Overview of MadGraph5 aMC@NLO...Mattelaer Olivier MadGraph5_aMC@NLO Plan 2 •Details of the...

Overview of MadGraph5_aMC@NLO

Olivier MattelaerUCLouvainCP3/CISM

Mattelaer Olivier MadGraph5_aMC@NLO

Plan

2

•Details of the computation•Evaluation of matrix-element•Phase-Space integration

•What is MG5_aMC

Mattelaer Olivier MadGraph5_aMC@NLO

What are my goals

• Justify why analytic computation are SLOWER than numerical computation

• Justify why adding cuts to the code are POSSIBLE but can lead to PROBLEM

• Overview of MG5_aMC➡ What does each package

• Details on small width handling

Title

3

Mattelaer Olivier MadGraph5_aMC@NLO

•Determine the production mechanism

• Evaluate the matrix-element

• Phase-Space Integration

4

Matrix-ElementCalculate a given process (e.g. gluino pair)

s s~ > go go WEIGHTED=2 page 1/1

Diagrams made by MadGraph5_aMC@NLO

s

1

s~

2

g

go

3

go

4

diagram 1 QCD=2, QED=0

s

1

go

3

sl

s~2

go4

diagram 2 QCD=2, QED=0

s

1

go

3

sr

s~2

go4

diagram 3 QCD=2, QED=0

s

1

go

4

sl

s~2

go3

diagram 4 QCD=2, QED=0

s

1

go

4

sr

s~2

go3

diagram 5 QCD=2, QED=0

σ =1

2s

!|M|2dΦ(n)

σ =1

2s

!|M|2dΦ(n)

Mattelaer Olivier MadGraph5_aMC@NLO

•Determine the production mechanism

• Evaluate the matrix-element

• Phase-Space Integration

4

Matrix-ElementCalculate a given process (e.g. gluino pair)

s s~ > go go WEIGHTED=2 page 1/1

Diagrams made by MadGraph5_aMC@NLO

s

1

s~

2

g

go

3

go

4

diagram 1 QCD=2, QED=0

s

1

go

3

sl

s~2

go4

diagram 2 QCD=2, QED=0

s

1

go

3

sr

s~2

go4

diagram 3 QCD=2, QED=0

s

1

go

4

sl

s~2

go3

diagram 4 QCD=2, QED=0

s

1

go

4

sr

s~2

go3

diagram 5 QCD=2, QED=0

σ =1

2s

!|M|2dΦ(n)

σ =1

2s

!|M|2dΦ(n)

Easy

Hard

VeryHard

(in general)

Mattelaer Olivier MadGraph5_aMC@NLO

Matrix Elemente+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

5

M = e2(u�µv)gµ⌫q2

(v�⌫u)

Mattelaer Olivier MadGraph5_aMC@NLO

Matrix Element

1

4

X

pol

|M|2 =1

4

X

pol

M⇤M

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

5

M = e2(u�µv)gµ⌫q2

(v�⌫u)

Mattelaer Olivier MadGraph5_aMC@NLO

Matrix Element

X

pol

uu = 6p+m

1

4

X

pol

|M|2 =1

4

X

pol

M⇤M

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

5

M = e2(u�µv)gµ⌫q2

(v�⌫u)

Mattelaer Olivier MadGraph5_aMC@NLO

Matrix Element

X

pol

uu = 6p+m

1

4

X

pol

|M|2 =1

4

X

pol

M⇤M

e4

4q4Tr[ 6p1�µ 6p2�⌫ ]Tr[ 6p3�µ 6p4�⌫ ]

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

5

M = e2(u�µv)gµ⌫q2

(v�⌫u)

Mattelaer Olivier MadGraph5_aMC@NLO

Matrix Element

X

pol

uu = 6p+m

1

4

X

pol

|M|2 =1

4

X

pol

M⇤M

e4

4q4Tr[ 6p1�µ 6p2�⌫ ]Tr[ 6p3�µ 6p4�⌫ ]

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

5

8e4

q4[(p1.p3)(p2.p4) + (p1.p4)(p2.p3)]

M = e2(u�µv)gµ⌫q2

(v�⌫u)

Mattelaer Olivier MadGraph5_aMC@NLO

Matrix Element

Very Efficient (few computation to perform to get that number)

X

pol

uu = 6p+m

1

4

X

pol

|M|2 =1

4

X

pol

M⇤M

e4

4q4Tr[ 6p1�µ 6p2�⌫ ]Tr[ 6p3�µ 6p4�⌫ ]

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

5

8e4

q4[(p1.p3)(p2.p4) + (p1.p4)(p2.p3)]

M = e2(u�µv)gµ⌫q2

(v�⌫u)

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

Z

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

Z

Need to compute |Ma |2 |Mz |2 2Re(M*a Mz)

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

Z

Need to compute |Ma |2 |Mz |2 2Re(M*a Mz)

So for M Feynman diagram we need to compute different term

M2

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

Z

Need to compute |Ma |2 |Mz |2 2Re(M*a Mz)

So for M Feynman diagram we need to compute different term

M2

The number of diagram scales factorially with the number of particle

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

e+ e- > mu+ mu- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

mu+

3

mu-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

mu+

3

mu-

4

diagram 2 QCD=0, QED=2

Z

Need to compute |Ma |2 |Mz |2 2Re(M*a Mz)

So for M Feynman diagram we need to compute different term

M2

The number of diagram scales factorially with the number of particle

In practise possible up to 2>4

Mattelaer Olivier MadGraph5_aMC@NLO

Helicity• Evaluate M for fixed helicity of external particles

➡ Multiply M with M* -> |M|^2 ➡ Loop on Helicity and average the results

e+ e- > e+ e- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

e+

3

e-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

e+

3

e-

4

diagram 2 QCD=0, QED=2

e+

1

e+

3

a

e-2

e-4

diagram 3 QCD=0, QED=2

e+

1

e+

3

z

e-2

e-4

diagram 4 QCD=0, QED=2

7

Idea

M = (u e �µv)gµ⌫q2

(v e �⌫u)

Mattelaer Olivier MadGraph5_aMC@NLO

Helicity• Evaluate M for fixed helicity of external particles

➡ Multiply M with M* -> |M|^2 ➡ Loop on Helicity and average the results

e+ e- > e+ e- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

e+

3

e-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

e+

3

e-

4

diagram 2 QCD=0, QED=2

e+

1

e+

3

a

e-2

e-4

diagram 3 QCD=0, QED=2

e+

1

e+

3

z

e-2

e-4

diagram 4 QCD=0, QED=2

Numbers for given helicity and momenta

7

Idea

M = (u e �µv)gµ⌫q2

(v e �⌫u)

Mattelaer Olivier MadGraph5_aMC@NLO

Helicity• Evaluate M for fixed helicity of external particles

➡ Multiply M with M* -> |M|^2 ➡ Loop on Helicity and average the results

e+ e- > e+ e- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

e+

3

e-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

e+

3

e-

4

diagram 2 QCD=0, QED=2

e+

1

e+

3

a

e-2

e-4

diagram 3 QCD=0, QED=2

e+

1

e+

3

z

e-2

e-4

diagram 4 QCD=0, QED=2

Numbers for given helicity and momenta

Lines present in the code. {

7

Idea

M = (u e �µv)gµ⌫q2

(v e �⌫u)

v1 = fct(~p1,m1)

u2 = fct(~p2,m2)

v3 = fct(~p3,m3)

u4 = fct(~p4,m4)

Mattelaer Olivier MadGraph5_aMC@NLO

Helicity• Evaluate M for fixed helicity of external particles

➡ Multiply M with M* -> |M|^2 ➡ Loop on Helicity and average the results

e+ e- > e+ e- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

e+

3

e-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

e+

3

e-

4

diagram 2 QCD=0, QED=2

e+

1

e+

3

a

e-2

e-4

diagram 3 QCD=0, QED=2

e+

1

e+

3

z

e-2

e-4

diagram 4 QCD=0, QED=2

Numbers for given helicity and momenta

Lines present in the code. {

7

Idea

M = (u e �µv)gµ⌫q2

(v e �⌫u)

v1 = fct(~p1,m1)

u2 = fct(~p2,m2)

v3 = fct(~p3,m3)

u4 = fct(~p4,m4)

Mattelaer Olivier MadGraph5_aMC@NLO

Helicity• Evaluate M for fixed helicity of external particles

➡ Multiply M with M* -> |M|^2 ➡ Loop on Helicity and average the results

e+ e- > e+ e- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

e+

3

e-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

e+

3

e-

4

diagram 2 QCD=0, QED=2

e+

1

e+

3

a

e-2

e-4

diagram 3 QCD=0, QED=2

e+

1

e+

3

z

e-2

e-4

diagram 4 QCD=0, QED=2

Numbers for given helicity and momenta

Lines present in the code. {

7

Idea

M = (u e �µv)gµ⌫q2

(v e �⌫u)

v1 = fct(~p1,m1)

u2 = fct(~p2,m2)

v3 = fct(~p3,m3)

u4 = fct(~p4,m4)

Mattelaer Olivier MadGraph5_aMC@NLO

Helicity• Evaluate M for fixed helicity of external particles

➡ Multiply M with M* -> |M|^2 ➡ Loop on Helicity and average the results

e+ e- > e+ e- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

e+

3

e-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

e+

3

e-

4

diagram 2 QCD=0, QED=2

e+

1

e+

3

a

e-2

e-4

diagram 3 QCD=0, QED=2

e+

1

e+

3

z

e-2

e-4

diagram 4 QCD=0, QED=2

Numbers for given helicity and momentaCalculate propagator wavefunctions

Lines present in the code. {

7

Idea

M = (u e �µv)gµ⌫q2

(v e �⌫u)

v1 = fct(~p1,m1)

u2 = fct(~p2,m2)

v3 = fct(~p3,m3)

u4 = fct(~p4,m4)

Wa = fct(v1, u2,ma,�a)

Mattelaer Olivier MadGraph5_aMC@NLO

Helicity• Evaluate M for fixed helicity of external particles

➡ Multiply M with M* -> |M|^2 ➡ Loop on Helicity and average the results

e+ e- > e+ e- WEIGHTED=4 page 1/1

Diagrams made by MadGraph5

e+

1

e-

2

a

e+

3

e-

4

diagram 1 QCD=0, QED=2

e+

1

e-

2

z

e+

3

e-

4

diagram 2 QCD=0, QED=2

e+

1

e+

3

a

e-2

e-4

diagram 3 QCD=0, QED=2

e+

1

e+

3

z

e-2

e-4

diagram 4 QCD=0, QED=2

Numbers for given helicity and momentaCalculate propagator wavefunctionsFinally evaluate amplitude (c-number)

Lines present in the code. {

7

Idea

M = (u e �µv)gµ⌫q2

(v e �⌫u)

v1 = fct(~p1,m1)

u2 = fct(~p2,m2)

v3 = fct(~p3,m3)

u4 = fct(~p4,m4)

Wa = fct(v1, u2,ma,�a)M = fct(v3, u4,Wa)

