NLO: How to?

Celine Degrande, Rikkert Frederix,
Olivier Mattelaer, Marco Zar
 o1• It is an automatic meta-code that write the code for computing the
CERN-PH-TH/2014-064

cross-section and generating events for any process at collider• For detail
The automated computation of tree-level andPreprint typeset in JHEP style - PAPER VERSION

Preprint typeset in JHEP style - HYPER VERSION

CP3-14-18, LPN14-066
MCNET-14-09, ZU-TH 14/14

Prepared for submission to JHEPMadGraph 5 : Going Beyond

next-to-leading order differential cross sections, andtheir matching to parton shower simulations

Nikhef/2018-015
TUM-HEP-1138/18
October 22, 2021

arXiv:1405.0301v2 [hep-ph] 21 Jul 20141106.0522

1405.0301

Johan Alwall(1) , Michel Herquet(2) , Fabio Maltoni(3) , Olivier Mattelaer(3) , Tim Stelzer(4)(1)

J. Alwalla , R. Frederixb , S. Frixioneb , V. Hirschic , F. Maltonid , O. Mattelaerd ,H.-S. Shaoe , T. Stelzerf , P. Torriellig , M. Zarohi

Theoretical Physics Department, Fermi National Accelerator Laboratory, P. O. Box 500,
Batavia, IL 60510, USA(2)
Nikhef Theory Group, Kruislaan 409, 1098 SJ Amsterdam, The Netherlands(3)
Centre for Cosmology, Particle Physics and Phenomenology (CP3) Université Catholiquede Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium(4)Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green
Street, Urbana, IL 61801

The automation of next-to-leading order electroweak
calculations

1804.10017

aDepartment of Physics, National Taiwan University, Taipei 10617, Taiwan
PH Department, TH Unit, CERN, CH-1211 Geneva 23, Switzerlandc
SLAC National Accelerator Laboratory, 2575 Sand Hill Road,
Menlo Park, CA 94025-7090 USAdCP3, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgiume
Department of Physics and State Key Laboratory of Nuclear Physics and Technology,
Peking University, Beijing 100871, Chinaf
University of Illinois, Urbana, IL 61801-3080, USAg
Physik-Institut, Universität Zürich, Winterthurerstrasse 190, 8057 Zurich, SwitzerlandhSorbonne Universités, UPMC Univ. Paris 06, UMR 7589, LPTHE,
F-75005, Paris, Francei
CNRS, UMR 7589, LPTHE, F-75005, Paris, France

Older (but still useful!) papers
Alwall, Demin, De Visscher, Frederix, Herquet, 0706.2334
Maltoni, Stelzer, hep-ph/0208156
b

R. Frederix,a S. Frixione,b V. Hirschi,c D. Pagani,a H.-S. Shao,d M. Zaroea
Abstract:
MadGraph
5 is the newversionMünchen,of the MadGraphmatrix1, element generator,
Physik Department
T31, Technische
UniversitätJames-Franck-Str.
writtenin Garching,
the Python
programming language. It implements a number of new, efficient algoD-85748
Germanybrithmsprovideimproved
andfunctionality
in all aspects of the program. It
INFN,that
Sezionedi Genova,
Via performance
Dodecaneso 33,
I-16146,
Genoa, Italycfeaturesanewuserinterface,
severalnew
outputformats
includingInstitute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland C++ process libraries ford
Pythia8, andfull compatibility
with
FeynRules
for new physics
models implementation,
Laboratoirede PhysiqueThéorique etHautesEnergies (LPTHE),
UMR 7589,
Sorbonne
et CNRS,for
4 place75252
Paris05,inFrance
allowing
forUniversité
event generation
any Jussieu,
model thatcanbe Cedex
writtenthe form of a Lagrangian.
e
Nikhef,SciencePark105,
NL-1098
XG
Amsterdam,
The
Netherlands
MadGraph 5 builds on the same philosophy as the previous versions, and its design allows
it E-mail:to be used
as a collaborative platform
where theoretical, phenomenological and simulation
rikkert.frederix@tum.de,
Stefano.Frixione@cern.ch,projects
can be developed and thendistributed to the high-energy community. We describe thehirschva@itp.phys.ethz.ch,
davide.pagani@tum.de,ideas
and the most important developmentsof the code and illustrate its capabilities through ahuasheng.shao@lpthe.jussieu.fr,
m.zaro@nikhef.nl
few simple phenomenological examples.
Abstract: We present the key features relevant to the automated computation of all
the leading- Monteand next-to-leading
orderHadronic
contributions
to short-distance cross sections in
Keywords:
Carlo, MadGraph,
Colliders.
a mixed-coupling expansion, with special emphasis on the first subleading NLO term in
the QCD+EW scenario, commonly referred to as NLO EW corrections. We discuss, inparticular, the FKS subtraction in the context of a mixed-coupling expansion; the extensionof the FKS subtraction to processes that include final-state tagged particles, defined by• NLO QCD and EW corrections can be include• Matrix elements of different multiplicities can be combine• at LO (CKKW or MLM• at NLO (FxFx or UNLOPS)sd

