Generating multi-jet events with MadGraph

Yoshitaro Takaesu (KEK)

October 27, 2016 1

Overview: Simulation for LHC

October 27, 2016 2

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.

October 27, 2016 3

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.

October 27, 2016 4

What is MadGraph?

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Matrix-Element & Event Generator

October 27, 2016 5

Input

Event generator (MadEvent)

Output

Matrix-Element Generator (“MadGraph”)

+ Fortran Code

Model + process

Events

October 27, 2016 6

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.

October 27, 2016 7

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.

October 27, 2016 20

Leading color summation

Color-flow sampling

( ~ 40,000 for gg -> 7g )

October 27, 2016 21

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

October 27, 2016 22

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.

October 27, 2016 28

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.

October 27, 2016 29

October 27, 2016 30

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

October 27, 2016 41

Amplitude

Color Basis

Helicity &Color

Sum

Recursive Relations

Color-Flow Basis

– Compilable

– Symmetric

– Gauge invariant

October 27, 2016 42

Off-shell Recursive Relations

Divide MG code by C.O. Amp

are