Mattelaer Olivier MadGraph5_aMC@NLO

Comparison

8

M diag N particle

Analytical

Helicity

Recycling

M2

M

(N!)2

(N!) 2N

M (N − 1)! 2(N−1)

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

s~

2

gt

3

t~4

g

b~

6

b

b5

diagram 2 QCD=4, QED=0

s

1

s~

2

g

t

3

t~ 4g

b5

b~

6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

s~

2

gt

3

t~4

g

b~

6

b

b5

diagram 2 QCD=4, QED=0

s

1

s~

2

g

t

3

t~ 4g

b5

b~

6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both:

0 0

0

9

M1 M2

|M |2 = |M1 +M2|2

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

s~

2

gt

3

t~4

g

b~

6

b

b5

diagram 2 QCD=4, QED=0

s

1

s~

2

g

t

3

t~ 4g

b5

b~

6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

s~

2

gt

3

t~4

g

b~

6

b

b5

diagram 2 QCD=4, QED=0

s

1

s~

2

g

t

3

t~ 4g

b5

b~

6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both:

01

1

9

M1 M2

|M |2 = |M1 +M2|2

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

s~

2

gt

3

t~4

g

b~

6

b

b5

diagram 2 QCD=4, QED=0

s

1

s~

2

g

t

3

t~ 4g

b5

b~

6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

s~

2

gt

3

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g

b~

6

b

b5

diagram 2 QCD=4, QED=0

s

1

s~

2

g

t

3

t~ 4g

b5

b~

6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both:

Identical

1 1

1

9

M1 M2

|M |2 = |M1 +M2|2

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

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3

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g

b~

6

b

b5

diagram 2 QCD=4, QED=0

s

1

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t

3

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b5

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6

g

diagram 3 QCD=4, QED=0

s

1

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5

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g

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3

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4

diagram 4 QCD=4, QED=0

s

1

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2

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5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

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gt

3

t~4

g

b

5

b~

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diagram 1 QCD=4, QED=0

s

1

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6

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b5

diagram 2 QCD=4, QED=0

s

1

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3

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b5

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6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both:

6 6

6

9

M1 M2

|M |2 = |M1 +M2|2

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

s~

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3

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g

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6

b

b5

diagram 2 QCD=4, QED=0

s

1

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3

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6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

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5

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3

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4

diagram 4 QCD=4, QED=0

s

1

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2

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5

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g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

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s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

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gt

3

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6

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b5

diagram 2 QCD=4, QED=0

s

1

s~

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g

t

3

t~ 4g

b5

b~

6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both:

67

7

9

M1 M2

|M |2 = |M1 +M2|2

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

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3

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6

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b5

diagram 2 QCD=4, QED=0

s

1

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3

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6

g

diagram 3 QCD=4, QED=0

s

1

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5

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3

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4

diagram 4 QCD=4, QED=0

s

1

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2

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5

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g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

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s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

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3

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6

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b5

diagram 2 QCD=4, QED=0

s

1

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3

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b5

b~

6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both:

7

Identical

7

7

9

M1 M2

|M |2 = |M1 +M2|2

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

s~

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3

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6

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b5

diagram 2 QCD=4, QED=0

s

1

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3

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6

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diagram 3 QCD=4, QED=0

s

1

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3

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4

diagram 4 QCD=4, QED=0

s

1

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5

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g

t~

4

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3

diagram 5 QCD=4, QED=0

t

3

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b5

b~

6

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s

1

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s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

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2

gt

3

t~4

g

b

5

b~

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diagram 1 QCD=4, QED=0

s

1

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6

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b5

diagram 2 QCD=4, QED=0

s

1

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3

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6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

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b

5

b~6

g

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3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both:

Identical

8 8

8

9

M1 M2

|M |2 = |M1 +M2|2

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

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6

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b5

diagram 2 QCD=4, QED=0

s

1

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6

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diagram 3 QCD=4, QED=0

s

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diagram 4 QCD=4, QED=0

s

1

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4

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3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

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s

1

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s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

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diagram 1 QCD=4, QED=0

s

1

s~

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gt

3

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6

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b5

diagram 2 QCD=4, QED=0

s

1

s~

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g

t

3

t~ 4g

b5

b~

6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both:

89

9

9

M1 M2

|M |2 = |M1 +M2|2

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

b~6

diagram 1 QCD=4, QED=0

s

1

s~

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3

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6

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b5

diagram 2 QCD=4, QED=0

s

1

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3

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6

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diagram 3 QCD=4, QED=0

s

1

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5

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3

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4

diagram 4 QCD=4, QED=0

s

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5

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g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

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s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

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gt

3

t~4

g

b

5

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diagram 1 QCD=4, QED=0

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1

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b5

diagram 2 QCD=4, QED=0

s

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3

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6

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diagram 3 QCD=4, QED=0

s

1

s~

2

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b

5

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3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both:

810

10

9

M1 M2

|M |2 = |M1 +M2|2

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

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diagram 1 QCD=4, QED=0

s

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b5

diagram 2 QCD=4, QED=0

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6

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diagram 3 QCD=4, QED=0

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diagram 4 QCD=4, QED=0

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3

diagram 5 QCD=4, QED=0

t

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b5

b~

6

g

s

1

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s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

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gt

3

t~4

g

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5

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diagram 1 QCD=4, QED=0

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3

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6

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b5

diagram 2 QCD=4, QED=0

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3

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6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

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b

5

b~6

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t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both:

10 9

11

9

M1 M2

|M |2 = |M1 +M2|2

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

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diagram 1 QCD=4, QED=0

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1

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b5

diagram 2 QCD=4, QED=0

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diagram 3 QCD=4, QED=0

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3

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4

diagram 4 QCD=4, QED=0

s

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5

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g

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4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

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s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

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5

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diagram 1 QCD=4, QED=0

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1

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3

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6

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b5

diagram 2 QCD=4, QED=0

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1

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3

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6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

g

b

5

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g

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3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both:

10 10

12

9

M1 M2

|M |2 = |M1 +M2|2

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

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diagram 1 QCD=4, QED=0

s

1

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b5

diagram 2 QCD=4, QED=0

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diagram 3 QCD=4, QED=0

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3

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diagram 4 QCD=4, QED=0

s

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5

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g

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4

t t

3

diagram 5 QCD=4, QED=0

t

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b5

b~

6

g

s

1

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s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

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gt

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g

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5

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diagram 1 QCD=4, QED=0

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1

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6

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b5

diagram 2 QCD=4, QED=0

s

1

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3

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6

g

diagram 3 QCD=4, QED=0

s

1

s~

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b

5

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t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

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t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both:

10 10

12

2(N+1) 2(N+1)

9

M1 M2

|M |2 = |M1 +M2|2

Mattelaer Olivier MadGraph5_aMC@NLO

Real caseKnown

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

1

s~

2

gt

3

t~4

g

b

5

b~

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diagram 1 QCD=4, QED=0

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1

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b5

diagram 2 QCD=4, QED=0

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6

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diagram 3 QCD=4, QED=0

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3

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4

diagram 4 QCD=4, QED=0

s

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5

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t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

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b5

b~

6

g

s

1

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s~2

diagram 6 QCD=4, QED=0

s s~ > t t~ b b~ WEIGHTED=4 page 1/2

Diagrams made by MadGraph5

s

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gt

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g

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5

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diagram 1 QCD=4, QED=0

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1

s~

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gt

3

t~4

g

b~

6

b

b5

diagram 2 QCD=4, QED=0

s

1

s~

2

g

t

3

t~ 4g

b5

b~

6

g

diagram 3 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t

3

t~ t~

4

diagram 4 QCD=4, QED=0

s

1

s~

2

g

b

5

b~6

g

t~

4

t t

3

diagram 5 QCD=4, QED=0

t

3

t~ 4g

b5

b~

6

g

s

1

s

s~2

diagram 6 QCD=4, QED=0

Number of routines: Number of routines:

Number of routines for both: 12

10 102(N+1) 2(N+1)

N!*2(N+1) N! 10

Mattelaer Olivier MadGraph5_aMC@NLO

Comparison

11

M diag N particle

Analytical

Helicity

Recycling

M2

M

(N!)2

(N!) 2N

M (N − 1)! 2(N−1)

Mattelaer Olivier MadGraph5_aMC@NLO 12

M diag N particle

Analytical

Helicity

Recycling

Recursion Relation

Not used in Madgraph

M2

M

(N!)2

(N!) 2N

M (N − 1)! 2(N−1)

log(M) 2N 2(N−1)

Mattelaer Olivier MadGraph5_aMC@NLO

Comparison

13

M diag N particle 2 > 6

Analytical 1.6e9

Helicity 1.0e7

Recycling 6.5e5

Recursion Relation 3.2e4

M2

M

(N!)2

(N!) 2N

M (N − 1)! 2(N−1)

log(M) 2N 2(N−1)

Mattelaer Olivier MadGraph5_aMC@NLOBrussels October 2010  Tim Stelzer 

ALOHA ALOHA 

UFO  Helicity 

30  14

Mattelaer Olivier MadGraph5_aMC@NLOBrussels October 2010  Tim Stelzer 

ALOHA ALOHA 

UFO  Helicity 

30  14

Basically, any new operator can be handle by MG5/Pythia8 out of the box!

Mattelaer Olivier MadGraph5_aMC@NLO

• Numerical computation faster than analytical computation

• We are able to compute matrix-element➡ for large number of final state➡ for any BSM theory

15

To Remember

Mattelaer Olivier MadGraph5_aMC@NLO

Plan

16

•Details of the computation•Evaluation of matrix-element•Phase-Space integration

•What is MG5_aMC?