Abstract: We discuss the theoretical bases that underpin the automation of the computations of tree-level and next-to-leading order cross sections, of their matching to parton
shower simulations, and of the merging of matched samples that differ by light-parton multiplicities. We present a computer program, MadGraph5 aMC@NLO, capable of handling
all these computations – parton-level fixed order, shower-matched, merged – in a unified
framework whose defining features are flexibility, high level of parallelisation, and humanintervention limited to input physics quantities. We demonstrate the potential of the program by presenting selected phenomenological applications relevant to the LHC and to a
1-TeV e+ e− collider. While next-to-leading order results are restricted to QCD corrections
to SM processes in the first public version, we show that from the user viewpoint no changes
d

 

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Iwate Collider School 2024sarXiv:1106.0522v1[hep-ph] 2 Jun 2011
:1804.10017v2[hep-ph] 21 Oct 2021

What isMadGraph5_aMC@NLO?

Software prerequisites:• Python 3.7+ (still compatible with Python 2.7• Fortran compiler supporting quadruple precision (for NLO• gfortran v4.6+ O• Optional:• gnuplo• FastJet (FJcore is included in the tarball• LHAPD• Herwig++ / Pythia
•…

)

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Where do I get it?
• On LaunchPad: https://launchpad.net/mg5amcnlo

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4

Where do I get it?
• On LaunchPad: https://launchpad.net/mg5amcnlo•tar -xzf MG5_aMC_v3.5.2.tar.g•cd MG5_aMC_v3_5_•./bin/mg5_aMCz

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Iwate Collider School 2024

Some exercises:• Exercise 1: Top pair production at LO• Exercise 2: Decay chains• Exercise 3: Unitarity in gauge theories• Exercise 4: Initial-state radiation in lepton collisions• Exercise 5: Higgs production at the ILC

Iwate Collider School 2024

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Exercise 1
Top pair production at LO• Basic questions• Generate the process (following the tutorial• Which partonic subprocesses contribute• How many Feynman diagrams has each subprocess• Output the cod• Compute the x-section at the LHC (13.6 TeV) for mt=170 Ge• Extra questions• Are b-quarks included in the initial state? If not, how can I include

them• Are diagrams with photons/Z included? If not, how can I include
them? How much does the cross-section change? What is‘WEIGHTED’• Recompute the tt ̄ cross-section for mt=170, 172, 174 … 180 GeV

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Exercise 1
solution• Generate the process (following the tutorial•> generate p p > t t
INFO: Checking for minimal orders which gives processes.
INFO: Please specify coupling orders to bypass this step.
INFO: Trying coupling order WEIGHTED=2
INFO: Trying process: g g > t t~ WEIGHTED=2
INFO: Process has 3 diagrams
INFO: Trying process: u u~ > t t~ WEIGHTED=2
INFO: Process has 1 diagrams
INFO: Trying process: u c~ > t t~ WEIGHTED=2
INFO: Trying process: c u~ > t t~ WEIGHTED=2
INFO: Trying process: c c~ > t t~ WEIGHTED=2
INFO: Process has 1 diagrams
INFO: Trying process: d d~ > t t~ WEIGHTED=2
INFO: Process has 1 diagrams
INFO: Trying process: d s~ > t t~ WEIGHTED=2
INFO: Trying process: s d~ > t t~ WEIGHTED=2
INFO: Trying process: s s~ > t t~ WEIGHTED=2
INFO: Process has 1 diagrams
INFO: Process u~ u > t t~ added to mirror process u u~ > t t~
INFO: Process c~ c > t t~ added to mirror process c c~ > t t~
INFO: Process d~ d > t t~ added to mirror process d d~ > t t~
INFO: Process s~ s > t t~ added to mirror process s s~ > t t~
5 processes with 7 diagrams generated in 0.075 s
Total: 5 processes with 7 diagrams

