presentation in the MadGraph meeting at U. of Pittsburgh 2012.05.12

1. Mul$-­‐Jet
Genera$on
-­‐
status
report
-­‐
Yoshitaro
Takaesu
(KEK)
November
16,
2013
1
In
collabora$on
with
Fabio,
Johan,
Kaoru
and
Tim

2. Importance
of
mul$-­‐jet
at
the
LHC
Mul2-­‐jet
signature
appears
in
many
New
Physics
models.
Event
Generator
should
be
able
to
generate
>
4
jets.
November
16,
2013
2

3. Limita$on
of
MG
Generated
Codes
(>
8MB)
cannot
be
compiled
in
usual
PC.
gg 5g
qg q5g
qq qq4g
November
16,
2013
3
8
MB
100
101
102
10
3
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

4. How
to
overcome
the
Limita$on
November
16,
2013
4
gg 5g
qg q5g
qq qq4g

5. Structure
of
QCD
Amp
November
16,
2013
5
gg gg
= ig2
s[fabe
fcde
( 1 · 3 2 · 4 1 · 4 2 · 3)
+ face
fbde
( 1 · 2 3 · 4 1 · 4 2 · 3)
+ fade
fbce
( 1 · 2 3 · 4 1 · 3 2 · 4)]a
b
c
d
fabc
= 2iTr [Ta
, Tb
]Tc Tr(T a
Tb
) =
1
2
ab
=
P(b,c,d)
Tr(T a
T (b)
T (c)
T (d)
)A(a (b) (c) (d))
= Tr(T a
Tb
Tc
Td
)A(abcd) + Tr(T a
Tb
Td
Tc
)A(abdc)
+ Tr(T a
Tc
Tb
Td
)A(acbd) + Tr(T a
Tc
Td
Tb
)A(acdb)
+ Tr(T a
Td
Tb
Tc
)A(adbc) + Tr(T a
Td
Tc
Tb
)A(adcb)
Color
flow
Color
Factor
color-­‐ordered
amp.
i:
Color
flow
M =
Ncf
i=1
CiAi Ncf (n 1)!

6. November
16,
2013
6
color
|M|2
=
Ncf
i,j color
Ci CjAi Aj
M =
Ncf
i=1
CiAi
STRATEGY
Divide
color
Ci Cj
A1
A2
A3
· · ·
ANcf 1
ANcf
• Speed
up
Amp
Evalua$on
• Off-­‐shell
Recursive
Rela2ons
•
Re-­‐organize
Color
Summa$on
1/Nc
expansion

7. Speed
up
Amp
Evalua$on
November
16,
2013
7

8. November
16,
2013
8
Off-­‐shell
Recursive
Rela$ons
Step
#

9. Time
performance
November
16,
2013
9
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
n3
n
4

10. November
16,
2013
10
Recursive
Rela$ons
for
gluonic
sub-­‐amplitude

11. Re-­‐organize
Color
Sum
November
16,
2013
11

12. November
16,
2013
12
1/Nc
expansion
Polynomial
of
Nc:
color
|M|2
=
Ncf
i,j color
Ci CjAi Aj
= Nm
c
i
|Ai|2
+
1
N2
c
Ai (Aj1,1 + Aj1,2 + · · · )
+
1
N4
c
Ai (Aj2,1 + Aj2,2 + · · · )
+ · · ·
(m = ng + nq/2)

13. Mul$-­‐jet
event
genera$on
• Generate
events
with
Leading
Color
Approxima2on
• For
each
event,
include
higher
order
correc2ons
into
its
weight.
November
16,
2013
13
color
|M|2
=
i
Nm
c |Ai|2
+
1
N2
c
Ai (Aj1,1 + Aj1,2 + · · · ) +
1
Nc2
2
Ai (Aj2,1 + Aj2,2 + · · · ) + · · ·
color
|M|2
=
i
Nm
c |Ai|2
+
1
N2
c
Ai (Aj1,1 + Aj1,2 + · · · ) +
1
Nc2
2
Ai (Aj2,1 + Aj2,2 + · · · ) + · · ·
= |M|2
d n

14. Leading
color
summa$on
Color-­‐flow
sampling
Ncf (m 1)! (
~
40,000
for
gg
-­‐>
7g
)
November
16,
2013
14
color
|M|2
=
Ncf
i=1
Nm
c |Ai|2
Too
LARGE
Event
is
a
set
of
momenta,
helici$es
and
a
color
flow