Mattelaer Olivier MadGraph5_aMC@NLO

Monte Carlo Integration

σ =1

2s

!|M|2dΦ(n)

Calculations of cross section or decay widths involve integrations over high-dimension phase space of very peaked functions:

17

Mattelaer Olivier MadGraph5_aMC@NLO

Monte Carlo Integration

σ =1

2s

!|M|2dΦ(n)

Calculations of cross section or decay widths involve integrations over high-dimension phase space of very peaked functions:

Dim[Φ(n)] ∼ 3n

17

Mattelaer Olivier MadGraph5_aMC@NLO

Monte Carlo Integration

σ =1

2s

!|M|2dΦ(n)

Calculations of cross section or decay widths involve integrations over high-dimension phase space of very peaked functions:

General and flexible method is needed

Dim[Φ(n)] ∼ 3n

17

Mattelaer Olivier MadGraph5_aMC@NLO 18

IntegrationI =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

Zdq2

(q2 �M2 + iM�)2

IN = 0.637 ± 0.307/√

N

ZdxC

Mattelaer Olivier MadGraph5_aMC@NLO 18

IntegrationI =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

Zdq2

(q2 �M2 + iM�)2

IN = 0.637 ± 0.307/√

N

ZdxC

V = VN = 0

• MonteCarlo• Trapezium• Simpson

Method of evaluation1/

pN

1/N4

1/N2

Mattelaer Olivier MadGraph5_aMC@NLO 18

IntegrationI =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

Zdq2

(q2 �M2 + iM�)2

IN = 0.637 ± 0.307/√

N

ZdxC

V = VN = 0

• MonteCarlo• Trapezium• Simpson

Method of evaluation1/

pN

1/N4

1/N2

simpson MC3 0,638 0,35 0,6367 0,8

20 0,63662 0,6100 0,636619 0,651000 0,636619 0,636

Mattelaer Olivier MadGraph5_aMC@NLO 19

IntegrationI =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

Zdq2

(q2 �M2 + iM�)2

IN = 0.637 ± 0.307/√

N

ZdxC

Method of evaluation1/

pN

1/N4

1/N2

More Dimension 1/pN

1/N2/d

1/N4/d

• MonteCarlo• Trapezium• Simpson

Mattelaer Olivier MadGraph5_aMC@NLO 20

IntegrationI =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

Zdq2

(q2 �M2 + iM�)2

IN = 0.637 ± 0.307/√

N

ZdxC

I =!

x2

x1

f(x)dx

V = (x2 − x1)

!x2

x1

[f(x)]2dx − I2 VN = (x2 − x1)2

1

N

N!

i=1

[f(x)]2 − I2

N

IN = (x2 − x1)1

N

N!

i=1

f(x)

Mattelaer Olivier MadGraph5_aMC@NLO 20

IntegrationI =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

Zdq2

(q2 �M2 + iM�)2

IN = 0.637 ± 0.307/√

N

ZdxC

I =!

x2

x1

f(x)dx

V = (x2 − x1)

!x2

x1

[f(x)]2dx − I2 VN = (x2 − x1)2

1

N

N!

i=1

[f(x)]2 − I2

N

IN = (x2 − x1)1

N

N!

i=1

f(x)

I = IN ±!

VN/N

Mattelaer Olivier MadGraph5_aMC@NLO 20

IntegrationI =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

Zdq2

(q2 �M2 + iM�)2

IN = 0.637 ± 0.307/√

N

ZdxC

I =!

x2

x1

f(x)dx

V = (x2 − x1)

!x2

x1

[f(x)]2dx − I2 VN = (x2 − x1)2

1

N

N!

i=1

[f(x)]2 − I2

N

IN = (x2 − x1)1

N

N!

i=1

f(x)

I = IN ±!

VN/N

V = VN = 0

Mattelaer Olivier MadGraph5_aMC@NLO 20

IntegrationI =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

Zdq2

(q2 �M2 + iM�)2

IN = 0.637 ± 0.307/√

N

ZdxC

I =!

x2

x1

f(x)dx

V = (x2 − x1)

!x2

x1

[f(x)]2dx − I2 VN = (x2 − x1)2

1

N

N!

i=1

[f(x)]2 − I2

N

IN = (x2 − x1)1

N

N!

i=1

f(x)

I = IN ±!

VN/N

V = VN = 0

Can be minimized!

Mattelaer Olivier MadGraph5_aMC@NLO 21

Importance Sampling

IN = 0.637 ± 0.307/√

N

I =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

Mattelaer Olivier MadGraph5_aMC@NLO 21

Importance Sampling

IN = 0.637 ± 0.307/√

N

I =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

I =

Z 1

0dx(1� cx2)

cos�⇡2x

�

(1� cx2)

Mattelaer Olivier MadGraph5_aMC@NLO 21

Importance Sampling

IN = 0.637 ± 0.307/√

N

I =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

=

! ξ2

ξ1

dξcos π

2x[ξ]

1−x[ξ]2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

I =

Z 1

0dx(1� cx2)

cos�⇡2x

�

(1� cx2)I =

Z 1

0dx(1� cx2)

cos�⇡2x

�

(1� cx2)

Mattelaer Olivier MadGraph5_aMC@NLO 21

Importance Sampling

IN = 0.637 ± 0.307/√

N

I =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

=

! ξ2

ξ1

dξcos π

2x[ξ]

1−x[ξ]2

≃ 1

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

I =

Z 1

0dx(1� cx2)

cos�⇡2x

�

(1� cx2)I =

Z 1

0dx(1� cx2)

cos�⇡2x

�

(1� cx2)

Mattelaer Olivier MadGraph5_aMC@NLO 21

Importance Sampling

IN = 0.637 ± 0.307/√

N

I =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

=

! ξ2

ξ1

dξcos π

2x[ξ]

1−x[ξ]2

≃ 1

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

I =

Z 1

0dx(1� cx2)

cos�⇡2x

�

(1� cx2)I =

Z 1

0dx(1� cx2)

cos�⇡2x

�

(1� cx2)

Mattelaer Olivier MadGraph5_aMC@NLO 21

Importance Sampling

IN = 0.637 ± 0.307/√

N

I =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

=

! ξ2

ξ1

dξcos π

2x[ξ]

1−x[ξ]2

IN = 0.637 ± 0.031/√

N

≃ 1

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

I =

Z 1

0dx(1� cx2)

cos�⇡2x

�

(1� cx2)I =

Z 1

0dx(1� cx2)

cos�⇡2x

�

(1� cx2)

Mattelaer Olivier MadGraph5_aMC@NLO 21

Importance Sampling

IN = 0.637 ± 0.307/√

N

I =

! 1

0

dx cosπ

2x

IN = 0.637 ± 0.307/√

N

=

! ξ2

ξ1

dξcos π

2x[ξ]

1−x[ξ]2

IN = 0.637 ± 0.031/√

N

≃ 1

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

I =

Z 1

0dx(1� cx2)

cos�⇡2x

�

(1� cx2)

The Phase-Space parametrization is important to have an efficient computation!

I =

Z 1

0dx(1� cx2)

cos�⇡2x

�

(1� cx2)

Mattelaer Olivier MadGraph5_aMC@NLO

•Generate the random point in a distribution which is close to the function to integrate.

•This is a change of variable, such that the function is flatter in this new variable.

•Needs to know an approximate function.

22

Importance SamplingKey Point

Adaptative Monte-Carlo•Create an approximation of the function on the flight!

Mattelaer Olivier MadGraph5_aMC@NLO 23

1. Creates bin such that each of them have the same contribution.➡Many bins where the function is large

2. Use the approximate for the importance sampling method.

Algorithm

Adaptative Monte-Carlo•Create an approximation of the function on the flight!

Mattelaer Olivier MadGraph5_aMC@NLO

•Events are generated according to our best knowledge of the function

➡Basic cut include in this “best knowledge”➡Custom cut are ignored

24

Cut Impact

No cut Run card cut Custom cut

Mattelaer Olivier MadGraph5_aMC@NLO 25

Cut Impact

No cut Run card cut Custom cut

Might miss the contribution and think it is just zero.

No cut Run card cut Custom cut

Mattelaer Olivier MadGraph5_aMC@NLO

Example: QCD 2 → 2

u u~ > g g QED=0 page 1/1

Diagrams made by MadGraph5

u

1

u~

2

g

3

g

4

g

diagram 1 QCD=2

u

1

g

3

u~

2

g

4

u

diagram 2 QCD=2

u

1

g

4

u~

2

g

3

u

diagram 3 QCD=2

u u~ > g g QED=0 page 1/1

Diagrams made by MadGraph5

u

1

u~

2

g

3

g

4

g

diagram 1 QCD=2

u

1

g

3

u~

2

g

4

u

diagram 2 QCD=2

u

1

g

4

u~

2

g

3

u

diagram 3 QCD=2

u u~ > g g QED=0 page 1/1

Diagrams made by MadGraph5

u

1

u~

2

g

3

g

4

g

diagram 1 QCD=2

u

1

g

3

u~

2

g

4

u

diagram 2 QCD=2

u

1

g

4

u~

2

g

3

u

diagram 3 QCD=2

/ 1

s=

1

(p1 + p2)2/ 1

t=

1

(p1 � p3)2/ 1

u=

1

(p1 � p4)2

Three very different pole structures contributing to the same matrix element.

26

Mattelaer Olivier MadGraph5_aMC@NLO

Let’s cut the problem in piece

27

|MT |2 =|M1 |2 + |M2 |2

|M1 |2 + |M2 |2 |MT |2

Z|Mtot|2 =

Z Pi |Mi|2Pj |Mj |2

|Mtot|2 =X

i

Z |Mi|2Pj |Mj |2

|Mtot|2

Mattelaer Olivier MadGraph5_aMC@NLO

Let’s cut the problem in piece

27

|MT |2 =|M1 |2 + |M2 |2

|M1 |2 + |M2 |2 |MT |2

⇡ 1

Z|Mtot|2 =

Z Pi |Mi|2Pj |Mj |2

|Mtot|2 =X

i

Z |Mi|2Pj |Mj |2

|Mtot|2

Mattelaer Olivier MadGraph5_aMC@NLO

Let’s cut the problem in piece

27

|MT |2 =|M1 |2 + |M2 |2

|M1 |2 + |M2 |2 |MT |2

⇡ 1

Z|Mtot|2 =

Z Pi |Mi|2Pj |Mj |2

|Mtot|2 =X

i

Z |Mi|2Pj |Mj |2

|Mtot|2

– One diagram is manageable– All other peaks taken care of by denominator sum

Key Idea

Mattelaer Olivier MadGraph5_aMC@NLO

Let’s cut the problem in piece

27

|MT |2 =|M1 |2 + |M2 |2

|M1 |2 + |M2 |2 |MT |2

⇡ 1

Z|Mtot|2 =

Z Pi |Mi|2Pj |Mj |2

|Mtot|2 =X

i

Z |Mi|2Pj |Mj |2

|Mtot|2

– One diagram is manageable– All other peaks taken care of by denominator sum

Key Idea

N Integral– Errors add in quadrature so no extra cost– Parallel in nature

Mattelaer Olivier MadGraph5_aMC@NLO 28

Z|Mtot|2 =

Z Pi |Mi|2Pj |Mj |2

|Mtot|2 =X

i

Z |Mi|2Pj |Mj |2

|Mtot|2

term of the above sum.

each term might not be gauge invariant

Mattelaer Olivier MadGraph5_aMC@NLO

What’s the difference between weighted and unweighted?

Weighted:

Same # of events in areas of phase space with very different probabilities:events must have different weights

29

Event generation

Mattelaer Olivier MadGraph5_aMC@NLO

# events is proportional to the probability of areas of phase space:events have all the sameweight (”unweighted”)

Events distributed as in nature

What’s the difference between weighted and unweighted?

Unweighted:

30

Event generation

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

31

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

31

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

31

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

31

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

Number between 0 and 1 (assuming positive function)-> re-interpret as the probability to keep the events

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

31

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

Number between 0 and 1 (assuming positive function)-> re-interpret as the probability to keep the events

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

P(xi)max( f )

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

31

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

Number between 0 and 1 (assuming positive function)-> re-interpret as the probability to keep the events

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

P(xi)max( f )

Let’s reduce the sample size by playing the lottery.For each events throw the dice and see if we keep or reject the events

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

31

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

Number between 0 and 1 (assuming positive function)-> re-interpret as the probability to keep the events

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

P(xi)max( f )

Let’s reduce the sample size by playing the lottery.For each events throw the dice and see if we keep or reject the events

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

P(xi)max( f ) ≃max( f )

N

n

∑i=1

1

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

f(x)

32

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

1. pick xi

f(x)

32

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

1. pick xi

f(x)2. calculate

32

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

f(xi)

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

1. pick xi

3. pick f(x)

2. calculate

32

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

y ∈ [0, max( f )]

f(xi)

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

1. pick xi

3. pick f(x)

2. calculate

4. Compare:if accept event,

32

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

y ∈ [0, max( f )]

y < f(xi)

f(xi)

Mattelaer Olivier MadGraph5_aMC@NLO

Event generation

1. pick xi

3. pick f(x)

2. calculate

4. Compare:if accept event,

else reject it.