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Exercise 1
solution• Which partonic subprocesses contribute•> display processes
Process: g g > t t~ WEIGHTED=2
Process: u u~ > t t~ WEIGHTED=2
Process: c c~ > t t~ WEIGHTED=2
Process: d d~ > t t~ WEIGHTED=2
Process: s s~ > t t~ WEIGHTED=2?

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Exercise 1
solution• Which partonic subprocesses contribute•> display processes
Process: g g > t t~ WEIGHTED=2
u u~ > t t~ WEIGHTED=2
Process:u u~ > t t~ WEIGHTED=2
Process: c c~ > t t~ WEIGHTED=2
Process: d d~ > t t~ WEIGHTED=2
Process: s s~ > t t~ WEIGHTED=22

page 1/1

g g > t t~ WEIGHTED=2

2

4

2

4

g

u~

g

t~

t~

g

g

t

u

t

g

g

3

1
diagram 1

31
diagram 1

QCD=2, QED=0

3
g

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dia

QCD=2, QED=02

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1t

Exercise 1
solution• Which partonic subprocesses contribute•> display processes
Process: g g > t t~ WEIGHTED=2
Process: u u~ > t t~ WEIGHTED=2
Process: c c~ > t t~ WEIGHTED=2
Process: d d~ > t t~ WEIGHTED=2
Process: s s~ > t t~ WEIGHTED=2(pp ! tt̄) =Xab

dx1 dx2 fa (x1 , µF )fb (x2 , µF ) ⇥ ˆ (ab ! tt̄)?

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QCD
masterformula:Z

What does it mean?
(pp ! tt̄) =ab

dx1 dx2 fa (x1 , µF )fb (x2 , µF ) ⇥ ˆ (ab ! tt̄)

t~

 

fi

4

s

2

u~

t

3

10

P

6.5 TeVg

QCD=2, QED=0ŝ = x1 x2 S = x1 x2 (13TeV)2
Iwate Collider School 2024

u

6.5 TeVdiagram 1

parton a inside the proton with
momentum fraction x? fa(x)• μF is a scale which separates
low energy from high energy
dynamic• The partonic scattering occurs
at a reduced energy:P1• What is the probability to ndu u~ > t t~ WEIGHTED=2Z
XExercise 1
solution• How many Feynman diagrams has each subprocess•> display diagrams
g g > t t~ WEIGHTED=2

page 1/1

2

4

2

4

t~

g
g

u u~ > t t~ WEIGHTED=2

2

4

t~

u~
g

t~

g

t

g

g

t

t

u

3

1
diagram 1t~1

3
diagram 2

QCD=2, QED=0

QCD=2, QED=0

3

1
3

2
g

diagram 1

QCD=2, QED=0t

gg: 3 diagramstgqq:̄ 1 diagram

t~

1

4
QCD=2, QED=011:

Iwate Collider School 2024?

diagram 3

Exercise 1
solution• Output the cod•> output mytestdir

INFO: initialize a new directory: mytestdir
INFO: remove old information in mytestdir
INFO: Creating files in directory P0_gg_ttx
INFO: Generating Feynman diagrams for Process: g g > t t~ WEIGHTED=2
INFO: Finding symmetric diagrams for subprocess group gg_ttx
INFO: Creating files in directory P0_qq_ttx
INFO: Generating Feynman diagrams for Process: u u~ > t t~ WEIGHTED=2
INFO: Finding symmetric diagrams for subprocess group qq_ttx
History written to /Users/marcozaro/Physics/MadGraph/MG5_aMC_v2_2_2/mytestdir/Cards/proc_card_mg5.dat
Generated helas calls for 2 subprocesses (0 diagrams) in 0.000 s
Wrote files for 16 helas calls in 0.102 s
Export UFO model to MG4 format
ALOHA: aloha creates FFV1 routines
ALOHA: aloha creates VVV1 set of routines with options: P0
save configuration file to /Users/marcozaro/Physics/MadGraph/MG5_aMC_v2_2_2/mytestdir/Cards/me5_configuration.txt
INFO: Use Fortran compiler gfortran
INFO: Generate jpeg diagrams
INFO: Generate web pages
Output to directory /Users/marcozaro/Physics/MadGraph/MG5_aMC_v2_2_2/mytestdir done.

