FeynRules New models phenomenology made easy

Transcription

1 FeynRules New models phenomenology made easy Claude Duhr March 11, 2008 MC4BSM

2 Why yet another tool..? FeynRules Example: - How to add a new sector to the SM Conclusion

3 Why yet another tool..? In general, a new model is given by a Lagrangian, containing all the particles and their mutual interactions. At some point, one would like to compare the model with experiment. Needs in general some hard calculations: - cross-sections - decay rates - radiative corrections

4 Why yet another tool..? Fortunately, several tools are available to do the calculations - MC generators (MadGraph, CalcHep, CompHEP, AMEGIC++) - FeynArts,... New model (Lagrangian, new particles,...) Existing tools (Programming language, files containing the new particles and interactions,...)

5 Mathematica based package that calculates Feynman rules from a Lagrangian. No special requirements on the form of the Lagrangian. FeynRules Particle types supported so far: scalars, fermions (Dirac and Majorana), vectors, spin-2, ghosts.

6 FeynRules The FR model file contains all the information about the model: - Particles & fields - Parameters (masses, coupling constants,...) - mixing matrices - etc. The syntax of the FR model-files is an extension of syntax used in FeynArts. Feynman rules are calculated by Mathematica using the information from the model-file and the Lagrangian. The vertices can be exported into a TeX-file.

7 FeynRules The informations given in the model-file, together with the vertices obtained by FR, is generic enough to allow for an interface to other existing tools. FR creates all files needed to run the new model just by knowing the FR model-file and the Lagrangian. Interfaces available so far - FeynArts - MadGraph/MadEvent (CD, M. Herquet) - CalcHep/CompHep (CD, N. Christensen) - Sherpa (CD, S. Schumann)

8 FeynRules Model-file Particles, parameters,... Lagrangian FeynRules TeX Feynman Rules Interfaces FeynArts MadGraph CalcHep Sherpa...

9 Validation Standard model: 29 key-processes tested against the stock version - FeynArts - MadGraph - CalcHep/CompHep: both in unitary and Feynman gauge - Sherpa: Validation procedure in progress 3-site model: 222 key-processes tested in CalcHep/CompHep

10 Validation Standard model: 29 key-processes tested against the stock version...

11 Validation 3-site model: 222 key-processes tested in CalcHep/CompHep...

12 Example: The Hill model SM SCALAR AND EXTRA SINGLET(S) J. J. VAN DER BIJ Institut für Physik, Albert-Ludwigs Universität Freiburg, H. Herderstr. 3, Freiburg i.b., Deutschland [arxiv: ] L = 1 2 (D µφ) (D µ Φ) λ 0 8 (Φ Φ f 2 0 ) ( µh) 2 λ 1 8 (2f 1H Φ Φ) 2

13 Example: The Hill model SM SCALAR AND EXTRA SINGLET(S) J. J. VAN DER BIJ Institut für Physik, Albert-Ludwigs Universität Freiburg, H. Herderstr. 3, Freiburg i.b., Deutschland To include this new sector in FeynArts and Monte Carlo s, you just need to add a few lines to the SM model file. L = 1 2 (D µφ) (D µ Φ) λ 0 8 (Φ Φ f 2 0 ) ( µh) 2 λ 1 8 (2f 1H Φ Φ) 2 [arxiv: ]

14 The Hill model L = 1 2 (D µφ) (D µ Φ) λ 0 8 (Φ Φ f 2 0 ) ( µh) 2 λ 1 8 (2f 1H Φ Φ) 2 SM Higgs Hill field f 0 = 246GeV f 1 = 600GeV λ 0 = 0, 1 λ 1 = 0, 25

15 The Hill model L = 1 2 (D µφ) (D µ Φ) λ 0 8 (Φ Φ f 2 0 ) ( µh) 2 λ 1 8 (2f 1H Φ Φ) 2 SM Higgs Hill field If the SM Higgs acquires a vev, then the Hill ( field acquires ) a vev too. Φ = ( 0 f0 ) H = f 2 0 2f 1

16 The Hill model L = 1 2 (D µφ) (D µ Φ) λ 0 ( ) 8 (Φ Φ f 2 0 ) ( µh) 2 λ 1 8 (2f 1H Φ Φ) 2 SM Higgs Hill field The mass matrix of the two scalars is ( (λ0 + λ 1 )f 2 0 λ 1 f 0 f 1 ) M H = λ 1 f 0 f 1 λ 1 f 2 1 Just use Mathematica to diagonalize the matrix...