15. Results
November
16,
2013
15

16. November
16,
2013
16
gg_6g NLO diff
Entries 61
Mean -0.9229
RMS 0.5551
-3 -2.5 -2 -1.5 -1 -0.5 0
0
2
4
6
8
10
12
14
gg_6g NLO diff
Entries 61
Mean -0.9229
RMS 0.5551
gg_6g NLO diff
= Nm
c
i
|Ai|2
+
1
N2
c
Ai (Aj1,1 +Aj1,2 +···)
color
|M|2
color
|M|2
=
Ncf
i=1
N(n 2)
c (N2
c 1)|Ai|2

17. November
16,
2013
17
ug_u3g NLNc diff
Entries 1000
Mean 2.63
RMS 2.916
-100 -80 -60 -40 -20 0 20 40 60 80 100
0
100
200
300
400
500
ug_u3g NLNc diff
Entries 1000
Mean 2.63
RMS 2.916
ug_u3g NLNc diff
ug_u3g LNc diff
Entries 1000
Mean -27.28
RMS 13.15
-100 -80 -60 -40 -20 0 20 40 60 80 100
0
20
40
60
80
100
120
ug_u3g LNc diff
Entries 1000
Mean -27.28
RMS 13.15
ug_u3g LNc diff
color
|M|2
=
Ncf
i=1
(N2
c 1)n 1
Nn 1
c
|Ai|2

18. November
16,
2013
18
Event
Genera$on
@LNc
pp
>
W
+
2
jets
W
+
3
jets
W
+
4
jets
MG5
(pb)
10673
4807.9
±
13.2
2913
±
7.6
LNc
CO
(pb)
11076
4623.8
±
11.9
2460
±
6
•
gg
-­‐>
3,4,5
g
process
is
now
generated
without
major
problem
and
agree
with
MG5
(3,4g).
pp
>
W+2,3,4
jets
is
also
studied
recently
and
roughly
agree
with
MG5.
Preliminary

19. 0.9
1
2 3 4 5 6 7
ratio
Final particles
107
108
10
9
1010
10
11
1012
CrossSection(fb)
gg -> ng Cross Section
CFS (LCA)
COMIX
MG5
November
16,
2013
19

20. November
16,
2013
20
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
0 50 100 150 200 250 300 350
dXsec/dpT1(pb)
pT1 (GeV)
gg > 4g pT1
MG5 Exact
CFsamp LNc
0
5000
10000
15000
20000
25000
30000
35000
-3 -2 -1 0 1 2 3
dXsec/dy1(pb)
y1 (GeV)
gg > 4g y1
MG5 Exact
CFsamp LNc
10
100
1000
10000
100000
1e+06
0 50 100 150 200 250 300 350
dXsec/dpT1(pb)
pT1 (GeV)
gg > 4g pT1
MG5 Exact
CFsamp LNc
100
1000
10000
100000
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
dXsec/ddR12(pb)
dR12 (GeV)
gg > 4g dR12
MG5 Exact
CFsamp LNc
pT 1
(Linear
scale)
pT 1
(Log
scale)
1 R12
gg gggg

21. November
16,
2013
21
dxadxbd n =
2
s
1
4 2n 2
dy1 · · · dyndp2
T 1 · · · dp2
T n 1
d 1
2
· · ·
d n 1
2
A
liee
bit
of
Phase
Space
Study
Alterna2ve
parameteriza2on
for
MadEvent:
suitable
for
kinema2cal
cuts
,
e.g.,
p_T
cut
or
rapidity
cut.

22. November
16,
2013
22
2
3
4
5
6
7
8
0 50 100 150 200 250 300 350 400 450 500
MG5
3ch
tch
4
5
6
7
-5 -4 -3 -2 -1 0 1 2 3 4 5
MG5
3ch
tch
pT 1
1
5
6
7
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
MG5
3ch
tch
R23
3
4
5
6
7
8
0 200 400 600 800 1000 1200 1400 1600
MG5
3ch
tch
M12
gg ggg (3.5
%
unweigh2ng
eff.)

23. November
16,
2013
23
-4
-3
-2
-1
0
1
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
MG5
3ch
tch
-4
-3
-2
-1
0
1
0 200 400 600 800 1000 1200 1400 1600
MG5
3ch
tch
-2
-1
0
1
2
800 1000 1200 1400 1600 1800 2000
MG5
3ch
tch
-3
-2
-1
0
1
-3 -2 -1 0 1 2 3
MG5
3ch
tch
pT 1
1
R23
M12
gg ggg
pT 1 > 1000GeV

24. November
16,
2013
24
Amplitude
Phase
Space
Color
Sum
Recursive
Rela$ons
Channels
For
fast
mul$-­‐jet
genera$on

25. OutLook
• Efficient
Phase
Space
integra2on
• Include
higher
order
correc2ons
in
1/Nc.
• Generate
events
with
quarks
• Detailed
study
for
many
distribu2ons
of
Mul2-­‐
jet
events
November
16,
2013
25