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Exercise 1
solution• Compute the cross-section at the LHC (13.5 TeV) for mt=170 Ge•> launc

The following switches determine which programs are run:
1 Run the pythia shower/hadronization:
pythia=NOT INSTALLED
2 Run PGS as detector simulator:
pgs=NOT INSTALLED
3 Run Delphes as detector simulator:delphes=NOT INSTALLED
4 Decay particles with the MadSpin module:
madspin=OFF
5 Add weight to events based on coupling parameters:
reweight=OFF
Either type the switch number (1 to 5) to change its default setting,or set any switch explicitly (e.g. type 'madspin=ON' at the prompt)
Type '0', 'auto', 'done' or just press enter when you are done.
[0, 4, 5, auto, done, madspin=ON, madspin=OFF, madspin, reweight=ON, ... ][60s to answer]•> 0 (let’s keep it simple ;-Do you want to edit a card (press enter to bypass editing)?
1 / param: param_card.dat
2 / run: run_card.dat
you can also
- enter the path to a valid card or banner.
- use the 'set' command to modify a parameter directly.
The set option works only for param_card and run_card.
Type 'help set' for more information on this command.
- call an external program (ASperGE/MadWidth/...).
Type 'help' for the list of available command[0, done, 1, param, 2, run, enter path][60s to answer]

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Exercise 1
solution• Compute the cross-section at the LHC (13.5 TeV) for mt=170 Ge
run_card

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param_card

Exercise 1
solution• Compute the cross-section at the LHC (8 TeV) for mt=172 Ge• One can also set the parameters without editing the cards(useful for scripting•> set ebeam1 680•> set ebeam2 680•> set MT 172•> done

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Exercise 1
solution• Compute the cross-section at the LHC (8 TeV) for mt=172 Ge• One can also set the parameters without editing the cards(useful for scripting•> set ebeam1 680•> set ebeam2 680•> set MT 172•> done. . .
Working on SubProcesses
P0_gg_ttx
P0_qq_ttx
INFO: Idle: 0, Running: 1, Completed: 1 [ current time: 15h13 ]INFO: End survey
refine 10000
Creating Jobs
INFO: Refine results to 10000
P0_gg_ttx
P0_qq_ttx
INFO: Idle: 6, Running: 4, Completed: 3 [ 3.2s ]INFO: Idle: 2, Running: 4, Completed: 7 [ 6.6s ]INFO: Idle: 0, Running: 1, Completed: 12 [ 9.7s ]INFO: Combining runs
INFO: finish refinerefine 10000
Creating Jobs
INFO: Refine results to 10000
P0_gg_ttx
P0_qq_ttx
INFO: Combining runs
INFO: finish refine
combine_events
INFO: Combining Events=== Results Summary for run: run_01 tag: tag_1 ===Cross-section :160.1 +- 0.2302 pb
Nb of events : 10000

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Monitor via the web interface

Iwate Collider School 2024

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Exercise 1
solution• Script it• open a text le (mymg5amc.txt) and put the commands
insidegenerate p p > t t
output mytestdi
launc
set ebeam1 680
set ebeam2 680
set MT 17• launch MG5_aMC@NLO with that l•./bin/mg5_amc mymg5amc.txt