17 ( ) Mass eigenvalues: ( Mass eigenstates: Φ = The Hill ( model ( h 1 = h cos α + H sin α h 2 = h sin α + H cos α ( ) ( ) 0 0 f 0 + h = m 1 = 78, 5GeV m 2 = 326GeV = cos + ( α = 0, 60321

18 The Hill model Consequences: - All SM Higgs (Yukawa, gauge) couplings get doubled. t th t th 1, t th 2 sin co y t y t sin α y t cos α, All SM Higgs couplings get modified (mixing angle). - New self-couplings ) among h1 and h2. h 1 h 1 h 2 : cos αλ 1 (f 1 cos 2 α + 3f 0 sin α cos α 2f 1 sin 2 α)

19 The Hill model Consequences: - All SM Higgs (Yukawa, gauge) couplings get doubled. t th t th 1, t th 2 sin co y t y t sin α y t cos α, All SM Higgs couplings get modified (mixing angle). Lots of things need to be changed in the SM implementation to get the Hill model! Let FeynRules do the job! - New self-couplings ) among h1 and h2. h 1 h 1 h 2 : cos αλ 1 (f 1 cos 2 α + 3f 0 sin α cos α 2f 1 sin 2 α)

20 Model building with FeynRules Step 1: Add all the parameters of the new sector to the model file: L = 1 2 (D µφ) (D µ Φ) λ 0 8 (Φ Φ f 2 0 ) ( µh) 2 Cosine of the mixing angle λ 1 8 (2f 1H Φ Φ) 2

21 Model building with FeynRules Step 1: Add all the parameters of the new sector to the model file: L = 1 2 (D µφ) (D µ Φ) λ 0 8 (Φ Φ f0 2 ) Additional information needed 2 e.g. for the MC 1 2 ( integration. µh) 2 Cosine of the mixing angle λ 1 8 (2f 1H Φ Φ) 2

22 Model building with FeynRules Step II: Add all the particles of the new sector to the model file: Mass eigenstate L = 1 2 (D µφ) (D µ Φ) λ 0 8 (Φ Φ f 2 0 ) ( µh) 2 λ 1 8 (2f 1H Φ Φ) 2 Mixing

23 Model building with FeynRules Step III: The lagrangian describing the new sector (Unitary gauge) L = 1 2 (D µφ) (D µ Φ) λ 0 8 (Φ Φ f 2 0 ) ( µh) 2 λ 1 8 (2f 1H Φ Φ) 2

24 Phenomenology with FeynRules Now we are ready to do some phenomenology... ( Let s consider the following process in the framework of Hill model e + e Zb b µ + µ b b At a CoM energy of 500GeV. Let s first have a look at the one-loop corrections. Use FeynArts

25 Phenomenology with FeynRules The results obtained by FeynRules can be easily exported to FeynArts: This produces a FeynArts model-file which can be read by FeynArts.

26 Phenomenology with FeynRules

27 Phenomenology with FeynRules The results obtained by FeynRules can be easily exported tomc generators: This produces all the files needed to implement the Hill model into an MC. Let s have a look at our process!

28 Phenomenology with FeynRules The results obtained by FeynRules can be easily exported tomc generators: This produces all the files needed to implement the Hill model into an MC. Let s have a look at our process!

29 Phenomenology with FeynRules The results obtained by FeynRules can be easily exported tomc generators: This produces all the files needed to implement the Hill model into an MC. Let s have a look at our process!

30 Phenomenology with FeynRules e m m e m m Z Z Z Z e h1 e h2 b b b b graph 6

31 Phenomenology with MadGraph h1 Z h2

32 Phenomenology with CalcHep 10 4 h1 e e Zbb Nevents 4GeV bin 100fb Z h M bb GeV

33 Conclusion FeynRules is a Mathematica -based package to extract Feynman rules from a lagrangian. The output of FeynRules is completely generic and can be easily interfaced to other available codes. Available interfaces: - FeynArts - MadGraph/MadEvent - CalcHep/CompHep - Sherpa -... The code can be downloaded from

