This document discusses a method for generating multi-jet events using MadGraph. It notes that multi-jet signatures are important for new physics models but current matrix element generators cannot simulate more than 5 jets. The method uses off-shell recursive relations to speed up amplitude evaluations and reorganizes color summation using a 1/Nc expansion. It generates leading color approximation events and includes higher order corrections to event weights. Results are shown for gluonic processes demonstrating the ability to generate leading order multi-jet events.

1. Generating multi-jet events
with MadGraph
Yoshitaro Takaesu (KEK)
July 24, 2016 1

2. Overview: Simulation for LHC
July 24, 2016 2
Parton Shower Generator
Matrix Element Generator
Event Generator
DetectorSimulator

3. Importance of multi-jet at the LHC
Multi-jet signature
appears in many
New Physics models.
Event Generator
should be able to
generate > 4 jets.
July 24, 2016 3

4. Status of ME Generators
Model Alpgen HELAC Sherpa MadGraph
SM 6 jets 10 jets ? 6,7 jets 4,5 jets
MSSM ✕ ？ 5 jets 4,5 jets
Others ✕ ✕ 5 jets 4,5 jets
There is no ME generator
which can simulate New Physics with > 5 jets.
July 24, 2016 4

5. What is MadGraph?
5
Matrix-Element & Event Generator
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Input
Event generator (MadEvent)
Output
Matrix-Element Generator (“MadGraph”)
+ Fortran Code
Model + process
Events

6. July 24, 2016 6
MG
MSSM,
ADD,
2HDM,
etc
Feyn-
Rules
Higher
Dim. Op.
Spin-3/2
Spin-2
NLO
Interface
PYTHIA
DetectorSimulator
ROOT
Lagrangian

7. Limitation of MG
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The file size of codes for QCD processes
Cannot be Compiled

8. Structure of QCD Amp
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Color flow
Color Factor
color-ordered amp.
i: Color flow

9. How to overcome
the Limitation
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10. July 24, 2016 10
STRATEGY
Divide
• Speed up Amp Evaluation
• Off-shell Recursive Relations
• Re-organize Color Summation
1/Nc expansion

11. Speed up Amp Evaluation
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12. July 24, 2016 12
Off-shell Recursive Relations
Lv.1
Lv.2
Lv.3

13. Time performance
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@ 1 helicity &
Phase pace point

14. July 24, 2016 14
Model dependent Model independent
Recursive Relation Feynman Diagram
Hybrid
Alpgen(SM)
COMIX (SM)
HELAC (SM, MSSM?)
MadGraph, AMEGIC, compHEP

15. July 24, 2016 15
Recursive Relations
for gluonic sub-amplitude

16. July 24, 2016 16
@ 1 helicity &
Phase pace point

17. Re-organize Color Sum
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18. July 24, 2016 18
1/Nc expansion
Polynomial of Nc:

19. Multi-jet event generation
• Generate events with Leading Color
Approximation
• For each event, include higher order
corrections into its weight.
July 24, 2016 19

20. Leading color Event Generation
Color-flow sampling
( ~ 40,000 for gg -> 7g )
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Too LARGE
Event is a set of momenta,helicities and a color flow

21. Sample Results
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22. July 24, 2016 22

23. July 24, 2016 23

24. July 24, 2016 24

25. Total cross sections
July 24, 2016 25

26. July 24, 2016 26
(Linear scale) (Log scale)

27. Conclusion
• We proposed a method to generate multi-jet
events with MadGraph.
– Implemented gluonic off-shell recursive relations
and generate color-ordered amps.
– Generated LO events by sampling color flows
– Shown results for gluonic processes for LO event
generation.
July 24, 2016 27

28. OutLook
• Generate events with quarks
• Include higher order corrections in 1/Nc exp
• Detailed study for many distributions of Multi-
jet events with our method
• Apply the framework to New Physics Pheno
July 24, 2016 28