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Exercise 1
Extra questions:• Are b-quarks included in the initial state? If not, how can I
include them?
•> display processes
Process: g g > t t~ WEIGHTED=2
Process: u u~ > t t~ WEIGHTED=2
Process: c c~ > t t~ WEIGHTED=2
Process: d d~ > t t~ WEIGHTED=2
Process: s s~ > t t~ WEIGHTED=2• No b-quark appears. Note that at the startup you hav• You can add the b/b̄ to the multiparticle label•> define p = p b b•> display multiparticle• For consistency one should use a model with mb=•> import model sm-no_b_mas
Defined multiparticle p = g u c d s u~ c~ d~ s~Defined multiparticle j = g u c d s u~ c~ d~ s~Defined multiparticle p = g u c d s u~ c~ d~ s~ b b~

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Exercise 1
Extra questions:19:

Iwate Collider School 2024

Exercise 1
Extra questions:• Are b-quarks included in the initial state? If not, how can I include
them?

19
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Exercise 1
Extra questions:• Are b-quarks included in the initial state? If not, how can I include
them?
• Regenerate the proces•> generate p p > t t~•> display processes
Process: g g > t t~ WEIGHTED=2
Process: u u~ > t t~ WEIGHTED=2
Process: c c~ > t t~ WEIGHTED=2
Process: d d~ > t t~ WEIGHTED=2
Process: s s~ > t t~ WEIGHTED=2
Process: b b~ > t t~ WEIGHTED=2

s

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Exercise 1
Extra questions:• Are b-quarks included in the initial state? If not, how can I include
them?
• Regenerate the proces•> generate p p > t t~•> display processes
Process: g g > t t~ WEIGHTED=2
Process: u u~ > t t~ WEIGHTED=2
Process: c c~ > t t~ WEIGHTED=2
Process: d d~ > t t~ WEIGHTED=2
Process: s s~ > t t~ WEIGHTED=2
Process: b b~ > t t~ WEIGHTED=2• Does it make a big difference•> output•> launch•> set ebeam1 4000•> set ebeam2 4000•> set MT 172
?

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Exercise 1
Extra questions:• Are b-quarks included in the initial state? If not, how can I include
them?
• Regenerate the proces•> generate p p > t t~•> display processes
Process: g g > t t~ WEIGHTED=2
Process: u u~ > t t~ WEIGHTED=2
Process: c c~ > t t~ WEIGHTED=2
Process: d d~ > t t~ WEIGHTED=2
Process: s s~ > t t~ WEIGHTED=2
Process: b b~ > t t~ WEIGHTED=2• Does it make a big difference•> output•> launch•> set ebeam1 4000•> set ebeam2 4000•> set MT 172

Without
Cross-section :160.1 +- 0.2302 pb
Nb of events : 10000

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Iwate Collider School 2024

Cross-section :160.4 +- 0.231 pb
Nb of events : 10000

Exercise 1
Extra questions:20:

Iwate Collider School 2024

Exercise 1
Extra questions:• Are diagrams with photons/z included? If not, how can I include
them? How much does the cross-section change? What is that
‘WEIGHTED’?

20:

Iwate Collider School 2024

Exercise 1
Extra questions:• Are diagrams with photons/z included? If not, how can I include
them? How much does the cross-section change? What is that
‘WEIGHTED’?
•> display diagramsu u~ > t t~ WEIGHTED=2

page 1/1

g g > t t~ WEIGHTED=2

2

4

2

2

4

g

u~

g

t~

t~

g

g

t

u

t

g

g

3

1

• No photon/z appear.
• Are we missing anything important?
diagram 1

3

1

QCD=2, QED=0

diagram 1:

20

diagram 2

QCD=2, QED=03

2

Iwate Collider School 2024

1

g

t

t

Exercise 1
Extra questions:• Are diagrams with photons/z included? If not, how can I include
them? How much does the cross-section change? What is that
‘WEIGHTED’•> display diagram• No photon/z appear• Are we missing anything important

?

