Transcript
Toward multi-jet events generation with MadGraph
Yoshitaro Takaesu
February 4, 2016 1
Overview: Simulation for LHC
February 4, 2016 2
Parton Shower Generator
Matrix Element Generator
σ =
a,b
dx1dx2Da/ pDb/ p
1
2s|M (ab→ c1, · · · , cn )|2dΦn
Event Generator
Detector Simulator
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
February 4, 2016 4
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
February 4, 2016 6
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
February 4, 2016 8
February 4, 2016 9
MG5
MSSM, ADD,
2HDM,etc
Feyn-Rules
Higher Dim. Op.
Spin-3/2
Spin-2
NLO
Interface
PYTHIA
Detector Simulator
ROOT
Lagrangian
Limitation of MGGenerated Codes (> 8MB) cannot be compiled in usual PC.
February 4, 2016 10
8 MB
100
101
102
103
104
105
2 3 4 5 6
log
10 F
ile S
ize (
KB
)
# of Final State Particles
gg > ngug > ug nguu > uu ng
The file size of codes for QCD processes
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
|A i |2+
1
N 2c i ,j
A1i j +
1
N 4c i ,j
A2i j + · · ·
Off-shell recursive relations (c.f. Alpgen)
Structure of QCD Amp
February 4, 2016 12
Tr (T aT b) =1
2δab
Color flow
Color Factorcolor-ordered amp.
i: Color flow
February 4, 2016 13
Color Flow
Structure of QCD Amp
February 4, 2016 14
Tr (T aT b) =1
2δab
Color flow
Color Factorcolor-ordered amp.
i: Color flow
How to overcomethe Limitation
February 4, 2016 15
February 4, 2016 16
STRATEGY
Divide
• Speed up Amp Evaluation• Off-shell Recursive Relations
• Re-organize Color Summation1/Nc expansion
Speed up Amp Evaluation
February 4, 2016 17
February 4, 2016 18
Off-shell Recursive Relations
Step #
# of vertex evaluations
February 4, 2016 19
Time performance
February 4, 2016 20
0
0.05
0.1
0.15
0.2
0.25
0.3
4 5 6 7 8
Tim
e (m
s)
Final Gluons
Recursive
Non-Recursive
n3
n4
February 4, 2016 21
Recursive Relations for gluonic sub-amplitude
~ 10 times faster matrix element calculation
Re-organize Color Sum
February 4, 2016 22
February 4, 2016 23
1/Nc expansion
Polynomial of Nc:
= N mc
i
|A i |2 +
1
N 2c
A∗i (A j 1,1 + A j 1,2 + · · · )
+1
N 4c
A∗i (A j 2,1 + A j 2,2 + · · · )
February 4, 2016 24
= N mc
i
|A i |2 +
1
N 2c
A∗i (A j 1,1 + A j 1,2 + · · · )
February 4, 2016 25
= N mc
i
|A i |2 +
1
N 2c
A∗i (A j 1,1 + A j 1,2 + · · · )
February 4, 2016 26
color
|M |2 =
N c f
i = 1
(N 2c − 1)n− 1
N n− 1c
|A i |2
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
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 mc
i
|A i |2 +
1
N 2c
A∗i (A j 1 , 1
+ A j 1 , 2+ · · · ) +
1
N c2
2
A∗i (A j 2 , 1
+ A j 2 , 2+ · · ·) + · · ·
February 4, 2016 28
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 mc |A i |
2 +1
N 2c
A∗i (A j 1 , 1
+ A j 1 , 2+ · · · ) +
1
N c2
2
A∗i (A j 2 , 1
+ A j 2 , 2+ · · ·) + · · ·
color
|M |2 =
i
N mc |A i |
2 +1
N 2c
A∗i (A j 1 , 1
+ A j 1 , 2+ · · · ) +
1
N c2
2
A∗i (A j 2 , 1
+ A j 2 , 2+ · · ·) + · · ·
σ = |M |2dΦn
Huge # of integration channels
i_th Channel
|M |2dΦn = i |D i |2
j |D j |2|M |2dΦn =
i
|M |2
j |D j |2|D i |
2dΦn
Channel Optimization
Convergence
# of Channels (~10,000 channels for gg > 6g)
~ 100 channels for gg > 6g
represent singularities
Results
LC ch: the result of this study (with Recursive amp., Leading Color and the channeling based on peripheral singularities)
LC no ch: baseline results (with Recursive amp., 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
106
107
108
109
Cro
ss S
ecti
on
(pb)
gg -> ng Cross Section
LC ch
LC no ch
MG5 LC
Sherpa
0.9
1.0
1.1
2 3 4 5 6Rat
io t
o L
C.n
o.c
h
Final Gluons (n)
Cross section
32
Distributions: gg -> 4g
33
1e+06
1e+07
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
dX
sec
/ dd
R (
g3
g4)
dR (g3g4)
LC ch
MG LC
10000
100000
1e+06
0 10 20 30 40 50 60 70 80 90 100
dX
sec
/ d
m (
g3g
4)
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
dX
sec
/ d
pT
(g4
)
pT (g4)
LC ch
MG LC
100000
1e+06
1e+07
-5 -4 -3 -2 -1 0 1 2 3 4 5
dX
sec
/ d
y (
g4)
y (g4)
LC ch
MG LC
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
dX
sec
/ dd
R (
g3
g5)
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
dX
sec
/ dd
R (
g4
g5)
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
dX
sec
/ d
pT
(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
dX
sec
/ d
y (
g5)
y (g5)
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
dX
sec
/ d
dR
(g5
g6
)
dR(g5g6)
gg6g.100k.100kwgtgg6g.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
dX
sec
/ d
dR
(g4
g6
)
dR(g4g6)
gg6g.100k.100kwgtgg6g.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
dX
sec
/ d
pT
(g6
)
pT (g6)
gg6g.100k.100kwgtgg6g.100k.100kunwgt
10000
100000
1e+06
-5 -4 -3 -2 -1 0 1 2 3 4 5
dX
sec
/ d
y (
g6)
y (g6)
gg6g.100k.100kwgtgg6g.100k.100kunwgt
LC ch WgtedLC ch Unwgted
LC ch WgtedLC ch Unwgted
LC ch WgtedLC ch Unwgted
LC ch WgtedLC ch Unwgted
LC ch WgtedLC ch Unwgted
Time measurement
36
103
104
105
106
107
2 3 4 5 6
Tim
e (s
ec)
Final Gluons (n)
gg -> ng Timing
LC ch
MG5 LC
Sherpa
LC ch parallel
MG5 LC parallel
100,000 events with 1 core CPU / ~ 100 core cluster (KEKCC)
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-jetMG5
New Physics with many jets
top related