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35 Example of how to get vertices The Strongly-Interacting Light Higgs G. F. Giudice a, C. Grojean a,b, A. Pomarol c, R. Rattazzi ( ) ( a,d ( ) ( ) [hep-ph/ ] ( ) ( ) c ( H 2f 2 µ H H ) ( µ H H ) + c ( ) ( ) T ( ) H D µ H H D 2f 2 ( ) µ H ( ) ) + ic HW g 16π 2 f 2 (Dµ H) σ i (D ν H)W i µν + ic HBg 16π 2 f 2 (Dµ H) (D ν H)B µν

36 Getting Feynman rules c ( H 2f 2 µ H H ) ( µ H H ) ( ( ) ( ) ) ( ) ( ( ) ( + c ( ) ( ) T H ) ) D µ H H D 2f 2 µ H ) + ic ( ) HW g 16π 2 f 2 (Dµ H) σ i (D ν H)Wµν i + ic HBg 16π 2 f 2 (Dµ H) (D ν H)B µν

37 Getting Feynman rules

38 Getting Feynman rules

39 Getting Feynman rules Kaluza-Klein States from Large Extra Dimensions Tao Han (a), Joseph D. Lykken (b) and Ren-Jie Zhang (a) (a) Department of Physics, University of Wisconsin, Madison, WI (b) Theory Group, Fermi National Accelerator Laboratory, Batavia, IL [hep-ph/ ] Particle content: - Spin 2 graviton, KK-scalars - Fermions - Scalars - Gauge bosons

40 Getting Feynman rules Lagrangian coupling the fermions to the graviton and the KKscalar: κ 1 L n F (κ) = 1 2 [( h n η µν h µν, n )ψiγ µ D ν ψ m ψ h n ψψ ψiγµ ( µ h n ν h nµν )ψ ] + 3ω 2 φ n ψiγ µ D µ ψ 2ωm ψ φ n ψψ + 3ω 4 µ φ n ψiγ µ ψ. (44) Very complicated structure as far as Feynman rules are concerned, but we are only a few steps away from the Feynman rules...

41 Getting Feynman rules Step 1: Add all the parameters in the lagrangian to the model file: κ 1 L n F (κ) = 1 2 [ ( h n η µν h µν, n )ψiγ µ D ν ψ [ m ψ h n ψψ + 1 ] 2 ψiγµ ( µ h n ν h n µν )ψ + 3ω 2 φ n ψiγ µ D µ ψ 2ωm φ n ψ ψψ + 3ω 4 µ φ n ψiγ µ ψ

42 Getting Feynman rules Step II: Add all the particles in the lagrangian to the model file: κ 1 L n F (κ) = 1 2 [ ( h n η µν h µν, n )ψiγ µ D ν ψ [ m ψ h n ψψ + 1 ] 2 ψiγµ ( µ h n ν h n µν )ψ + 3ω 2 φ n ψiγ µ D µ ψ 2ωm φ n ψ ψψ + 3ω 4 µ φ n ψiγ µ ψ

43 Getting Feynman rules Step III: The lagrangian κ 1 L n F (κ) = 1 2 [ ( h n η µν h µν, n )ψiγ µ D ν ψ [ m ψ h n ψψ + 1 ] 2 ψiγµ ( µ h n ν h n µν )ψ + 3ω 2 φ n ψiγ µ D µ ψ 2ωm φ n ψ ψψ + 3ω 4 µ φ n ψiγ µ ψ

44 Getting Feynman rules Step IV: The FeynmanRules

45 Getting Feynman rules Step IV: The FeynmanRules

46 Getting Feynman rules Step IV: The FeynmanRules

47 Getting Feynman rules Step IV: The FeynmanRules

48 Getting Feynman rules Step III: The lagrangian κ 1 L n F (κ) = 1 2 [ ( h n η µν h µν, n )ψiγ µ D ν ψ [ m ψ h n ψψ + 1 ] 2 ψiγµ ( µ h n ν h n µν )ψ + 3ω 2 φ n ψiγ µ D µ ψ 2ωm φ n ψ ψψ + 3ω 4 µ φ n ψiγ µ ψ

49 Getting Feynman rules Step IV: The FeynmanRules

50 Getting Feynman rules Step IV: The FeynmanRules

51 Getting Feynman rules Step IV: The FeynmanRules

52 Getting Feynman rules Step IV: The FeynmanRules