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Exercise 1
4
4
g
µ
ν
µ ν
2 µ
µgExtraν questions:m)γm)γ(p/4] =r[]/2 γ p/1 γ ] T r[(p/3 + T
r[(p/3(p+m)γ
Mp/|2 γ=p/T/4 −1 γr[p(p1 · p2 )2 (p1 · p2 )2

I include• Are diagrams with photons/z included?µνIf not, how can
µν

them?
How
much
does
the
cross-sectionchange?
What
is
that
g
g
s3
s1 s22 s3 s4 s2 2
ss21
s1
ss
2 s3 s4=| g v̄(p2 )= gγµv̄(pu(p21)) γµ u(p1 )ū(p3 ) γνū(pu(p34))|M‘WEIGHTED’
p
·
p
p
·
p
1
2
1
2
>
display
diagram•!
!
appear• No photon/z
s1 s2 s3 s4 2 s1 s2 s3 s4 2
2
2
we |missing= anything(|M) |)|M | important=(|M |• Are|Mu u~ > t t~ WEIGHTED=2

u u~ > t t~ QED=22

2s1 s2 s3 s4

4
u~

u~

2
∼ αs

g

22
∼∼ααs ediagram 1s.

QCD=0, QED=2t31
diagram 2

4

t~

g

u

21

2
:

?

Iwate Collider School 2024

4

2
∼ αe
3

QCD=2, QED=0

2

u~

t~

1

?

diagram 1

2

t

u

3

4

a

t

1

page 1/1

s1 s2 s3 s4

2

t~

u

page 1/1

QCD=2, QED=0

4

g
2
µ
ν
T
r[(
p
|M 4| = T r[p/24γ p/1 γ ]
/3
2
(p
·
p
)
g
1
2
g
µ
ν
µ ν
2 µ
µ
ν
m)γ
m)γ(p/4] =r[]/2 γ p/1 γ 2] T r[(p/3 +2 T
r[(p/3(p+m)γ
Mp/|2 γ=p/T/4 −1 γr[p(p1 · p2 ) (p1 · p2 )s1 s2 s3 s4
2
s2
s1
|M |
= gIf not,v̄(phowγµI u(pAre diagrams with photons/z
included?
include2 ) can
1)
µν
µν
them?
How
much
does
the
cross-sectionchange?
What
is
that
g
g
s3
s1 s22 s3 s4 s2 2
ss21
s1
ss
2 s3 s4=| g v̄(p2 )= gγµv̄(pu(p21)) γµ u(p1 )ū(p3 ) !
γνū(pu(p34))|M‘WEIGHTED’2p·p
1 |M2| =p1 · p2(|M |> display diagram

Exercise 1
Extra questions:

•

•
!
!
appear• No photon/z
s1 s2 s3 s4 2 s1s1ss22ss33ss44 2
22
we |missing= anything(|M) |)|M | important=(|M |• Are|Mu u~ > t t~ WEIGHTED=2

u u~ > t t~ QED=22

2s1 s2 s3 s4

4
u~

u~

2
∼ αs

g

22
∼∼ααs ediagram 1

Iwate Collider School 2024

QCD=0, QED=2

4

αe
! 0.1
αs
t~

g

t

3

1
diagram 2

4
?

s

.

u

21

2
:

?

2
∼ αe
3

∼

2

u~

t~

1

QCD=2, QED=02

page 1/1

2
∼ αs

t

u

3

1

4

a

t

diagram 1

s1 s2 s3 s4

2

t~

u

page 1/1

QCD=2, QED=0Exercise 1
Extra questions:• Are diagrams with photons/z included? If not, how can I include
them? How much does the cross-section change?
What is ‘WEIGHTED’•> display diagram• No photon/z appear• Are we missing anything important? Does not seem the cas• How to have them anyway• MG5 exploits the hierarchy between QCD and QED
couplings in order to give the leading (i.e. with most QCD)
contribution to the cross-section by defaul• It assign WEIGHTED order =1(=2) to QCD (QED) vertices
and generates the process with minimum WEIGHTED order
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Exercise 1
Extra questions:• Are diagrams with photons/z included? If not, how can I include
them? How much does the cross-section change?
What is ‘WEIGHTED’•> display diagram• No photon/z appear• Are we missing anything important? Does not seem the cas• How to have them anyway• MG5 exploits the hierarchy between QCD and QED
couplings in order to give the leading (i.e. with most QCD)
contribution to the cross-section by defaul• It assign WEIGHTED order =1(=2) to QCD (QED) vertices
and generates the process with minimum WEIGHTED order
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Exercise 1
Extra questions:23:

