Overview of MadGraph5 [email protected] Olivier MadGraph5_aMC@NLO Plan 2 •Details of the...
Transcript of Overview of MadGraph5 [email protected] 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
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:
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
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:
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~
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:
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
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:
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~
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:
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
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:
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~
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:
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~
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:
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~
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:
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~
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:
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~
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: 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 “$” forbids the Z to be onshell but the photon invariant mass can be at MZ (i.e. on shell substraction).
• The “/” is to be avoid if possible since this leads to violation of gauge invariance.
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Mattelaer Olivier MadGraph5_aMC@NLO
WARNING
• NEXT SLIDE is generated with bw_cut =5
• This is TOO SMALL to have a physical meaning (15 the default value used in previous plot is better)
• This was done to illustrate more in detail how the “$” 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)