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Generating multi-jet events with MadGraph
Yoshitaro Takaesu (KEK)
October 27, 2016 1
Overview: Simulation for LHC
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Parton Shower Generator
Matrix Element Generator
Event Generator
Detector Simulator
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.
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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.
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What is MadGraph?
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Matrix-Element & Event Generator
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Input
Event generator (MadEvent)
Output
Matrix-Element Generator (“MadGraph”)
+ Fortran Code
Model + process
Events
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MG
MSSM, ADD,
2HDM,etc
Feyn-Rules
Higher Dim. Op.
Spin-3/2
Spin-2
NLO
Interface
PYTHIA
Detector Simulator
ROOTLagrangian
Limitation of MGGenerated Codes (> 8MB) cannot be compiled in usual PC.
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8 MB
The file size of codes for QCD processes
Structure of QCD Amp
October 27, 2016 8Color flow
Color Factorcolor-ordered amp.
i: Color flow
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Color Flow
Structure of QCD Amp
October 27, 2016 10Color flow
Color Factorcolor-ordered amp.
i: Color flow
How to overcomethe Limitation
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STRATEGY
Divide
Speed up • Amp EvaluationOff• -shell Recursive Relations
• Re-organize Color Summation1/Nc expansion
Speed up Amp Evaluation
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Off-shell Recursive Relations
Step #
# of vertex evaluations
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Time performance
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Recursive Relations for gluonic sub-amplitude
Re-organize Color Sum
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1/Nc expansion
Polynomial of Nc:
Multi-jet event generation
Generate events with • Leading Color Approximation
For each event, include • higher order corrections into its weight.
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Leading color summation
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
Higher order corrections
• For each event with a color flow
– Specify needed color flows for the higher order corrections
– Evaluate higher order corrections for the phase space point and reweight
– Re-unweight
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Sample Results
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Total cross sections
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Distributions
ConclusionWe 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.
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OutLook
Include higher order corrections in • 1/Nc exp.
Generate events with quarks•
Detailed study for many distributions of Multi• -jet events
Apply the framework to New Physics • Pheno.
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In color decomposition, we usually use Gell-Man matrices or modified matrices for .
Gell-Man:
Modified:
Color-Flow decomposition uses another set of matrices for .
Here are the generators of .
By using this basis, we can simplify the color factors as much as we can: 0 or 1.
Color-Flow basis
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QCD Lagrangian can be written as
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We rewrite this by introducing a U(1) gauge boson
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9 U(3) gluons are independent and their generator matrices are
The color of a gluon can be expressed by a set of color indeces: (i, j).
There is also the abelian gluon in this theory.
Feynman Rules 1
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Color Flow diagrams
Color Flow
Feynman Rules 2
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The abelian gluon is decoupled from U(3) gluons.
This is the color-flow decomposition of a n-gluon amplitude.
From these rules, we evaluate a color-fixed scattering amplitude.
n-gluon amplitude
: (n-1)! non-cyclic permutaions
For n-gluon case, are the same asthe Color-Ordered ones.
color factor: 0 or1 partial amplitude
We add abelian gluon amplitudes to the U(3) gluon ones.
e.g.)
1 quark line and amplitude
There are other contributions from propagating abelian gluons
e.g.)
2 quark lines and amplitude
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Amplitude
Color Basis
Helicity &Color
Sum
Recursive Relations
Color-Flow Basis
– Compilable
– Symmetric
– Gauge invariant
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Off-shell Recursive Relations
Divide MG code by C.O. Amp
are