Iwate Collider School 2024

Exercise 1
Extra questions:• Are diagrams with photons/z included? If not, how can I include
them? How much does the cross-section change?
•> generate p p > t t~ WEIGHTED=4•> display diagrams

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Exercise 1
Extra questions:• Are diagrams with photons/z included? If not, how can I include
them? How much does the cross-section change?
•> generate p p > t t~ WEIGHTED=4•> display diagramss s~ > t t~ WEIGHTED=4

2

4

s~

page 1/

2

4
s~

t~

a

g

t

s

QCD=0, QED=2

2

t~

z

t

s

3

1

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Iwate Collider School 2024

diagram 3

QCD=0, QED=2

3

1
diagram 2

4
s~

t

s

3

1
diagram 1t~

QCD=2, QED=0Exercise 1
Extra questions:• Are diagrams with photons/z included? If not, how can I include
them? How much does the cross-section change?
•> generate p p > t t~ WEIGHTED=4•> display diagrams•> output …
•> launch•> …
s s~ > t t~ WEIGHTED=4

2

4

s~

page 1/

2

4
s~

t~

a

3

1

diagram 1

QCD=0, QED=2

2

t~

z

t

s

3

1

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diagram 3

QCD=0, QED=2

t

s

3

1
diagram 2

4s~

Iwate Collider School 2024

g

t

s

t~

QCD=2, QED=0Exercise 1
Extra questions:• Are diagrams with photons/z included? If not, how can I include
them? How much does the cross-section change?
•> generate p p > t t~ WEIGHTED=4•> display diagrams•> output …
•> launch•> …
s s~ > t t~ WEIGHTED=4

2

4

s~

page 1/

2

4
s~

t~

a

3

1

diagram 1

Cross-section :160.8 +- 0.1999 pb
Nb of events : 10000

QCD=0, QED=22

WEIGHTED=

t~

z

t

s

3

1

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Iwate Collider School 2024

diagram 3

QCD=0, QED=2

t

s

3

1
diagram 2

4s~

Cross-section :160.4 +- 0.231 pb
Nb of events : 10000

g

t

s

t~

QCD=2, QED=0Exercise 1
Extra questions:24:

Iwate Collider School 2024

Exercise 1
Extra questions:• Alternatively, one can specify the coupling power•> generate p p > t t~ QED=2• orders which are not speci ed are unconstrained

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Exercise 1
Extra questions:• Alternatively, one can specify the coupling power•> generate p p > t t~ QED=2• orders which are not speci ed are unconstrained• In order to have only the QED contributio•> generate p p > t t~ QED=2 QCD=0

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Iwate Collider School 2024

Exercise 1
Extra questions:• Recompute the tt ̄ cross-section for mt=170, 172, 174 … 180
Ge• Be smart! Script it!
• Create a txt le myttbar_scan.txt
generate p p > t t~
output mytestdir2
launchset ebeam1 4000
set ebeam2 4000
set MT 170
launchset MT 172
launchset MT 174
launchset MT 176
launchset MT 178
launchset MT 180•./bin/mg5_aMC myttbar_scan.tx
t

 

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Iwate Collider School 2024

Exercise 1
Extra questions:• Recompute the tt ̄ cross-section for mt=170, 172, 174 … 180

Ge• Be smart! Script it!
• You can also launch an existing folder, without regenerating thecodlaunch mytestdir2
set ebeam1 4000
set ebeam2 4000
set MT 170
launchset MT 172
launchset MT 174
launchset MT 176
launchset MT 178
launchset MT 180

 

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Exercise 1
Extra questions:• Recompute the tt ̄ cross-section for mt=170, 172, 174 … 180
GeV

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Exercise 1
Extra questions:• Recompute the tt ̄ cross-section for mt=170, 172, 174 … 180
GeV

which folder is what?
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Iwate Collider School 2024

Exercise 1
Extra questions:• Recompute the tt ̄ cross-section for mt=170, 172, 174 … 180 Ge• Be smart! Script it!
• You can specify the name (instead of run_01…) with -n NAME
launch mytestdir2 -n run_MT170
set ebeam1 4000
set ebeam2 4000
set MT 170
launch -n run_MT172
set MT 172
launch -n run_MT174
set MT 174
launch -n run_MT176
set MT 176
launch -n run_MT178
set MT 178
launch -n run_MT180
set MT 180

