This document describes a method for efficiently generating multi-gluon events using color-flow decomposition and optimized phase space integration. It focuses on generating leading color order gluon scattering processes up to 6 gluons. The key challenges addressed are the large number of diagrams, heavy color summation, and huge number of integration channels. The method shows good agreement with MadGraph for distributions in 4 and 5 gluon processes and allows generation of 6 gluon events, improving on previous methods that could only handle up to 4 gluons. Future work will include next-to-leading color terms and quark subprocesses to generate a wide variety of multi-jet events for the LHC.

1. Yoshitaro Takaesu
KIAS/KNRC
Generating multi-gluon events with
the color-flow decomposition and
optimized phase space integration
In collaborationwith J. Alwal, K. Hagiwara (KEK), F. Maltoni (UCL)
and T. Stelzer (UIU)

2. Introduction
2
• Accurate simulation of multi-jet events based on Matrix-Element
calculations would become more important at the upgraded LHC.
Flexible multi-jet event generator is desired which can deal with
SM and many possibilities of New Physics in the same footing.
MadGraph5 + multi-jet (> 4 jets)
• Production & Decay of more massive particles
• Harder & more ISRs
• Spin-correlationsof pair-produced particles
• Sub structureof broad jets
New Physics signal multi-jet SM BG&
Alpgen
Helac
Sherpa

3. Problems in multi-jet generation
3
2. Heavy Color Summation
3. Huge # of integration channels
1. Huge # of diagrams
Channel Optimization
Color-Flow decomposition (1/Nc expansion)
Off-shell recursive relations
F.A.Berens, W.T.Giele, NPB306 (1988)
Y.T, K.Hagiwara, EPJC71:1668 (2011),J.Alwal
for MG
F. Maltoni et.al., PRD67 (2003)

4. 2. Heavy Color Summation
4
February 11, 2016
Color flow
Color Factor
color-ordered amp.
i: Color flow

5. February 11, 2016
5
1/Nc expansion
Polynomial of Nc:

6. February 11, 2016
6
@ 100 phase space points
@ 100 phase space points

7. February 11, 2016
7
@ 106 phase space points
@ 61 phase space points

8. Problems in multi-jet generation
8
2. Heavy Color Summation
3. Huge # of integration channels
1. Huge # of diagrams
Channel Optimization
Color-Flow decomposition (1/Nc expansion)
Off-shell recursive relations
F.A.Berens, W.T.Giele, NPB306 (1988)
Y.T, K.Hagiwara, EPJC71:1668 (2011),J.Alwal
for MG
F. Maltoni et.al., PRD67 (2003)

9. 3. Huge # of integration channels
i_th Channel
Channel Optimization
Convergence
# of Channels (~10,000 channels for gg > 6g)
~ 100 channels for gg > 6g
representsingularities F.Maltoni, T.Stelzer JHEP0302:027(2003)

10. Results
Leading Color
gluon scatteringprocess
as the first step

11. Cross section
11
Agrees with MG LC
Error of LC Approx. is
just what is expected

12. Distributions: gg -> 4g
12
Good agreement with MG LC results

13. Distributions: gg -> 5g
13
Failed
Bad example
Passes self-consistency checks

14. Distributions: gg -> 6g
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LC ch Wgted
LC ch Unwgted
LC ch Wgted
LC ch Unwgted
LC ch Wgted
LC ch Unwgted
LC ch Wgted
LC ch Unwgted
LC ch Wgted
LC ch Unwgted

15. Time measurement (preliminary)
15
Our reduced channeling seems not to sacrifice the computational
time significantly. (need more study on gg>6g ?)
100,000 eventswith 1 core CPU or ~ 100 core cluster (KEKCC)

16. Summary & Outlook
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• It is shown that gg > 6g events can be generated at Leading Color
Order, using recursive amps and peripheral channeling.
• Inclusion of NLC and quark subprocesses are next step.
aMC@NLO with many jets
Tree, LC
NLCquark subprocesses
multi-jet
MG5
New Physics with many jets