FeynRules Status and Plans
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- Bertram Stafford
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1 FeynRules Status and Plans Claude Duhr in collaboration with N. D. Christensen and B. Fuks + P. de Aquino, C. Degrande, D. Grellscheid, W. Link, F. Maltoni, + O. Mattelaer, C. Speckner, S. Schumann, M. Wiebusch MadGraph Week 2010, VUB Bruxelles, October 6th 2010
2 Outline A Roadmap for BSM physics Status: What is FeynRules..? Status of the current public version (1.4.10) Plans: New interfaces Superfields Mass diagonalisation Web validation interface
3 A Roadmap for the LHC Idea Data
4 A Roadmap for the LHC Idea Model Building Model Lagrangian Pen&Paper Constraints Publication Data
5 A Roadmap for the LHC Idea Model Building Model Lagrangian Pen&Paper Constraints Publication Phenomenology ME / MC PS / Had. Fast Sim. Publication Data
6 A Roadmap for the LHC Idea Model Building Model Lagrangian Pen&Paper Constraints Publication Phenomenology ME / MC PS / Had. Fast Sim. Publication Experiment PS / Had. Exp. SW. Full Sim. Publication Data
7 A Roadmap for the LHC Workload is tripled, due to disconnected fields of expertise. Error-prone, painful validation at each step. Proliferation of private MC s/pythia tunings: No clear documentation. Not traceable. We need more than just papers to communicate between theorists and experimentalists!
8 A Roadmap for the LHC Theory Pheno Experiment Publications
9 A Roadmap for the LHC Idea Theory Pheno Experiment Lagrangian FeynRules MC / ME PS / Had. Publications Fast Sim. Full Sim. Data
10 FeynRules in a nutshell FeynRules is a Mathematica package that allows to derive Feynman rules from a Lagrangian. Current public version: , available from The only requirements on the Lagrangian are: All indices need to be contracted (Lorentz and gauge invariance) Locality Supported field types: spin 0, 1/2, 1, 2 & ghosts
11 FeynRules in a nutshell FeynRules comes with a set of interfaces, that allow to export the Feynman rules to various matrix element Introduction generators. From FeynRules to FeynArts so far The new FeynRules interface to FeynArts Conclusion Welcome in the FeynRules era Interfaces coming with current public version CalcHep / CompHep FeynArts / FormCalc MadGraph 4 Sherpa Whizard / Omega C. Degrande The new FeynRules interface C. Degrande c
12 FeynRules in a nutshell FeynRules comes with a set of interfaces, that allow to export the Feynman rules to various matrix Introduction element From FeynRules to FeynArts so far generators. The new FeynRules interface to FeynArts Conclusion For each tool, the right input Interfaces coming with current public version: CalcHep / CompHep FeynArts / FormCalc MadGraph 4 Sherpa Whizard / Omega C. Degrande C. Degrande The new FeynRules interface
13 FeynRules in a nutshell The input requested form the user is twofold. The Model File: Definitions of particles and parameters (e.g., a quark) F[1] == {ClassName -> q, SelfConjugate -> False, Indices -> {Index[Colour]}, Mass -> {MQ, 200}, Width -> {WQ, 5} } The Lagrangian: L = 1 4 Ga µν G µν a + i q γ µ D µ q M q qq L = -1/4 FS[G,mu,nu,a] FS[G,mu,nu,a] + I qbar.ga[mu].del[q,mu] - MQ qbar.q
14 FeynRules in a nutshell Once this information has been provided, FeynRules can be used to compute the Feynman rules for the model: FeynmanRules[ L ]
15 FeynRules in a nutshell Once this information has been provided, FeynRules can be used to compute the Feynman rules for the model: FeynmanRules[ L ]
16 FeynRules in a nutshell Equivalently, we can export the Feynman rules to a matrix element generator, e.g., for MadGraph 4, WriteMGOutput[ L ] This produces a set of files that can be directly used in the matrix element generator ( plug n play ). interactions.dat q q G GG QCD G G G MGVX1 QCD G G G G MGVX2 QCD QCD particles.dat q q~ F S ZERO ZERO T d 1 G G V C ZERO ZERO O G 21 couplings.dat GG(1) = -G GG(1) = -G MGVX1 = G MGVX2 = G^2
17 FeynRules Model-file Particles, parameters,... Lagrangian FeynRules TeX Feynman Rules Translation Interfaces FeynArts MadGraph CalcHep Sherpa Whizard Golem Herwig
18 Implemented models CalcHep Herwig MadGraph Sherpa Whizard SM c c c c c cmssm c c c c c MSSM c c c NMSSM c 2HDM c UED c c ADD c Technicolor
19 Implemented models SM cmssm MSSM NMSSM 2HDM UED ADD Technicolor CalcHep Herwig MadGraph Sherpa Whizard c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c
20 Implemented models Standard Model* (CD, N. Christensen) Most general two Higgs doublet model* (CD, M. Herquet) Minimal Higgsless Model* (N. Christensen) * available at Validation of the models:
21 Implemented models: (Susy) Full MSSM* (B. Fuks) NMSSM (B. Fuks) R-symmetric MSSM (B. Fuks) RPV MSSM (B. Fuks) * available at
22 Implemented models: (ED) Universal Extra Dimensions* (P. de Aquino) Large extra dimensions* (P. de Aquino) Randall-Sundrum I (P. de Aquino) * available at
23 Implemented models: (Effective) Strongly interacting Little Higgs (C. Degrande) Composite Top model (C. Degrande) Chiral perturbation theory (C. Degrande) * available at
24 Improvements for the future FeynRules can handle mixing of particles, however the mass matrices must be diagonalized manually by the user. SUSY models have to be implemented in component fields. Many interfaces are running, but matrix element generators can only handle a very limited set of color/ Lorentz structures.
