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feynrules tutorial · 2010. 2. 21. · 2 ∂ µ s ∂µ s − 1 2! m2 s + λ sh v 2 " s2 + λ s s 4...

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FeynRules Tutorial Claude Duhr Yeti’10, January 13 2010 IPPP/Durham Sonntag, 21. Februar 2010

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  • FeynRules TutorialClaude Duhr

    Yeti’10, January 13 2010IPPP/Durham

    Sonntag, 21. Februar 2010

  • • Many tools exist for HEP computations that allow to perform computations in an easy an automated way:

    Tools for HEP tools

    ➡ Symbolic tools: FeynArts, FormCalc, ... ➡ Matrix element generators: CalcHep/CompHep, MadGraph,

    Sherpa, Whizard/Omega...➡ MC event generators: Herwig, Pythia, Sherpa,...➡ Spectrum generators: SoftSusy,...➡ DM relic density: MicrOmegas,...➡ FastSim: Delphes, PGS, ...➡ ...

    Sonntag, 21. Februar 2010

  • • Many of these tools are able to handle a generic (renormalizable) QFT model.

    • Most of the codes only have only a limited set of models implemented (SM, MSSM, ...).

    • For more general models, the information on the model (particles, vertices, ...) must come “from the outside”, i.e., must be provided by the user.

    Tools for HEP tools

    Sonntag, 21. Februar 2010

  • • Implementing a model from scratch into a HEP tool can be a tedious and error prone task:

    Tools for HEP tools

    ➡ Vertices must be entered one at the time.➡ Each code uses its own conventions (factors of ±1, ±i, ...).➡ Each code uses a different programming language.➡ Painful validation for each model.

    Sonntag, 21. Februar 2010

  • FeynRules• Mathematica package that allows to derive Feynman rules

    directly form a Lagrangian.

    • No special requirements on the form of the Lagrangian (apart from Lorentz and gauge invariance).

    • Supported field types:➡ Scalars➡ Fermions (Dirac & Majorana)➡ Vectors➡ Spin 2 ➡ Ghosts

    Sonntag, 21. Februar 2010

  • Lagrangian

    FeynArts

    Translation Interfaces

    TeX Feynman Rules

    Model-fileParticles, parameters, ...

    FeynRules

    MadGraph CalcHep Sherpa

    FeynRules

    Whizard

    Sonntag, 21. Februar 2010

  • A simple model of Dark Matter• During the next four hours, we will implement a very

    simple model of Dark Matter into FeynRules, and export the model to two different HEP tools to study its phenomenology:

    ➡ MicrOmegas:Compute the DM annihilation rate and the DM relic density

    ➡ MadGraph:Generate the matrix element and compute the cross section for DM production at the LHC.

    Sonntag, 21. Februar 2010

  • A simple model of Dark Matter• The model we will consider consists in the addition of a

    singlet scalar S, protected by a Z2 symmetry (i.e., S is Z2-odd, whereas all SM particles are Z2-even).

    FeynRules Tutorial

    Claude DuhrIPPP/Durham

    January 12, 2010

    1 Introduction

    The main topic of this tutorial is FeynRules, a Mathematica package that allows to derive Feynmanrules from a Lagrangian and to implement them into various HEP tools in an automated way. Inparticular, during this tutorial we will

    • implement a simple model of Dark Matter into FeynRules and derive its Feynman rules.

    • export the model to MicrOmegas to compute the DM relic density.

    • export the model to MadGraph to study its LHC phenomenology.