32

∫ f(x)dx =1N

N

∑i=1

f(xi) =1N

N

∑i=1

f(xi)max( f )

max( f )

y ∈ [0, max( f )]

y < f(xi)

f(xi)

Mattelaer Olivier MadGraph5_aMC@NLO

MC integrator

33

Event generation

Mattelaer Olivier MadGraph5_aMC@NLO

MC integrator

O

dσ

dO

33

Event generation

Mattelaer Olivier MadGraph5_aMC@NLO

MC integrator

Acceptance-Rejection

O

dσ

dO

33

Event generation

Mattelaer Olivier MadGraph5_aMC@NLO

Event generator

MC integrator

Acceptance-Rejection

O

dσ

dO

33

Event generation

Mattelaer Olivier MadGraph5_aMC@NLO

Event generator

MC integrator

Acceptance-Rejection

O

dσ

dO

O

dσ

dO

33

Event generation

Mattelaer Olivier MadGraph5_aMC@NLO

Event generator

MC integrator

Acceptance-Rejection

☞ This is possible only if f(x)<∞ AND has definite sign!

O

dσ

dO

O

dσ

dO

33

Event generation

Mattelaer Olivier MadGraph5_aMC@NLO 34

Monte-Carlo Summary

• Slow Convergence (especially in low number of Dimension)

• Need to know the function • Impact on cut

Bad Point

Mattelaer Olivier MadGraph5_aMC@NLO 34

Monte-Carlo Summary

• Slow Convergence (especially in low number of Dimension)

• Need to know the function • Impact on cut

Bad Point

Good Point

•Complex area of Integration•Easy Error estimate•quick estimation of the integral•Possibility to have unweighted events

Mattelaer Olivier MadGraph5_aMC@NLO 35

Tree (B)SM

NLO(QCD)(SM)

NLO(QCD)(BSM)

NLO(EW)(SM)

LoopInduced (B)SM

Fix Order

+Parton Shower

Merged Sample

Type of generation

!"#$%&'()$((&*&+#,&-./."%&"0&12345!"#$%&'()$((&*&+#,&-./."%&"0&12345 67

!"#$%&'()'*+&,-./%0

s~ c > w+ g WEIGHTED=3 QED=1 QCD=1 [ all= QCD ] page 1/2

Diagrams made by MadGraph5_aMC@NLO

c2 w+ 3

s~

s~1

g4

s~

sg

loop diagram 1 QCD=3, QED=1

s~

1

g4

s~

c2

g

c~w+

3

s~

loop diagram 2 QCD=3, QED=1

c2

w+ 3

s~

s~

1

s~g

g

4

g

loop diagram 3 QCD=3, QED=1

c2

w+ 3

s~

s~

1

gs~

g

4

s~

loop diagram 4 QCD=3, QED=1

c2

g4

c~

s~

1

gs~

w+

3

c~

loop diagram 5 QCD=3, QED=1

s~

1

s~

g

c2

c

g

4

c

w+

3

loop diagram 6 QCD=3, QED=1

NLO corrections

NNLO corrections

N3LO or NNNLO corrections

LO predictions

⇤ = ⇤Born

⇤1 +

�s

2⇥⇤(1) +

��s

2⇥

⇥2⇤(2) +

��s

2⇥

⇥3⇤(3) + . . .

⌅

Mattelaer Olivier MadGraph5_aMC@NLO 35

Tree (B)SM

NLO(QCD)(SM)

NLO(QCD)(BSM)

NLO(EW)(SM)

LoopInduced (B)SM

Fix Order

+Parton Shower

Merged Sample

Type of generation

!"#$%&'()$((&*&+#,&-./."%&"0&12345!"#$%&'()$((&*&+#,&-./."%&"0&12345 67

!"#$%&'()'*+&,-./%0

s~ c > w+ g WEIGHTED=3 QED=1 QCD=1 [ all= QCD ] page 1/2

Diagrams made by MadGraph5_aMC@NLO

c2 w+ 3

s~

s~1

g4

s~

sg

loop diagram 1 QCD=3, QED=1

s~

1

g4

s~

c2

g

c~w+

3

s~

loop diagram 2 QCD=3, QED=1

c2

w+ 3

s~

s~

1

s~g

g

4

g

loop diagram 3 QCD=3, QED=1

c2

w+ 3

s~

s~

1

gs~

g

4

s~

loop diagram 4 QCD=3, QED=1

c2

g4

c~

s~

1

gs~

w+

3

c~

loop diagram 5 QCD=3, QED=1

s~

1

s~

g

c2

c

g

4

c

w+

3

loop diagram 6 QCD=3, QED=1

Mattelaer Olivier MadGraph5_aMC@NLO 35

Tree (B)SM

NLO(QCD)(SM)

NLO(QCD)(BSM)

NLO(EW)(SM)

LoopInduced (B)SM

Fix Order

+Parton Shower

Merged Sample

Type of generation

!"#$%&'()$((&*&+#,&-./."%&"0&12345!"#$%&'()$((&*&+#,&-./."%&"0&12345 67

!"#$%&'()'*+&,-./%0

s~ c > w+ g WEIGHTED=3 QED=1 QCD=1 [ all= QCD ] page 1/2

Diagrams made by MadGraph5_aMC@NLO

c2 w+ 3

s~

s~1

g4

s~

sg

loop diagram 1 QCD=3, QED=1

s~

1

g4

s~

c2

g

c~w+

3

s~

loop diagram 2 QCD=3, QED=1

c2

w+ 3

s~

s~

1

s~g

g

4

g

loop diagram 3 QCD=3, QED=1

c2

w+ 3

s~

s~

1

gs~

g

4

s~

loop diagram 4 QCD=3, QED=1

c2

g4

c~

s~

1

gs~

w+

3

c~

loop diagram 5 QCD=3, QED=1

s~

1

s~

g

c2

c

g

4

c

w+

3

loop diagram 6 QCD=3, QED=1

ME ↓

PS →

Mattelaer Olivier MadGraph5_aMC@NLO

LO Feature

36

Mattelaer Olivier MadGraph5_aMC@NLO

LO Feature

36

Γ = ?Auto-Width

Parameter scan

~ 20% agreement

unmatched with ME/PS matching

Importance of the MC

very bad close to deg.!region

Recast of efficiencies in gluino simplified mod’

with K. Sakurai, M. Papucci, L. Zeune

ATOM/experiment ATOM/experiment

Mattelaer Olivier MadGraph5_aMC@NLO

LO Feature

36

Γ = ?Auto-Width

Parameter scan

~ 20% agreement

unmatched with ME/PS matching

Importance of the MC

very bad close to deg.!region

Recast of efficiencies in gluino simplified mod’

with K. Sakurai, M. Papucci, L. Zeune

ATOM/experiment ATOM/experiment

normalized to one

Systematics

BSM re-weighting|Mnew |2 / |Mold |2

Mattelaer Olivier MadGraph5_aMC@NLO

LO Feature

36

Interference

Mattelaer Olivier Looping up to be MAD 8

Some New FunctionInterference

NP^2==1 NP^2<=1

2

O(⇤2)

+

O(⇤)

2

O(⇤0)

+

NP^2>0

Γ = ?Auto-Width

Parameter scan

~ 20% agreement

unmatched with ME/PS matching

Importance of the MC

very bad close to deg.!region

Recast of efficiencies in gluino simplified mod’

with K. Sakurai, M. Papucci, L. Zeune

ATOM/experiment ATOM/experiment

normalized to one

Systematics

BSM re-weighting|Mnew |2 / |Mold |2

Mattelaer Olivier MadGraph5_aMC@NLO

LO Feature

36

Interference

Mattelaer Olivier Looping up to be MAD 8

Some New FunctionInterference

NP^2==1 NP^2<=1

2

O(⇤2)

+

O(⇤)

2

O(⇤0)

+

NP^2>0

Γ = ?Auto-Width

Parameter scan

~ 20% agreement

unmatched with ME/PS matching

Importance of the MC

very bad close to deg.!region

Recast of efficiencies in gluino simplified mod’

with K. Sakurai, M. Papucci, L. Zeune

ATOM/experiment ATOM/experiment

normalized to one

Systematics

BSM re-weighting|Mnew |2 / |Mold |2

Plugin

Interfacez >

e+ e

-

page

1/1

Diag

ram

s m

ade

by M

adG

raph

5_aM

C@NL

O

e+

2

e-

3

z1

dia

gram

1

QCD

=0, Q

ED=1

Mattelaer Olivier MadGraph5_aMC@NLO

LO Feature

36

Interference

Mattelaer Olivier Looping up to be MAD 8

Some New FunctionInterference

NP^2==1 NP^2<=1

2

O(⇤2)

+

O(⇤)

2

O(⇤0)

+

NP^2>0

Narrow-width

Γ = ?Auto-Width

Parameter scan

~ 20% agreement

unmatched with ME/PS matching

Importance of the MC

very bad close to deg.!region

Recast of efficiencies in gluino simplified mod’

with K. Sakurai, M. Papucci, L. Zeune

ATOM/experiment ATOM/experiment

normalized to one

Systematics

BSM re-weighting|Mnew |2 / |Mold |2

Plugin

Interfacez >

e+ e

-

page

1/1

Diag

ram

s m

ade

by M

adG

raph

5_aM

C@NL

O

e+

2

e-

3

z1

dia

gram

1

QCD

=0, Q

ED=1

Mattelaer Olivier MadGraph5_aMC@NLO 37

Decaypage 1/10

Diagrams made by MadGraph5_aMC@NLO

u1

u3

a

c2

c4

a

ve~

8

e- 7w-

e+ 5

ve6

w+

diagram 1 HIG=0, HIW=0, NP=0, QCD=0, QED=6

u1

u3

a

c2

c4

a

ve~

8

e- 7w-

e+ 5

ve6

w+

diagram 2 HIG=0, HIW=0, NP=2, QCD=0, QED

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 3 HIG=0, HIW=0, NP=2, QCD=0, QED=5

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 4 HIG=0, HIW=0, NP=2, QCD=0, QED