25 New Developments In spring 2010, we locked up 13 experts in a room in a nice monastry for 5 days, and let them gather new ideas... FeynRules 2010 Workshop Idea: Lock 13 experts in a (very nice) Monaster Exceptional interactions with MC s developers As a result, many new projects got started (in fact too many to review them all here...) Celine Sasha Priscila Martin Benj Christian Claude Will Olivier David Neil Thomas
26 New Developments Mass Diagonalisation Superfields FeynRules Web validation FeynArts FormCalc UFO
27 New Developments Mass Diagonalisation Superfields FeynRules Web validation FeynArts FormCalc UFO
28 :e Ø gw g 8-Hv* Yu@Index@Generation, 3D, Index@Generation, 1DDL ê H2* Sqrt@2DL, -Hv* Yu@Index@ 8 H2*, gsqrt@2dl, s Ø 2 p-hv* AlfaS Yu@Index@Generation,, DiagonalizationHSEigensystem, 3D, Index@Generation, UW, 80, m3ddl Z <Lê H2* Ø Sqrt@2DL< Diagonalization@HEigensystem, CKMD, 8MD, MS, MB<D -> 88-Hv* (N. Yd@Index@Generati Christensen, g 2 + gw -Hv* Yd@Index@Generation, 1D, Index@Generation, 2DDL ê H2* Sqrt@2DL, M. Wiebusch) gw v -Hv* Yd@Index@Generation, 1D, Index@Generation, 3DDL ê H2* Sqrt@2DL<, 8-Hv* Yd@Index@Generation, 2D, Index@Generation, - v Yu 1,1 1DDL- ê H2* v Yu 1,2 Sqrt@2DL, - v Yu 1,3 -Hv* Yd@Index@ H2* Sqrt@2DL, -Hv* Yd@Index@Generation, 2D, Index@Generation, DDL 2 ê H2* Sqrt@2DL< 8-Hv* Yd@Index@Generation, 3D, Index@Generation, - v Yu 2,1DDL - ê H2* v Yu 2,2 Sqrt@2DL, - v Yu 2,3-Hv* Yd@Index@ H2* Sqrt@2DL, -Hv* Yd@Index@Generation, 3D, Index@Generation, 3DDL, ê H2* Sqrt@2DL< Mass Matrix diagonalization 2 2 In the future, FeynRules will perform the DiagonalizationHHEigensystem, diagonalization automatically. CKMU, 8m u, m c, m t <L Ø sorted list of rules Input 1: Lagrangian qlbar[s1,l1,f1,i].ur[s1,f2,i] Yu[f1,f2] Eps[l1,l2] Phibar[l2] :e Ø gw g Input 2: Mixing relations, g s Ø 2 p AlfaS, DiagonalizationHSEigensystem, UW, 80, m Z <L Ø - v Yd 1,1 - v Yd 1,2 - v Yd 1,3 g 2 + gw uq[s, #, o] == CKMU.uqp[s, #, o] DiagonalizationIHEigensystem, CKMD, 9m d, m s, m b =M Ø Output 1: Mass matrix to be diagonalized In[22]:= DiagonalizationHHEigensystem, CKMU, 8m u, m c, m t <L 2 Ø2 Output 2: Rotation rules Out[22]= v Yd 2,2 - v Yu - v Yd 2,3 1,1 - v Yu 1, v Yd 3,2 - v Yu - v Yd 3,3 2,1 - v Yu 2, v Yu 3,1 - v Yu 3,2 - v Yu 3, v Yd 2, v Yd 3,1 2 2, Alfa - v Yu 1,3Ø e2 4 p, 2 2, - v Yu 2,3 2 2 ProjP@s1, sd - v Yu 3,1 - v Yu 3,2 - v Yu 3,3 PRIVATE`MR$RightMixing@uqp@Index@Spin, sd, Index@Generation, 1D, HP + L s1,s ICKMUH1, 1L! uq s,1,o + CKMUH2, 1L! uq s,2,o + CKMUH3, 1L! uq s,3,o M v Yd 1,1 - v Yd 1,2 In[19]:= To?? be PRIVATE`MR$RightMixing done: numerical code for the diagonalization v Yd 1,3 2 2 v Yd 2,1 v Yd 2,2 v Yd 2,3
