about 500 GeV to about 3 TeV, depending on the values of other parameters. |
| 82 | * gt: The effective strength of technicolor interactions. Parametrizes the corrections of the electroweak interactions to the technicolor sector, which are typically O(g/gt), with g being the weak coupling constant. In particular, the mixing of the composite spin-one states with the electroweak gauge bosons, and therefore also the coupling of |
| 83 | the composite spin-one states to the standard model fermions, is O(g/gt). Allowed values range from about 1 to about 10. |
| 84 | * S: The (contribution of the lowest spin-one states to the) S parameter. Recommended values come from naive estimates of the S parameter (calculation of techniquark loops), which gives S=0.15 for MWT and S=0.3 for NMWT. |
| 85 | * MH: The mass of the composite Higgs boson. |
| 86 | * rs: Parametrizes the couplings of the Higgs to the composite spin-one states. Expected to be O(1). |
| 87 | |
| 88 | The implementation supports unitary gauge. The standard model section has only Cabibbo mixing, and the electron and the muon, as well as the up, down and strange quarks, are taken to be massless. |
| 89 | |
78 | | In order to validate our implementation, we have performed the following tests. |
79 | | * '''!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: |
80 | | * [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.'' |
81 | | * [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.'' |
82 | | * B. Fuks '', private communication''. |
83 | | * '''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__. |
84 | | * '''1 to 2''' decay widths for all Standard Model particles and their superpartners (320 channels), for MG-FR and MG-ST: [/attachment/wiki/MSSM/decay.tgz decay.tgz]. |
85 | | * '''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__. |
86 | | * Leptonic initial states (twice 149 channels): [/attachment/wiki/MSSM/lept.tgz lept.tgz]. |
87 | | * Quark initial state (twice 181 channels): [/attachment/wiki/MSSM/quark.tgz quark.tgz]. |
88 | | * Gauge boson initial states (twice 291 channels): [/attachment/wiki/MSSM/vv.tgz vv.tgz]. |
89 | | * Other (twice 15 channels): [/attachment/wiki/MSSM/other.tgz other.tgz]. |
90 | | * '''2 to 3''' matrix element evaluation for given phase space points: not available yet. |
91 | | * Note: we have __some disagreements__ (red spots in the jpg-files). They are due to |
92 | | * A certain amount of __bugs in the CH-ST implementation__. |
93 | | * __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: [/attachment/wiki/MSSM/sa.tgz sa.tgz]. |
| 94 | The implementation of the following MWTC processes through the FeynRules interface was cross-checked with the already existing implementation in LanHEP (see references): |
| 95 | * pp > jj at 1400 GeV |
| 96 | * pp > mu+mu- at 1400 GeV |
| 97 | Furthermore, the matrix element generated for qq~>mu+mu- was checked by hand for a few phase space points. |
| 98 | |
| 99 | '''Toumas also cross-checked some associate production processes (i.e. W-strahlung from techni-rho)''' |