Seminar @ U of Tokyo: 2014.04.14

1. Toward multi-jet events
generation with MadGraph
Yoshitaro Takaesu
February 4, 2016 1

2. Overview: Simulation for LHC
February 4, 2016 2
Parton Shower Generator
Matrix Element Generator
σ =
a,b
dx1dx2Da/ pDb/ p
1
2ˆs
|M (ab→ c1, ··· , cn )|2
dΦn
Event Generator
DetectorSimulator

3. What is MadGraph?
3
Matrix-Element & Event Generator
February 4, 2016 3
Input
Event generator (MadEvent)
Output
Matrix-Element Generator (“MadGraph”)
+ Fortran Code
Model + process
Events

4. February 4, 2016 4

5. 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.
February 4, 2016 5

6. February 4, 2016 6

7. 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.
February 4, 2016 7

8. February 4, 2016 8

9. February 4, 2016 9
MG5
MSSM,
ADD,
2HDM,
etc
Feyn-
Rules
Higher
Dim. Op.
Spin-3/2
Spin-2
NLO
Interface
PYTHIA
DetectorSimulator
ROOT
Lagrangian

10. Limitation of MG
Generated Codes (> 8MB) cannot be compiled in usual PC.
February 4, 2016 10
8 MB
100
10
1
10
2
103
104
105
2 3 4 5 6
log10
FileSize(KB)
# of Final State Particles
gg > ng
ug > ug ng
uu > uu ng
The file size of codes for QCD processes

11. Problems in multi-jet generation
11
2. Heavy Color Summation
3. Huge # of integration channels
1. Huge # of diagrams
Channel Optimization
Color-Flow decomposition (1/Nc expansion)
color
|M |2
=
i
|Ai |2
+
1
N 2
c i ,j
A1
i j +
1
N 4
c i ,j
A2
i j + ···
Off-shell recursive relations (c.f. Alpgen)

12. Structure of QCD Amp
February 4, 2016 12
Tr(Ta
Tb
) =
1
2
δab
Color flow
Color Factor
color-ordered amp.
i: Color flow

13. February 4, 2016 13
Color Flow

14. Structure of QCD Amp
February 4, 2016 14
Tr(Ta
Tb
) =
1
2
δab
Color flow
Color Factor
color-ordered amp.
i: Color flow

15. How to overcome
the Limitation
February 4, 2016 15

16. February 4, 2016 16
STRATEGY
Divide
• Speed up Amp Evaluation
• Off-shell Recursive Relations
• Re-organize Color Summation
1/Nc expansion

17. Speed up Amp Evaluation
February 4, 2016 17

18. February 4, 2016 18
Off-shell Recursive Relations
Step #

19. # of vertex evaluations
February 4, 2016 19

20. Time performance
February 4, 2016 20
0
0.05
0.1
0.15
0.2
0.25
0.3
4 5 6 7 8
Time(ms)
Final Gluons
Recursive
Non-Recursive
n
3
n
4

21. February 4, 2016 21
Recursive Relations
for gluonic sub-amplitude
~ 10 times faster matrix element calculation

22. Re-organize Color Sum
February 4, 2016 22

23. February 4, 2016 23
1/Nc expansion
Polynomial of Nc:
= N m
c
i
|Ai |2
+
1
N 2
c
A∗
i (Aj 1,1 + Aj 1,2 + ···)
+
1
N 4
c
A∗
i (Aj 2,1 + Aj 2,2 + ···)

24. February 4, 2016 24
= N m
c
i
|Ai |2
+
1
N 2
c
A∗
i (Aj 1,1 + Aj 1,2 + ···)

25. February 4, 2016 25
= Nm
c
i
|Ai |2
+
1
N2
c
A∗
i (Aj 1,1 + Aj 1,2 + ···)

26. February 4, 2016 26
color
|M |2
=
N cf
i = 1
(N 2
c − 1)n− 1
N n− 1
c
|Ai |2

27. Leading color summation
Color-flow sampling
( ~ 5,000 for gg -> 6g )
February 4, 2016 27
Too LARGE
Event is a set of momenta,helicities and a color flow

28. 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
= N m
c
i
|Ai |2
+
1
N 2
c
A∗
i (Aj 1, 1 + Aj 1, 2 + ···) +
1
N c2
2
A∗
i (Aj 2, 1 + Aj 2, 2 + ···) + ···
February 4, 2016 28