29 New Developments Mass Diagonalisation Superfields FeynRules Web validation FeynArts FormCalc UFO
30 New Developments Superfields FeynArts FormCalc FeynRules Mass Diagonalisation UFO Web validation
31 Superpotential Superfields (B. Fuks) ü In Superfields + 1 ê 2 * M@i, jd QL@iD QL@jD + 1 ê 6 * l@i, j, kd QL@iD QL@jD QL@kD; In SuperW the future, FeynRules will allow the use of superfields. 1 In[25]:= Out[26]= SuperW := al@id QL@iD + 1 ê 2 * M@i, jd QL@iD QL@jD + 1 ê 6 * l@i, j, kd QL@iD QL i QL j M i,j + al i QL i Example: Superpotential for left-handed quarks 6 QL i QL j QL k l i,j,k QL i QL j M i,j + al i QL i ü In Components W = a i Q Li + M ij Q Li Q Lj λ ijkq Li Q Lj Q 2Components@SuperWDD; Print@WZ1@@1DDD; WZ1 = WZ1@@2DD; Lk 2Components@HC@SuperWDDD; In[30]:= WZ1 = Timing@SF2Components@SuperWDD; Print@WZ2@@1DDD; Print@WZ1@@1DDD; WZ2 = WZ2@@2DD; WZ1 = WZ1@@2DD; W WZ2 = a[i] = Timing@SF2Components@HC@SuperWDDD; QL[i] + 1/2*M[i, j] QL[i] QL[j] + 1/6*l[i, Print@WZ2@@1DDD; j, k] QL[i] QL[j] WZ2 QL[k] = WZ2@@2 WZ1@@2, 5DD FeynRules then converts the superfields into component fields: Out[32]= SF2Components[ W ] L FTerm3 i sql j sql k l i,j,k FTerm3 k sql i sql j l i,j,k FTerm3 j sql i sql k l i,j,k - 1 k l i,j,k FTerm3 k sql i sql j l i,j,k FTerm3 j sql i sql k l i,j,k FTerm3 i sql j M i,j FTerm3 2 FTerm3 j sql i M i sql 1 6 sql k l i,j,k ql sp$2,i.ql sp$2,j 1 sql j i,j,k ql sp$2,i.ql sp$2,k sql i l i,j,k ql sp$2,j.ql sp$2,k - 1,i.qL sp$2,j sql j l i,j,k ql sp$2,i.ql sp$2,k sql i l i,j,k ql sp$2,j.ql sp$2,k M i,j ql sp$2,i.ql sp$2,j - al i FTerm3 2 M i i,j ql
32 New Developments Superfields FeynArts FormCalc FeynRules Mass Diagonalisation UFO Web validation
33 New Developments FeynArts FormCalc UFO Superfields FeynRules Web validation Mass Diagonalisation
34 FeynArts interface (C. Degrande, CD) A new interface to FeynArts has been developed that allows to implement arbitrary Lorentz structures. FeynRules Model-dependent couplings (cf. couplings.f and interactions.dat).mod -file FeynArts.gen -file (Model-independent) Lorentz structures (cf. HELAS)
35 FeynArts interface (C. Degrande, CD) A new interface to FeynArts has been developed that allows to implement arbitrary Lorentz structures. FeynRules Model-dependent couplings (cf. couplings.f and interactions.dat).mod -file FeynArts.gen -file (Model-independent) Lorentz structures (cf. HELAS) This development goes along with a new version of FormCalc able to deal with multi-fermion interactions.
