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MadGraph + MadEvent

Learn about MadGraph and MadEvent, tools for automatically calculating 1-loop cross sections and generating Feynman diagrams and amplitudes. Tim Stelzer and Fabio Maltoni discuss the features and capabilities.

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MadGraph + MadEvent

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  1. MadGraph + MadEvent + MadGraph/MadEvent Automatically Calculate 1-Loop Cross Sections ! Can ? Not Yet! Tim Stelzer Fabio Maltoni

  2. Outline • Why am I here? • MadGraph • Topology Generation • Diagram/Amplitude Generation • MadEvent • Single Diagram Enhanced MC 02

  3. Why Am I Here? • Currently MadGraph/MadEvent • Generates Born Level s • Uses Helicity Amplitudes • Generates Color-Connected Amps • Efficient Single-Diagram Integration • Soon it could • Subtraction of Reals • 1-loop diagrams • 1-loop helicity amplitudes?? 4

  4. MadGraph Matrix Element / Feynman Diagrams • Inspired by FeynArts. • Fortran computer program that: • Generates fortran helicity code (HELAS) to calculate tree level matrix elements • Includes color/symmetry factors • Creates postscript file of Feynman diagrams. 05

  5. MadGraph Examplepp -> W+ + 3 jets • Enter Process: pp > e+ ve jjj • Enter QCD Order: 3 • Enter QED Order: 2 (…… wait 2 minutes) • Generated 53 sub processes 06

  6. 1 Topologies 3 2 • Start with 3 external line topology • Add external line to 1 7

  7. 4 1 3 2 4 1 Topologies 3 2 • Start with 3 external line topology • Add external line to 1 7

  8. 4 1 1 3 4 2 2 4 3 1 Topologies 3 2 • Start with 3 external line topology • Add external line to 1 • Add external line to 2 7

  9. 4 1 1 4 3 2 2 4 3 3 1 2 4 1 Topologies 3 2 • Start with 3 external line topology • Add external line to 1 • Add external line to 2 • Add external line to 3 8

  10. 4 1 1 3 4 2 2 4 3 3 1 3 1 2 4 2 4 1 Topologies 3 2 • Start with 3 external line topology • Add external line to 1 • Add external line to 2 • Add external line to 3 • Add external line to vertex 8

  11. 3 1 2 4 Diagram/Amplitudesuu~ > uu~ • For each topology • Write all external wave functions call ixxxxx(p1, ……W1) call oxxxxx(p2,……W2) call ixxxxx(p3,…..W3) call oxxxxx(p4,…W4) • Choose vertex w/ only 1 unknown line • Determine allowed interactions and write wavefunction. call jioxxx(W1,W2, …….W5) • Continue until all lines known, write amp. call iovxxx(W3,W4,W5, …AMP(1)) 10

  12. Other Elements • Optimization • Color factors • Summing over partons • Loops? MADEVENT! 11

  13. Monte Carlo Integration • Advantages • Large numbers of dimensions • Complicated cuts • ONLY OPTION • Event generation • Limitations • Only works for function f(x) ≈ 1 12

  14. Adaptive M.C. (VEGAS) • Advantages • Grid adjusts to numerically flatten peaks • Flexible • Limitations • Adjusting grid takes time • Peaks must lie on integration variable 13

  15. Multi-Channel M.C. • Advantages • Allows for more complicated peaks • Limitations • Need to calculate all gi values for each point. (slow) • Each phase space channel must be invertible • N coupled equations for ai so only works for small number of channels. 15

  16. Single Diagram EnhancedMadEvent • Key Idea • Any single diagram is “easy” to integrate • Divide integration into pieces, based on diagrams • Get N independent integrals • Errors add in quadrature so no extra cost • No need to calculate “weight” function from other channels. • Can optimize # of points for each one independently • Parallel in nature • What about interference? • Never creates “new” peaks, so we’re OK 17

  17. MadEvent ExampleVector Bosons 18

  18. MadEvent Example Heavy Quarks and Higgs

  19. Conclusions • MadGraph Could Be Helpful for Automating NLO • Born cross section • Real Subtraction • Automated Integration and Phase Space • Loop Diagrams 20

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