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 5 HIG=0, HIW=0, NP=0, QCD=0, QED=6

c2c 4

a

u1

u3

ave~

8

e- 7w-w+

e+ 5

ve6

w+

diagram 6 HIG=0, HIW=0, NP=2, QCD=0, QED

Resonant Diagram

Mattelaer Olivier MadGraph5_aMC@NLO

• Process complicated to have the full process➡Including off-shell contribution

37

DecayNon Resonant Diagram

Problem

c u > c u e+ ve e- ve~ NP=2 WEIGHTED=20 HIW=1 HIG=1 page 3/12

Diagrams made by MadGraph5

c

1

c3

g e+5

ve 6w+

u2

ue- 7ve

u

4

z

ve~ 8

diagram 13 HIG=0, HIW=0, NP=0, QCD=2, QED=4

c

1

c3

g e+5

ve 6w+

u2

u ve~ 8e+u

4

ae- 7

diagram 14 HIG=0, HIW=0, NP=0, QCD=2, QED

c

1

c3

g e+5

ve 6w+

u2

u ve~ 8e+u

4

ze- 7

diagram 15 HIG=0, HIW=0, NP=0, QCD=2, QED=4

c1

c3

g

e+5

ve 6w+

u4

u~e- 7ve

u2

zve~ 8

diagram 16 HIG=0, HIW=0, NP=0, QCD=2, QED

c1

c3

g

e+5

ve 6w+

u4

u~ve~ 8e+

u2

ae- 7

diagram 17 HIG=0, HIW=0, NP=0, QCD=2, QED=4

c1

c3

g

e+5

ve 6w+

u4

u~ve~ 8e+

u2

ze- 7

diagram 18 HIG=0, HIW=0, NP=0, QCD=2, QED

page 1/10

Diagrams made by MadGraph5_aMC@NLO

u1

u3

a

c2

c4

a

ve~

8

e- 7w-

e+ 5

ve6

w+

diagram 1 HIG=0, HIW=0, NP=0, QCD=0, QED=6

u1

u3

a

c2

c4

a

ve~

8

e- 7w-

e+ 5

ve6

w+

diagram 2 HIG=0, HIW=0, NP=2, QCD=0, QED

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 3 HIG=0, HIW=0, NP=2, QCD=0, QED=5

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 4 HIG=0, HIW=0, NP=2, QCD=0, QED

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 5 HIG=0, HIW=0, NP=0, QCD=0, QED=6

c2c 4

a

u1

u3

ave~

8

e- 7w-w+

e+ 5

ve6

w+

diagram 6 HIG=0, HIW=0, NP=2, QCD=0, QED

Resonant Diagram

Mattelaer Olivier MadGraph5_aMC@NLO

• Process complicated to have the full process➡Including off-shell contribution

37

Decay

Solution• Only keep on-shell contribution

Non Resonant Diagram

Problem

c u > c u e+ ve e- ve~ NP=2 WEIGHTED=20 HIW=1 HIG=1 page 3/12

Diagrams made by MadGraph5

c

1

c3

g e+5

ve 6w+

u2

ue- 7ve

u

4

z

ve~ 8

diagram 13 HIG=0, HIW=0, NP=0, QCD=2, QED=4

c

1

c3

g e+5

ve 6w+

u2

u ve~ 8e+u

4

ae- 7

diagram 14 HIG=0, HIW=0, NP=0, QCD=2, QED

c

1

c3

g e+5

ve 6w+

u2

u ve~ 8e+u

4

ze- 7

diagram 15 HIG=0, HIW=0, NP=0, QCD=2, QED=4

c1

c3

g

e+5

ve 6w+

u4

u~e- 7ve

u2

zve~ 8

diagram 16 HIG=0, HIW=0, NP=0, QCD=2, QED

c1

c3

g

e+5

ve 6w+

u4

u~ve~ 8e+

u2

ae- 7

diagram 17 HIG=0, HIW=0, NP=0, QCD=2, QED=4

c1

c3

g

e+5

ve 6w+

u4

u~ve~ 8e+

u2

ze- 7

diagram 18 HIG=0, HIW=0, NP=0, QCD=2, QED

page 1/10

Diagrams made by MadGraph5_aMC@NLO

u1

u3

a

c2

c4

a

ve~

8

e- 7w-

e+ 5

ve6

w+

diagram 1 HIG=0, HIW=0, NP=0, QCD=0, QED=6

u1

u3

a

c2

c4

a

ve~

8

e- 7w-

e+ 5

ve6

w+

diagram 2 HIG=0, HIW=0, NP=2, QCD=0, QED

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 3 HIG=0, HIW=0, NP=2, QCD=0, QED=5

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 4 HIG=0, HIW=0, NP=2, QCD=0, QED

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 5 HIG=0, HIW=0, NP=0, QCD=0, QED=6

c2c 4

a

u1

u3

ave~

8

e- 7w-w+

e+ 5

ve6

w+

diagram 6 HIG=0, HIW=0, NP=2, QCD=0, QED

Resonant Diagram

Mattelaer Olivier MadGraph5_aMC@NLO 38

Theory

�full = �prod ⇤ (BR+O(�

M))

Comment

Narrow-Width Approx.Z

dq2����

1

q2 �M2 � iM�

����2

⇡ ⇡

M��(q2 �M2)

Mattelaer Olivier MadGraph5_aMC@NLO

• This is an Approximation!• This force the particle to be on-shell!

• Recover by re-introducing the Breit-wigner up-to a cut-off

38

Theory

�full = �prod ⇤ (BR+O(�

M))

Comment

Narrow-Width Approx.Z

dq2����

1

q2 �M2 � iM�

����2

⇡ ⇡

M��(q2 �M2)

Mattelaer Olivier MadGraph5_aMC@NLO

Decay chain

KIAS MadGrace school, Oct 24-29 2011 MadGraph 5 Olivier Mattelaer

Decay chains

• p p > t t~ w+, (t > w+ b, w+ > l+ vl), \ (t~ > w- b~, w- > j j), \ w+ > l+ vl

• Separately generate core process and each decay- Decays generated with the decaying particle as resulting wavefunction

• Iteratively combine decays and core processes

• Difficulty: Multiple diagrams in decays

mardi 25 octobre 2011

39

very long decay chains possible to simulate

directly in MadGraph!

Mattelaer Olivier MadGraph5_aMC@NLO

Decay chain

KIAS MadGrace school, Oct 24-29 2011 MadGraph 5 Olivier Mattelaer

Decay chains

• p p > t t~ w+, (t > w+ b, w+ > l+ vl), \ (t~ > w- b~, w- > j j), \ w+ > l+ vl

• Separately generate core process and each decay- Decays generated with the decaying particle as resulting wavefunction

• Iteratively combine decays and core processes

• Difficulty: Multiple diagrams in decays

mardi 25 octobre 2011

39

very long decay chains possible to simulate

directly in MadGraph!

• Full spin-correlation•Off-shell effects (up to cut-off)•NWA not used for the cross-section

Mattelaer Olivier MadGraph5_aMC@NLO 40

MadSpin

0.0001

0.001

0.01

0 25 50 75 100 125 150 175 200

1/σ

dσ

/dp T

(l+ ) [1/

GeV

]

pT(l+) [GeV]

Scalar Higgs

NLO Spin correlations onLO Spin correlations on

NLO Spin correlations offLO Spin correlations off

0.4

0.45

0.5

0.55

0.6

-1 -0.5 0 0.5 1

1/σ

dσ

/dco

s(φ)

cos(φ)

Scalar Higgs

NLO Spin correlations onLO Spin correlations on

NLO Spin correlations offLO Spin correlations off

Figure 5: Next-to-leading-order cross sections differential in pT (l+) (left pane) and in cosφ (rightpane) for ttH events with or without spin correlation effects. For comparison, also the leading-order results are shown. Events were generated with aMC@NLO, then decayed with MadSpin,and finally passed to Herwig for shower and hadronization.

0.0001

0.001

0.01

0 25 50 75 100 125 150 175 200

1/σ

dσ

/dp T

(l+ ) [1/

GeV

]

pT(l+) [GeV]

Pseudoscalar Higgs

NLO Spin correlations onNLO Spin correlations off

0.4

0.45

0.5

0.55

0.6

-1 -0.5 0 0.5 1

1/σ

dσ

/dco

s(φ)

cos(φ)

Pseudoscalar Higgs

NLO Spin correlations onNLO Spin correlations off

Figure 6: Next-to-leading-order cross sections differential in pT (l+) (left pane) and in cosφ(right pane) for ttA events with or without spin correlation effects. Events were generated withaMC@NLO, then decayed with MadSpin, and finally passed to Herwig for shower and hadroniza-tion.

that preserving spin correlations is more important than including NLO corrections for this

observable. However, we observe that the inclusion of both, as it is done here, is necessary

for an accurate prediction of the distribution of events with respect to cos(φ). In general, a

scheme including both spin correlation effects and QCD corrections is preferred: it retains

the good features of a NLO calculation, i.e. reduced uncertainties due to scale dependence

(not shown), while keeping the correlations between the top decay products.

The results for the pseudo-scalar Higgs boson are shown in Figure 6. The effects of the

spin correlations on the transverse momentum of the charged lepton are similar as in the

case of a scalar Higgs boson: about 10% at small pT , increasing to about 40% at pT = 200

GeV. On the other hand, the cos(φ) does not show any significant effect from the spin-

correlations. Therefore this observable could possibly help in determining the CP nature of

the Higgs boson, underlining the importance of the inclusion of the spin correlation effects.

– 14 –

Decay as post-processing Independently of event generationBut same accuracy (spin-correlation)Use NWA for cross-section

t t > w+ b

Mattelaer Olivier MadGraph5_aMC@NLO

Very small width

• Slows down the code• Can lead to numerical instability

41

Γ < 10−8M

Mattelaer Olivier MadGraph5_aMC@NLO

Very small width

• Slows down the code• Can lead to numerical instability

41

Γ < 10−8M

Solution

• Use a Fake-Width for the evaluation of the matrix-element

• Correct cross-section according to NWA formula Γfake

Γtrue

Mattelaer Olivier MadGraph5_aMC@NLO 42

What to remember•Analytical computation can be slower than numerical method

•Any BSM model are supported (at LO) •Phase Space integration are slow

•need knowledge of the function•cuts can be problematic

•Event generation are from free.•All this are automated in MG5_aMC@NLO

• Important to know the physical hypothesis

M

ADGRAPH5

aMC@NLO

Mattelaer Olivier MadGraph5_aMC@NLO

Plan

43

•What is MG5_aMC? •Details of the computation

•Evaluation of matrix-element•Phase-Space integration

•Tools/functionality of MG5_aMC

Mattelaer Olivier MadGraph5_aMC@NLO

List of package

44

• SysCalc (computation of systematics)• MadWidth (computation of width in NWA)• MadSpin (decay with full spin-correlation)• Re-Weighting (change of the weight of an event)• Shower / Detector Interface• MadWeight (Matrix-Element Method)• Interference• MadAnalysis5• Tau Decay• MadDM• GPU

Mattelaer Olivier MadGraph5_aMC@NLO 45

2-body decayh > b b~ page 1/1

Diagrams made by MadGraph5_aMC@NLO

b

2

b~

3

h1

diagram 1 QCD=0, QED=1

2 body decay

� =1

2MS

Zd�2|M|2

Mattelaer Olivier MadGraph5_aMC@NLO

•By Lorentz Invariance the matrix element is constant over the phase-space.