36 FeynArts interface (C. Degrande, CD) Example: L = g 1 Φ Q L σ µν T a t R G a µν
37 FeynArts interface (C. Degrande, CD) Example: L = g 1 Φ Q L σ µν T a t R G a µν FeynArts output: G G t t H t t G G t H G G t H T1 G1 N1 T1 C1 N2
38 FeynArts interface (C. Degrande, CD) Example: Classes coupling : L = g 1 Φ Q L σ µν T a t R G a µν C[ -F[9, {i}], F[9, {j}], V[4, {a}], V[4, {b}], S[1] ] == {{I*gc78*Conjugate[G1]*(SUNT[a, b, i, j] - SUNT[b, a, i, j])}, {I*G1*gc78*(SUNT[a, b, i, j] - SUNT[b, a, i, j])}, {(-I)*gc78*Conjugate[G1]*(SUNT[a, b, i, j] - SUNT[b, a, i, j])}, {(-I)*G1*gc78*(SUNT[a, b, i, j] - SUNT[b, a, i, j])}}
39 FeynArts interface (C. Degrande, CD) Example: Generic coupling : L = g 1 Φ Q L σ µν T a t R G a µν AnalyticalCoupling[s1 F[j1, mom1], s2 F[j2, mom2], s3 V[j3, mom3, {li3}], s4 V[j4, mom4, {li4}], s5 S[j5, mom5] ] == G[+1][s1 F[j1], s2 F[j2], s3 V[j3], s4 V[j4], s5 S[j5]]. {MetricTensor[li3,li4]NonCommutative[ChiralityProjector[-1]], MetricTensor[li3,li4]NonCommutative[ChiralityProjector[+1]], NonCommutative[DiracMatrix[li3], DiracMatrix[li4], ChiralityProjector[-1] ], NonCommutative[DiracMatrix[li3], DiracMatrix[li4], ChiralityProjector[+1] ]},
40 New Developments FeynArts FormCalc UFO Superfields FeynRules Web validation Mass Diagonalisation
41 New Developments UFO Web validation FeynRules FeynArts FormCalc Mass Diagonalisation Superfields
42 The UFO (P. de Aquino, CD, D. Grellscheid, W. Link, O. Mattelaer) UFO = Universal FeynRules Output Idea: Create Python modules that can be linked to other codes and contain all the information on a given model. The UFO is a self-contained Python code, and not tied to a specific matrix element generator. The content of the FR model files, together with the vertices, is translated into a library of Python objects, that can be linked to other codes. Golem, MadGraph 5 and Herwig++ will use the UFO.
43 The UFO & ALOHA The development of the UFO goes hand in hand with the development of ALOHA. Idea: ALOHA uses the information contained in the UFO to create the required HELAS routines on the fly! particles.py } vertices.py couplings.py MG 5 lorentz.py ALOHA UFO
44 The UFO & ALOHA Example: t t~ H reloaded! mg5>import model dim6 models.import_ufo: load particles models.import_ufo: load vertices mg5>generate g g > t t~ H INFO: Process has 16 diagrams mg5>output dim6 INFO: Generating Helas calls for process: g g > t t~ h INFO: Processing color information for process: g g > t t~ h Export UFO model to MG4 format ALOHA: aloha creates FFV8 routines ALOHA: aloha creates FFVV8 routines ALOHA: aloha creates FFVS2 routines ALOHA: aloha creates FFVVS2 routines
45 2 The UFO & ALOHA 5 2 h 5 g h g Example: t t~ H reloaded! t t 3 g t~ t 3 g t~ g 4 1 diagram diagram 2 page 1/ g g g g g t h t t~ t~ 3 h t~ 3 5 g g g g g g t t~ h h t t t~ diagram 3 diagram 1 diagram 4 diagram t~ 2 g 5 g h 5
46 New Developments UFO Web validation FeynRules FeynArts FormCalc Mass Diagonalisation Superfields
47 New Developments Web validation Mass Diagonalisation FeynRules UFO Superfields FeynArts FormCalc
48 Validation of new models FeynRules does not only provide the power to develop and validate new models, but also to validate them to an unprecendented level! A given model can be output to more than one matrix element generator, and their results can be compared Different conventions Different gauges Different ways of handling large cancellations. This procedure can easily be automatized!
49 Web validation
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54 A look into the future... The future release of FeynRules will allow even more to develop new models. study the phenomenology of new models. validate new implementations. However we still need to communicate the models to the experimentalists... Idea: Theory paper on the arxiv are not enough to communicate new ideas. so why not getting the model implementations directly instead?
55 Towards a database of models...
56 Conclusion The LHC is running, and we have to stay tuned! FeynRules is ready to cope with a large variety of models, ranging from model building, over phenomenology to experimental analysis. In particular, the chain UFO -> ALOHA -> MG5 is working flowlessly so far, making MG5 the probably most flexible BSM tool on the market.
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Neil D. Christensen CV 1
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