29. Multi-jet event generation
• Generate events with Leading Color
Approximation
• For each event, include higher order
corrections into its weight. (
February 4, 2016 29
color
|M |2
=
i
N m
c |Ai |2
+
1
N 2
c
A∗
i (Aj 1, 1 + Aj 1, 2 + ···) +
1
N c2
2
A∗
i (Aj 2, 1 + Aj 2, 2 + ···) + ···
color
|M |2
=
i
N m
c |Ai |2
+
1
N 2
c
A∗
i (Aj 1, 1 + Aj 1, 2 + ···) +
1
N c2
2
A∗
i (Aj 2, 1 + Aj 2, 2 + ···) + ···
σ = |M |2
dΦn

30. Huge # of integration channels
i_th Channel
|M |2
dΦn = i |Di |2
j |Dj |2
|M |2
dΦn =
i
|M |2
j |Dj |2
|Di |2
dΦn
Channel Optimization
Convergence
# of Channels (~10,000 channels for gg > 6g)
~ 100 channels for gg > 6g
representsingularities

31. Results
LC ch: the result of this study (with Recursiveamp., Leading Color
and the channeling based on peripheral singularities)
LC no ch: baseline results (with Recursiveamp., Leading Color,
but without SDE multi-channeling.
Very long calculation)
MG5 LC: MG5 results with just diagonal parts of the color matrix (Leading Color)
Sherpa: Sherpa results

32. 10
6
10
7
108
109
CrossSection(pb)
gg -> ng Cross Section
LC ch
LC no ch
MG5 LC
Sherpa
0.9
1.0
1.1
2 3 4 5 6
RatiotoLC.no.ch
Final Gluons (n)
Cross section
32

33. Distributions: gg -> 4g
33
1e+06
1e+07
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
dXsec/ddR(g3g4)
dR (g3g4)
LC ch
MG LC
10000
100000
1e+06
0 10 20 30 40 50 60 70 80 90 100
dXsec/dm(g3g4)
m (g3g4)
LC ch
MG LC
0.001
0.01
0.1
1
10
100
1000
10000
100000
1e+06
1e+07
10 20 30 40 50 60 70 80 90 100
dXsec/dpT(g4)
pT (g4)
LC ch
MG LC
100000
1e+06
1e+07
-5 -4 -3 -2 -1 0 1 2 3 4 5
dXsec/dy(g4)
y (g4)
LC ch
MG LC

34. Distributions: gg -> 5g
34
100000
1e+06
1e+07
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
dXsec/ddR(g3g5)
dR (g3g5)
LC ch Wgted
LC ch Unwgted
100000
1e+06
1e+07
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
dXsec/ddR(g4g5)
dR (g4g5)
LC ch Wgted
LC ch Unwgted
10
100
1000
10000
100000
1e+06
1e+07
0 10 20 30 40 50 60 70 80 90 100
dXsec/dpT(g5)
pT (g5)
LC ch Wgted
LC ch Unwgted
10000
100000
1e+06
1e+07
-5 -4 -3 -2 -1 0 1 2 3 4 5
dXsec/dy(g5)
y (g5)
LC ch Wgted
LC ch Unwgted

35. 100000
1e+06
1e+07
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
dXsec/ddR(g5g6)
dR(g5g6)
gg6g.100k.100kwgt
gg6g.100k.100kunwgt
Distributions: gg -> 6g (preliminary)
35
100000
1e+06
1e+07
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
dXsec/ddR(g4g6)
dR(g4g6)
gg6g.100k.100kwgt
gg6g.100k.100kunwgt
0.01
0.1
1
10
100
1000
10000
100000
1e+06
0 10 20 30 40 50 60 70 80 90 100
dXsec/dpT(g6)
pT (g6)
gg6g.100k.100kwgt
gg6g.100k.100kunwgt
10000
100000
1e+06
-5 -4 -3 -2 -1 0 1 2 3 4 5
dXsec/dy(g6)
y (g6)
gg6g.100k.100kwgt
gg6g.100k.100kunwgt
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

36. Time measurement
36
10
3
104
10
5
10
6
107
2 3 4 5 6
Time(sec)
Final Gluons (n)
gg -> ng Timing
LC ch
MG5 LC
Sherpa
LC ch parallel
MG5 LC parallel
100,000 eventswith 1 core CPU / ~ 100 corecluster (KEKCC)

37. Summary & Outlook
37
• It is shown that gg > 5g events can be generated at Leading Color
Order using recursive amps and peripheral channeling, which are
applicable to MG5.
• gg -> 6g need more study
aMC@NLO with many jets
Tree, LC
NLCquark subprocesses
multi-jet
MG5
New Physics with many jets