45

2-body decayh > b b~ page 1/1

Diagrams made by MadGraph5_aMC@NLO

b

2

b~

3

h1

diagram 1 QCD=0, QED=1

2 body decay

� =1

2MS

Zd�2|M|2

� =

p�(M2,m2

1,m22)|M|2

16⇡SM3

�(M2,m21,m

22) =

�M2 �m2

1 �m22

�2 � 4m21m

22

Mattelaer Olivier MadGraph5_aMC@NLO

•By Lorentz Invariance the matrix element is constant over the phase-space.

45

2-body decayh > b b~ page 1/1

Diagrams made by MadGraph5_aMC@NLO

b

2

b~

3

h1

diagram 1 QCD=0, QED=1

2 body decay

� =1

2MS

Zd�2|M|2

� =

p�(M2,m2

1,m22)|M|2

16⇡SM3

�(M2,m21,m

22) =

�M2 �m2

1 �m22

�2 � 4m21m

22

•Calculable analytically by FeynRules

Mattelaer Olivier MadGraph5_aMC@NLO

•Use FeynRules formula (instateneous)

46

MadWidth hep-ph/1402.1178

2-body

Mattelaer Olivier MadGraph5_aMC@NLO

•Use FeynRules formula (instateneous)

46

MadWidth hep-ph/1402.1178

2-body

Fast-Estimation of 3-body•Only use 2-body decay and PS factor

Mattelaer Olivier MadGraph5_aMC@NLO

•Use FeynRules formula (instateneous)

46

MadWidth hep-ph/1402.1178

2-body

Fast-Estimation of 3-body•Only use 2-body decay and PS factor

Relevant?

Mattelaer Olivier MadGraph5_aMC@NLO

•Use FeynRules formula (instateneous)

46

MadWidth hep-ph/1402.1178

2-body

Fast-Estimation of 3-body•Only use 2-body decay and PS factor

Relevant?

DONE

No

Mattelaer Olivier MadGraph5_aMC@NLO

•Use FeynRules formula (instateneous)

46

MadWidth hep-ph/1402.1178

2-body

Fast-Estimation of 3-body•Only use 2-body decay and PS factor

Relevant?

Channel Generation•Remove Sequence of 2-body/radiation diagram

DONE

NoMaybe

Mattelaer Olivier MadGraph5_aMC@NLO

•Use FeynRules formula (instateneous)

46

MadWidth hep-ph/1402.1178

2-body

Fast-Estimation of 3-body•Only use 2-body decay and PS factor

Relevant?

Channel Generation•Remove Sequence of 2-body/radiation diagram

Estimation of 3-body•Based on the diagram. Approx. PS/Matrix-Element

DONE

Relevant?

NoMaybe

Mattelaer Olivier MadGraph5_aMC@NLO

•Use FeynRules formula (instateneous)

46

MadWidth hep-ph/1402.1178

2-body

Fast-Estimation of 3-body•Only use 2-body decay and PS factor

Relevant?

Channel Generation•Remove Sequence of 2-body/radiation diagram

Estimation of 3-body•Based on the diagram. Approx. PS/Matrix-Element

DONE

Relevant?

NoMaybe

No

Mattelaer Olivier MadGraph5_aMC@NLO

•Use FeynRules formula (instateneous)

46

MadWidth hep-ph/1402.1178

2-body

Fast-Estimation of 3-body•Only use 2-body decay and PS factor

Relevant?

Channel Generation•Remove Sequence of 2-body/radiation diagram

Estimation of 3-body•Based on the diagram. Approx. PS/Matrix-Element

DONE

Relevant?

Numerical Integration

NoMaybe

No

Yes?

Mattelaer Olivier MadGraph5_aMC@NLO

•Use FeynRules formula (instateneous)

46

MadWidth hep-ph/1402.1178

2-body

Fast-Estimation of 3-body•Only use 2-body decay and PS factor

Relevant?

Channel Generation•Remove Sequence of 2-body/radiation diagram

Estimation of 3-body•Based on the diagram. Approx. PS/Matrix-Element

DONE

Relevant?

Numerical Integration

4

4

NoMaybe

No

Yes?

Mattelaer Olivier MadGraph5_aMC@NLO 47

MadWidth

Limitation• Only LO• No Loop Induced Decay• Valid in Narrow-width approximation• No hadronization effect

Lesson• Be aware of code limitation• Quite often those are not checked.

Mattelaer Olivier MadGraph5_aMC@NLO 48

Decaypage 1/10

Diagrams made by MadGraph5_aMC@NLO

u1

u3

a

c2

c4

a

ve~

8

e- 7w-

e+ 5

ve6

w+

diagram 1 HIG=0, HIW=0, NP=0, QCD=0, QED=6

u1

u3

a

c2

c4

a

ve~

8

e- 7w-

e+ 5

ve6

w+

diagram 2 HIG=0, HIW=0, NP=2, QCD=0, QED

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 3 HIG=0, HIW=0, NP=2, QCD=0, QED=5

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 4 HIG=0, HIW=0, NP=2, QCD=0, QED

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 5 HIG=0, HIW=0, NP=0, QCD=0, QED=6

c2c 4

a

u1

u3

ave~

8

e- 7w-w+

e+ 5

ve6

w+

diagram 6 HIG=0, HIW=0, NP=2, QCD=0, QED

Resonant Diagram

Mattelaer Olivier MadGraph5_aMC@NLO

• Process too complicated to compute all the Feynman Diagram

48

DecayNon Resonant Diagram

Problem

c u > c u e+ ve e- ve~ NP=2 WEIGHTED=20 HIW=1 HIG=1 page 3/12

Diagrams made by MadGraph5

c

1

c3

g e+5

ve 6w+

u2

ue- 7ve

u

4

z

ve~ 8

diagram 13 HIG=0, HIW=0, NP=0, QCD=2, QED=4

c

1

c3

g e+5

ve 6w+

u2

u ve~ 8e+u

4

ae- 7

diagram 14 HIG=0, HIW=0, NP=0, QCD=2, QED

c

1

c3

g e+5

ve 6w+

u2

u ve~ 8e+u

4

ze- 7

diagram 15 HIG=0, HIW=0, NP=0, QCD=2, QED=4

c1

c3

g

e+5

ve 6w+

u4

u~e- 7ve

u2

zve~ 8

diagram 16 HIG=0, HIW=0, NP=0, QCD=2, QED

c1

c3

g

e+5

ve 6w+

u4

u~ve~ 8e+

u2

ae- 7

diagram 17 HIG=0, HIW=0, NP=0, QCD=2, QED=4

c1

c3

g

e+5

ve 6w+

u4

u~ve~ 8e+

u2

ze- 7

diagram 18 HIG=0, HIW=0, NP=0, QCD=2, QED

page 1/10

Diagrams made by MadGraph5_aMC@NLO

u1

u3

a

c2

c4

a

ve~

8

e- 7w-

e+ 5

ve6

w+

diagram 1 HIG=0, HIW=0, NP=0, QCD=0, QED=6

u1

u3

a

c2

c4

a

ve~

8

e- 7w-

e+ 5

ve6

w+

diagram 2 HIG=0, HIW=0, NP=2, QCD=0, QED

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 3 HIG=0, HIW=0, NP=2, QCD=0, QED=5

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 4 HIG=0, HIW=0, NP=2, QCD=0, QED

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 5 HIG=0, HIW=0, NP=0, QCD=0, QED=6

c2c 4

a

u1

u3

ave~

8

e- 7w-w+

e+ 5

ve6

w+

diagram 6 HIG=0, HIW=0, NP=2, QCD=0, QED

Resonant Diagram

Mattelaer Olivier MadGraph5_aMC@NLO

• Process too complicated to compute all the Feynman Diagram

48

Decay

Solution• Only keep on-shell contribution

Non Resonant Diagram

Problem

c u > c u e+ ve e- ve~ NP=2 WEIGHTED=20 HIW=1 HIG=1 page 3/12

Diagrams made by MadGraph5

c

1

c3

g e+5

ve 6w+

u2

ue- 7ve

u

4

z

ve~ 8

diagram 13 HIG=0, HIW=0, NP=0, QCD=2, QED=4

c

1

c3

g e+5

ve 6w+

u2

u ve~ 8e+u

4

ae- 7

diagram 14 HIG=0, HIW=0, NP=0, QCD=2, QED

c

1

c3

g e+5

ve 6w+

u2

u ve~ 8e+u

4

ze- 7

diagram 15 HIG=0, HIW=0, NP=0, QCD=2, QED=4

c1

c3

g

e+5

ve 6w+

u4

u~e- 7ve

u2

zve~ 8

diagram 16 HIG=0, HIW=0, NP=0, QCD=2, QED

c1

c3

g

e+5

ve 6w+

u4

u~ve~ 8e+

u2

ae- 7

diagram 17 HIG=0, HIW=0, NP=0, QCD=2, QED=4

c1

c3

g

e+5

ve 6w+

u4

u~ve~ 8e+

u2

ze- 7

diagram 18 HIG=0, HIW=0, NP=0, QCD=2, QED

page 1/10

Diagrams made by MadGraph5_aMC@NLO

u1

u3

a

c2

c4

a

ve~

8

e- 7w-

e+ 5

ve6

w+

diagram 1 HIG=0, HIW=0, NP=0, QCD=0, QED=6

u1

u3

a

c2

c4

a

ve~

8

e- 7w-

e+ 5

ve6

w+

diagram 2 HIG=0, HIW=0, NP=2, QCD=0, QED

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 3 HIG=0, HIW=0, NP=2, QCD=0, QED=5

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 4 HIG=0, HIW=0, NP=2, QCD=0, QED

c2c 4

ave~ 8

e-7

w-

u1

u3

ae+

5

ve 6w+w-

diagram 5 HIG=0, HIW=0, NP=0, QCD=0, QED=6

c2c 4

a

u1

u3

ave~

8

e- 7w-w+

e+ 5

ve6

w+

diagram 6 HIG=0, HIW=0, NP=2, QCD=0, QED

Resonant Diagram

Mattelaer Olivier MadGraph5_aMC@NLO 49

Theory

�full = �prod ⇤ (BR+O(�

M))

Comment

Narrow-Width Approx.Z

dq2����

1

q2 �M2 � iM�

����2

⇡ ⇡

M��(q2 �M2)

Mattelaer Olivier MadGraph5_aMC@NLO

• This is an Approximation!• This force the particle to be on-shell!

• Recover by re-introducing the Breit-wigner up-to a cut-off

49

Theory

�full = �prod ⇤ (BR+O(�

M))

Comment

Narrow-Width Approx.Z

dq2����

1

q2 �M2 � iM�

����2

⇡ ⇡

M��(q2 �M2)

Mattelaer Olivier MadGraph5_aMC@NLO

KIAS MadGrace school, Oct 24-29 2011 MadGraph 5 Olivier Mattelaer

Decay chains

• p p > t t~ w+, (t > w+ b, w+ > l+ vl), \ (t~ > w- b~, w- > j j), \ w+ > l+ vl

• Separately generate core process and each decay- Decays generated with the decaying particle as resulting wavefunction

• Iteratively combine decays and core processes

• Difficulty: Multiple diagrams in decays

mardi 25 octobre 2011

50

Mattelaer Olivier MadGraph5_aMC@NLO

•Decay chains retain full matrix element for the diagrams compatible with the decay

• Full spin correlations (within and between decays)

•Full width effects•However, no interference with non-resonant diagrams ➡ Description only valid close to pole

mass➡ Cutoff at |m ± nΓ| where n is set in

run_card.