    2 The Model

    The model we will consider consists in the Standard Model (SM) augmented by a single singlet scalarfield S. For S to be a viable Dark Matter (DM) candidate it must be stable, or in other words theremust be a symmetry (“R-parity”) that prevents S from decaying. We choose here the minimal scenarioand we postulate a Z2 symmetry such that S is Z2-odd whereas all SM particles are Z2-even. theLagrangian for this model then takes the very simple form,

    L = LSM + LDM , (1)

    where LSMdenotes the SM Lagrangian, and the Dark Matter sector is,

    LDM =1

    2∂µS ∂

    µS −1

    2

    (

    m2S + λSH v2)

    S2 + λSS4 + λSHS

    2 Φ†Φ , (2)

    where v denotes the vev of the SM Higgs field

    Φ =

    (

    φ±,H + iφ0 + v√

    2

    )T

    (3)

    and mS denotes the mass of the scalar S. mS , λS and λSH are free parameters of the model. Here wechoose for the sake of the example mS = 70 GeV and λS = λSH = 0.02.

    1

    FeynRules Tutorial

    Claude DuhrIPPP/Durham

    January 12, 2010

    1 Introduction

    The main topic of this tutorial is FeynRules, a Mathematica package that allows to derive Feynmanrules from a Lagrangian and to implement them into various HEP tools in an automated way. Inparticular, during this tutorial we will

    • implement a simple model of Dark Matter into FeynRules and derive its Feynman rules.

    • export the model to MicrOmegas to compute the DM relic density.

    • export the model to MadGraph to study its LHC phenomenology.

    2 The Model

    The model we will consider consists in the Standard Model (SM) augmented by a single singlet scalarfield S. For S to be a viable Dark Matter (DM) candidate it must be stable, or in other words theremust be a symmetry (“R-parity”) that prevents S from decaying. We choose here the minimal scenarioand we postulate a Z2 symmetry such that S is Z2-odd whereas all SM particles are Z2-even. theLagrangian for this model then takes the very simple form,

    L = LSM + LDM , (1)

    where LSMdenotes the SM Lagrangian, and the Dark Matter sector is,

    LDM =1

    2∂µS ∂

    µS −1

    2

    (

    m2S + λSH v2)

    S2 + λSS4 + λSHS

    2 Φ†Φ , (2)

    where v denotes the vev of the SM Higgs field

    Φ =

    (

    φ±,H + iφ0 + v√

    2

    )T

    (3)

    and mS denotes the mass of the scalar S. mS , λS and λSH are free parameters of the model. Here wechoose for the sake of the example mS = 70 GeV and λS = λSH = 0.02.

    1

    • Implementing this model into FeynRules means➡ Defining the new particle.➡ Defining the new parameters.➡ Entering the Lagrangian into Mathematica.

    Sonntag, 21. Februar 2010

  • A simple model of Dark Matter• All instructions of how to

    • Solutions to all the problems are provided:

    ➡ Implement the model into FeynRules➡ Export it from FeynRules to MicrOmegas and MadGraph➡ Run MicrOmegas➡ Run MadGraphare given in the handout.

    ➡ for FeynRules in ~/FeynRules1.4.3/Yeti10_Bkup.➡ for MicOmegas in ~/micromegas_2.2.CPC.i/feynrules_bkup.➡ for MadGraph in ~/MG_ME_V4.4.32/HiggsStrahlung.

    • Feel free to ask as many questions as you like... and have fun!

    Sonntag, 21. Februar 2010

  • A simple model of Dark Matter• Solutions to all the problems are provided:

    ➡ for FeynRules in ~/FeynRules1.4.3/Yeti10_Bkup.➡ for MicOmegas in ~/micromegas_2.2.CPC.i/feynrules_bkup.➡ for MadGraph in ~/MG_ME_V4.4.32/HiggsStrahlung.

    • Feel free to ask as many questions as you like... and have fun!

    • Web pages:➡ for FeynRules: http://feynrules.phys.ucl.ac.be/➡ for MicOmegas: http://lappweb.in2p3.fr/lapth/micromegas/➡ for MadGraph: http://madgraph.phys.ucl.ac.be/

    Sonntag, 21. Februar 2010

    http://lappweb.in2p3.fr/lapth/micromegas/http://lappweb.in2p3.fr/lapth/micromegas/http://madgraph.phys.ucl.ac.behttp://madgraph.phys.ucl.ac.be

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