Seminar @ U of Tokyo: 2014.04.14

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