51

Decay chains

Mattelaer Olivier MadGraph5_aMC@NLO

Decay chains

Thanks to developments in MadEvent, also (very) long decay chains possible to simulate directly in MadGraph!

52

Mattelaer Olivier MadGraph5_aMC@NLO 53

MadSpin

One Event

offshell spin unweighted

No No YES

YES No No

YES YES No

YES YES YES

[Frixione, Leanen, Motylinski,Webber (2007)]

[Artoisenet, OM et al. 1212.3460]

Mattelaer Olivier MadGraph5_aMC@NLO 53

MadSpin

One Event

Decay Events

- smear the mass- flat decay

offshell spin unweighted

No No YES

YES No No

YES YES No

YES YES YES

[Frixione, Leanen, Motylinski,Webber (2007)]

[Artoisenet, OM et al. 1212.3460]

Mattelaer Olivier MadGraph5_aMC@NLO 53

MadSpin

One Event

Decay Events

- smear the mass- flat decay

offshell spin unweighted

No No YES

YES No No

YES YES No

YES YES YES

[Frixione, Leanen, Motylinski,Webber (2007)]

[Artoisenet, OM et al. 1212.3460]

Mattelaer Olivier MadGraph5_aMC@NLO 53

MadSpin

One Event

Decay Events

- smear the mass- flat decay

offshell spin unweighted

No No YES

YES No No

YES YES No

YES YES YES

|MP+D

LO|2/|MPLO|2- re-weight by

Decay Events II

[Frixione, Leanen, Motylinski,Webber (2007)]

[Artoisenet, OM et al. 1212.3460]

Mattelaer Olivier MadGraph5_aMC@NLO 53

MadSpin

One Event

Decay Events

- smear the mass- flat decay

offshell spin unweighted

No No YES

YES No No

YES YES No

YES YES YES

|MP+D

LO|2/|MPLO|2- re-weight by

Decay Events II

[Frixione, Leanen, Motylinski,Webber (2007)]

[Artoisenet, OM et al. 1212.3460]

Mattelaer Olivier MadGraph5_aMC@NLO 53

MadSpin

One Event

Decay Events

- smear the mass- flat decay

offshell spin unweighted

No No YES

YES No No

YES YES No

YES YES YES

|MP+D

LO|2/|MPLO|2- re-weight by

Decay Events II

- accept/reject method- reject the decay not the event

Final Sample

[Frixione, Leanen, Motylinski,Webber (2007)]

[Artoisenet, OM et al. 1212.3460]

Mattelaer Olivier MadGraph5_aMC@NLO 53

MadSpin

One Event

Decay Events

- smear the mass- flat decay

offshell spin unweighted

No No YES

YES No No

YES YES No

YES YES YES

|MP+D

LO|2/|MPLO|2- re-weight by

Decay Events II

- accept/reject method- reject the decay not the event

Final Sample

[Frixione, Leanen, Motylinski,Webber (2007)]

[Artoisenet, OM et al. 1212.3460]

Mattelaer Olivier MadGraph5_aMC@NLO 54

TTH Example

0.0001

0.001

0.01

0 25 50 75 100 125 150 175 200

1/σ

dσ

/dp T

(l+ ) [1/

GeV

]

pT(l+) [GeV]

Scalar Higgs

NLO Spin correlations onLO Spin correlations on

NLO Spin correlations offLO Spin correlations off

0.4

0.45

0.5

0.55

0.6

-1 -0.5 0 0.5 11/σ

dσ

/dco

s(φ)

cos(φ)

Scalar Higgs

NLO Spin correlations onLO Spin correlations on

NLO Spin correlations offLO Spin correlations off

Figure 5: Next-to-leading-order cross sections differential in pT (l+) (left pane) and in cosφ (rightpane) for ttH events with or without spin correlation effects. For comparison, also the leading-order results are shown. Events were generated with aMC@NLO, then decayed with MadSpin,and finally passed to Herwig for shower and hadronization.

0.0001

0.001

0.01

0 25 50 75 100 125 150 175 200

1/σ

dσ

/dp T

(l+ ) [1/

GeV

]

pT(l+) [GeV]

Pseudoscalar Higgs

NLO Spin correlations onNLO Spin correlations off

0.4

0.45

0.5

0.55

0.6

-1 -0.5 0 0.5 1

1/σ

dσ

/dco

s(φ)

cos(φ)

Pseudoscalar Higgs

NLO Spin correlations onNLO Spin correlations off

Figure 6: Next-to-leading-order cross sections differential in pT (l+) (left pane) and in cosφ(right pane) for ttA events with or without spin correlation effects. Events were generated withaMC@NLO, then decayed with MadSpin, and finally passed to Herwig for shower and hadroniza-tion.

that preserving spin correlations is more important than including NLO corrections for this

observable. However, we observe that the inclusion of both, as it is done here, is necessary

for an accurate prediction of the distribution of events with respect to cos(φ). In general, a

scheme including both spin correlation effects and QCD corrections is preferred: it retains

the good features of a NLO calculation, i.e. reduced uncertainties due to scale dependence

(not shown), while keeping the correlations between the top decay products.

The results for the pseudo-scalar Higgs boson are shown in Figure 6. The effects of the

spin correlations on the transverse momentum of the charged lepton are similar as in the

case of a scalar Higgs boson: about 10% at small pT , increasing to about 40% at pT = 200

GeV. On the other hand, the cos(φ) does not show any significant effect from the spin-

correlations. Therefore this observable could possibly help in determining the CP nature of

the Higgs boson, underlining the importance of the inclusion of the spin correlation effects.

– 14 –

TutorialOlivier Mattelaer

IPPP/Durham

Mattelaer Olivier MadGraph5_aMC@NLO

• follow the built-in tutorial

• cards meaning• meaning of QCD/QED• details of syntax ($/)• script• width computation • decay chain

56

Tutorial mapLearning MG5 BSM CASE

• check the model• width computation• signal generation

• decay chain• merging sample generation

• background/NLO generation

Learning MG5_aMC

Mattelaer Olivier MadGraph5_aMC@NLO

Where to find help?

• Ask me

• Use the command “help” / “help XXX”➡ “help” tell you the next command that you need to do.

• Launchpad:➡ https://answers.launchpad.net/madgraph5➡ FAQ: https://answers.launchpad.net/madgraph5/+faqs

58

Mattelaer Olivier MadGraph5_aMC@NLO

What are those cards?

• Read the Cards and identify what they do➡ param_card: model parameters➡ run_card: beam/run parameters and cuts

• https://answers.launchpad.net/madgraph5/+faq/2014

59

Mattelaer Olivier MadGraph5_aMC@NLO

Exercise II: Cards Meaning

• How do you change➡ top mass➡ top width➡ W mass➡ beam energy➡ pt cut on the lepton

60

Mattelaer Olivier MadGraph5_aMC@NLO

Exercise II : Syntax

• What’s the meaning of the order QED/QCD

• What’s the difference between➡ p p > t t~ ➡ p p > t t~ QED=2➡ p p > t t~ QED=0

• Compute the cross-section for each of those and check the diagram

• Generate VBF process

61

d d > w+ w- d d QCD=0 page 4/10

Diagrams made by MadGraph5

d

1

d5

a

d2

w- 4

u~

w+

3

d6

u

diagram 19 QCD=0, QED=4

d

1

d5

z

d2

w- 4

u~

w+

3

d6

u

diagram 20 QCD=0, QED=4

d

1

d

5

a

d2

d6

a

w+

3

w-4

diagram 21 QCD=0, QED=4

d1

d5

a

d2

d6

a

w+3

w-

w- 4

diagram 22 QCD=0, QED=4

d1

d5

a

d2

d6

a

w-4

w+

w+ 3

diagram 23 QCD=0, QED=4

d

1

d

5

a

d2

d6

z

w+

3

w-4

diagram 24 QCD=0, QED=4

➡ p p > t t~ QCD=0➡ p p > t t~ QED<=2➡ p p > t t~ QCD^2==2

Mattelaer Olivier MadGraph5_aMC@NLO

Exercise III: Syntax

• Generate the cross-section and the distribution (invariant mass) for ➡ p p > e+ e-➡ p p > z, z > e+ e-➡ p p > e+ e- $ z➡ p p > e+ e- / z

• Use the invariant mass distribution to determine the

Hint :To plot automatically distributions:mg5> install MadAnalysis

62

Mattelaer Olivier MadGraph5_aMC@NLO

Exercise IV: Automation/Width

• Compute the cross-section for the top pair production for 3 different mass points.➡ Do NOT use the interactive interface

• hint: you can edit the param_card/run_card via the “set” command [After the launch]

• hint: All command [including answer to question] can be put in a file. (run ./bin/mg5 PATH_TO_FILE)

➡ Remember to change the value of the width

• “set width 6 Auto” works

• cross-check that it indeed returns the correct width

63

Examples

File:

import model EWDim6generate p p > z zouput TUTO_DIM6launch set nevents 5000 set MZ 100

How to Run: ./bin/mg5_amc PATH

Mattelaer Olivier MadGraph5_aMC@NLO

Exercise V: Decay Chain

• Generate p p > t t~ h, fully decayed (fully leptonic decay for the top)➡ Using the decay-chain formalism➡ Using MadSpin

• Compare cross-section➡ which one is the correct one?➡ Why are they different?

• Compare the shape.

64

BSM Tutorial

MadGraph Tutorial. Beijing 2015

Exercise I: Check the model validity

• Check the model validity:➡ check p p > uv uv~➡ check p p > ev ev~➡ check p p > t t~ p1 p2

66

• This checks ➡ gauge invariance➡ lorentz invariance➡ that various way to compute the matrix element

provides the same answer

MadGraph Tutorial. Beijing 2015

Exercise II: Width computation

• Check with MG the width computed with FR:➡ generate uv > all all; output; launch➡ generate ev > all all; output; launch➡ generate p1 > all all; output; launch➡ generate p2 > all all; output; launch

• Check with MadWidth➡ compute_widths uv ev p1 p2➡ (or Auto in the param_card)

67

FR Number

0.00497 GeV

0.0706 GeV

0 GeV

0.0224 GeV

• Muv = 400 GeV Mev = 50 GeV λ=0.1 • m1 = 1GeV m2 = 100GeV m12 = 0.5 GeV

MadGraph Tutorial. Beijing 2015

Exercise III:

• Compute cross-section and distribution ➡ uv pair production with decay in top and / (semi leptonic

decay for the top

• Hint: The width of the new physics particles has to be set correctly in the param_card. ➡ You can either use “Auto” ➡ or use the value computed in exercise 1

• Hint: For sub-decay, you have to put parenthesis:➡ example:

p p > t t~ w+, ( t > w+ b, w+ >e+ ve), (t~ > b~ w-, w- > j j), w+ > l+ vl

68

�1 �2

arXiv:1402.1178

MadGraph Tutorial. Beijing 2015

Too Slow?

• Use MadSpin!➡ Use Narrow Width Approximation to factorize

production and decay

• instead of ➡ p p > t t~ w+, ( t > w+ b, w+ >e+ ve), (t~ > b~ w-, w- > j j),

w+ > l+ vl

• Do

➡ p p > t t~ w+

• At the question:

• At the next question edit the madspin_card and define the decay

69

arXiv:1212.3460

Mattelaer Olivier MadGraph5_aMC@NLO

Exercise IV: generate multiple multiplicity sample for pythia8

• We will do MLM matching➡ in the run_card.dat ickkw=1➡ the matching scale (Qcut) will be define in pythia

• in madgraph we use xqcut which should be smaller than Qcut (but at least 10-20 GeV)

70

Mattelaer Olivier MadGraph5_aMC@NLO

Exercise V: Have Fun

• Simulate Background

• Go to NLO (ask me the model)

• …

71

Mattelaer Olivier MadGraph5_aMC@NLO

Solution Learning MG5_aMC

72

Mattelaer Olivier MadGraph5_aMC@NLO

Exercise II: Cards Meaning

• How do you change➡ top mass➡ top width➡ W mass➡ beam energy➡ pt cut on the lepton

73

Param_card

Run_card

Mattelaer Olivier MadGraph5_aMC@NLO

• top mass

74

Mattelaer Olivier MadGraph5_aMC@NLO

• W mass

75

W Mass is an internal parameter! MG5 didn’t use this value!

So you need to change MZ or Gf or alpha_EW

Mattelaer Olivier MadGraph5_aMC@NLO

Exercise III: Syntax

• What’s the meaning of the order QED/QCD

• What’s the difference between➡ p p > t t~ ➡ p p > t t~ QED=2➡ p p > t t~ QED=0➡ p p > t t~ QCD^2==2

76

Mattelaer Olivier MadGraph5_aMC@NLO

Solution I : Syntax

• What’s the meaning of the order QED/QCD➡ By default MG5 takes the lowest order in QED!➡ p p > t t~ => p p > t t~ QED=0➡ p p > t t~ QED=2

• additional diagrams (photon/z exchange)

p p > t t~ QED=2

No significant QED contribution

p p > t t~

77

Mattelaer Olivier MadGraph5_aMC@NLO

• QED<=2 is the SAME as QED=2➡ quite often source of confusion since most of the people use

the = syntax

• QCD^2==2 ➡ returns the interference between the QCD and the QED

diagram

78

Mattelaer Olivier MadGraph5_aMC@NLO

Solution I Syntax

• generate p p > w+ w- j j➡ 76 processes➡ 1432 diagrams➡ None of them are VBF

79

• generate p p > w+ w- j j QED = 4➡ 76 processes➡ 5332 diagrams➡ VBF present! + those not VBF

• generate p p > w+ w- j j QED = 2➡ 76 processes➡ 1432 diagrams➡ None of them are VBF

• generate p p > w+ w- j j QCD = 0➡ 60 processes➡ 3900 diagrams➡ VBF present!

• generate p p > w+ w- j j QCD = 2➡ 76 processes➡ 5332 diagrams

• generate p p > w+ w- j j QCD = 4➡ 76 processes➡ 5332 diagrams

Mattelaer Olivier MadGraph5_aMC@NLO

Exercise IV: Syntax

• Generate the cross-section and the distribution (invariant mass) for ➡ p p > e+ e-➡ p p > z, z > e+ e-➡ p p > e+ e- $ z➡ p p > e+ e- / z

Hint :To have automatic distributions:mg5> install MadAnalysis

80

Mattelaer Olivier MadGraph5_aMC@NLO

p p > e+ e-(16 diagrams)

p p >z , z > e+ e-

p p > e+ e- $ z

(8 diagrams)

(16 diagrams)

p p > e+ e- /z(8 diagrams)

Z- onshell vetoNo Z 81

Mattelaer Olivier MadGraph5_aMC@NLO

p p > e+ e-(16 diagrams)

p p >z , z > e+ e-

p p > e+ e- $ z

(8 diagrams)

(16 diagrams)

p p > e+ e- /z(8 diagrams)

Z- onshell vetoNo Z

Correct Distribution

81

Mattelaer Olivier MadGraph5_aMC@NLO

p p > e+ e-(16 diagrams)

p p >z , z > e+ e-

p p > e+ e- $ z

(8 diagrams)

(16 diagrams)

p p > e+ e- /z(8 diagrams)

Z- onshell vetoNo Z

Correct Distribution

Z Peak

NO Z Peak

81

Mattelaer Olivier MadGraph5_aMC@NLO

p p > e+ e-(16 diagrams)

p p >z , z > e+ e-

p p > e+ e- $ z

(8 diagrams)

(16 diagrams)

p p > e+ e- /z(8 diagrams)

Z- onshell vetoNo Z

Correct Distribution

Z Peak

NO Z PeakNo z/a interference z/a interference

81

Mattelaer Olivier MadGraph5_aMC@NLO

p p > e+ e-(16 diagrams)

p p >z , z > e+ e-

p p > e+ e- $ z

(8 diagrams)

(16 diagrams)

p p > e+ e- /z(8 diagrams)

Z- onshell vetoNo Z

Correct Distribution

Z Peak

NO Z Peak

Wrong tail Correct tailNo z/a interference z/a interference

81

Mattelaer Olivier MadGraph5_aMC@NLO

|M⇤ �M | < BWcut ⇤ �

p p > e+ e- p p >z , z > e+ e- p p > e+ e- $ z

= +Onshell cut: BW_cut

(16 diagrams) (8 diagrams) (16 diagrams)

• The Physical distribution is (very close to) exact sum of the two other one.

• The “$” forbids the Z to be onshell but the photon invariant mass can be at MZ (i.e. on shell substraction).

• The “/” is to be avoid if possible since this leads to violation of gauge invariance.

82

Mattelaer Olivier MadGraph5_aMC@NLO

WARNING

• NEXT SLIDE is generated with bw_cut =5

• This is TOO SMALL to have a physical meaning (15 the default value used in previous plot is better)

• This was done to illustrate more in detail how the “$” syntax works.

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Mattelaer Olivier MadGraph5_aMC@NLO

$ explanationp p > e+ e- / Z

See previous slide warning

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(red curve) (blue curve)

Mattelaer Olivier MadGraph5_aMC@NLO

$ explanationp p > e+ e- / Z adding p p > e+ e- $ Z

See previous slide warning

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(red curve) (blue curve)

Mattelaer Olivier MadGraph5_aMC@NLO

$ explanationp p > e+ e- / Z adding p p > e+ e- $ Z

See previous slide warning

• Z onshell veto

5 times width area

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(red curve) (blue curve)

Mattelaer Olivier MadGraph5_aMC@NLO

$ explanationp p > e+ e- / Z adding p p > e+ e- $ Z

See previous slide warning

• Z onshell veto

• In veto area only photon contribution

5 times width area

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(red curve) (blue curve)

Mattelaer Olivier MadGraph5_aMC@NLO

$ explanationp p > e+ e- / Z adding p p > e+ e- $ Z

See previous slide warning

• Z onshell veto

• In veto area only photon contribution

• area sensitive to z-peak

5 times width area

15 times width area

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(red curve) (blue curve)

Mattelaer Olivier MadGraph5_aMC@NLO

$ explanationp p > e+ e- / Z adding p p > e+ e- $ Z

See previous slide warning

• Z onshell veto

• In veto area only photon contribution

• area sensitive to z-peak

• very off-shell Z, the difference between the curve is due to interference which are need to be KEPT in simulation.

5 times width area

15 times width area>15 times width area

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(red curve) (blue curve)

Mattelaer Olivier MadGraph5_aMC@NLO

$ explanationp p > e+ e- / Z adding p p > e+ e- $ Z

The “$” can be use to split the sample in BG/SG area

See previous slide warning

• Z onshell veto

• In veto area only photon contribution

• area sensitive to z-peak

• very off-shell Z, the difference between the curve is due to interference which are need to be KEPT in simulation.

5 times width area

15 times width area>15 times width area

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(red curve) (blue curve)

Mattelaer Olivier MadGraph5_aMC@NLO

• Syntax Like ➡ p p > z > e+ e- (ask one S-channel z)➡ p p > e+ e- / z (forbids any z)➡ p p > e+ e- $$ z (forbids any z in s-channel)

• ARE NOT GAUGE INVARIANT !

• forgets diagram interference.

• can provides un-physical distributions.

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Mattelaer Olivier MadGraph5_aMC@NLO

• Syntax Like ➡ p p > z > e+ e- (ask one S-channel z)➡ p p > e+ e- / z (forbids any z)➡ p p > e+ e- $$ z (forbids any z in s-channel)

• ARE NOT GAUGE INVARIANT !

• forgets diagram interference.

• can provides un-physical distributions.Avoid Those as much as possible!

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Mattelaer Olivier MadGraph5_aMC@NLO

• Syntax Like ➡ p p > z > e+ e- (ask one S-channel z)➡ p p > e+ e- / z (forbids any z)➡ p p > e+ e- $$ z (forbids any z in s-channel)

• ARE NOT GAUGE INVARIANT !

• forgets diagram interference.

• can provides un-physical distributions.Avoid Those as much as possible!check physical meaning and gauge/Lorentz invariance if you do.

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Mattelaer Olivier MadGraph5_aMC@NLO

• Syntax like

• p p > z, z > e+ e- (on-shell z decaying)

• p p > e+ e- $ z (forbids s-channel z to be on-shell)

• Are linked to cut

• Are more safer to use

• Prefer those syntax to the previous slides one

|M⇤ �M | < BWcut ⇤ �

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Mattelaer Olivier MadGraph5_aMC@NLO

Exercise V: Automation

• Look at the cross-section for the previous processfor 3 different mass points.➡ hint: you can edit the param_card/run_card via the “set”

command [After the launch]➡ hint: All command [including answer to question] can be put

in a file.

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Mattelaer Olivier MadGraph5_aMC@NLO

Exercise V: Automation

• File content:

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• Run it by:

• ./bin/mg5 PATH

• (smarter than ./bin/mg5 < PATH)

• If an answer to a question is not present: Default is taken automatically

Mattelaer Olivier MadGraph5_aMC@NLO

• generate p p > t t~ h

➡ decay t > w+ b, w+ > e+ ve➡ decay t~ >w- b~, w- > e- ve~➡ decay h > b b~

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Exercise VI: Decay

MadSpin

MadSpin Card

MadGraph• generate p p > t t~ h, (t > w+ b, w+ > e+ ve), (t~

>w- b~, w- > e- ve~), h > b b~

2m18.214s

0.004707

0.0030149m30.806s

Different here because of cut (not cut should be applied since 2.3.0)