V

 

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Exercise 1
Extra questions:• Recompute the tt ̄ cross-section for mt=170, 172, 174 … 180
GeV

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Exercise 2
decay chains• Theory: the top quark is an unstable particle• It decays: ~100% of times into b• The W boson decays too• 67% (2/3) of times into hadron• 22% (2/9) of times into “leptons” (e-νe or μ-νμ
• 11% (1/9) of times into -ν• A decayed pair of top quarks can be classi ed as• hadronic (both tops to hadrons• semileptonic (one top to hadrons, the other to leptons• dileptonic (both quarks to leptons)

)

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Exercise 2
decay chains• Questions• How often a top pair decays hadronically/semi-leptonically/di-

leptonically• Learn the syntax to specify decay chain• Generate the code for dileptonic top decay and compute thecross-section. Compare with the case where the top does notdecay (leave all parameters as default• Compute the cross section for mt=170, 175 and 180 GeV. Do
you see anything strange• What is the difference with p p > l+ l- vl vl~ b
b~?

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Exercise 2
Solution

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Iwate Collider School 2024

Exercise 2
Solution• Questions:• How often a top pair decays hadronically/semi-leptonically/dileptonically?

• Since the top always decays to Wb,
look at how a pair of W decays(b’s are stable)

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Iwate Collider School 2024

Exercise 2
Solution• Questions:• How often a top pair decays hadronically/semi-leptonically/dileptonically?

• Since the top always decays to Wb,
look at how a pair of W decays(b’s are stable)• Hadronically: 2/3 * 2/3 = 4/9

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Iwate Collider School 2024

Exercise 2
Solution• Questions:• How often a top pair decays hadronically/semi-leptonically/dileptonically?

• Since the top always decays to Wb,
look at how a pair of W decays(b’s are stable)• Hadronically: 2/3 * 2/3 = 4/9

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Iwate Collider School 2024

Exercise 2
Solution• Questions:• How often a top pair decays hadronically/semi-leptonically/dileptonically?

• Since the top always decays to Wb,

look at how a pair of W decays(b’s are stable)• Hadronically: 2/3 * 2/3 = 4/9• Semi-lep. (incl. ): 2 * 1/3 * 2/3 = 4/9

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Exercise 2
Solution• Questions:• How often a top pair decays hadronically/semi-leptonically/dileptonically?

• Since the top always decays to Wb,

look at how a pair of W decays(b’s are stable)• Hadronically: 2/3 * 2/3 = 4/9• Semi-lep. (incl. ): 2 * 1/3 * 2/3 = 4/9• Di-lep. (incl. ): 1/3 * 1/3 = 1/9

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Iwate Collider School 2024

Exercise 2
Solution• Questions• Learn the syntax to specify decay chain• > help generat-- generate diagrams for a given process
General leading-order syntax:
o generate INITIAL STATE > REQ S-CHANNEL > FINAL STATE $ EXCL S-CHANNEL / FORBIDDEN PARTICLES COUP1=ORDER1
COUP2^2=ORDER2 @N
o Example: generate l+ vl > w+ > l+ vl a $ z / a h QED=3 QCD=0 @1> Alternative required s-channels can be separated by "|":
b b~ > W+ W- | H+ H- > ta+ vt ta- vt~> If no coupling orders are given, MG5 will try to determineorders to ensure maximum number of QCD vertices.
> Desired coupling orders combination can be specified directly forthe squared matrix element by appending '^2' to the coupling name.
For example, 'p p > j j QED^2==2 QCD^==2' selects the QED-QCD
interference terms only. The other two operators '<=' and '>' aresupported. Finally, a negative value COUP^2==-I refers to theN^(-I+1)LO term in the expansion of the COUP order.
> To generate a second process use the "add process" command
Decay chain syntax:
o core process, decay1, (decay2, (decay2', ...)), ... etc
o Example: generate p p > t~ t QED=0, (t~ > W- b~, W- > l- vl~), t > j j b @2
> Note that identical particles will all be decayed

Something like this!

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

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Exercise 2
Solution

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Exercise 2
Solution• Questions:• Generate the code for dileptonic top decay and compute thecross-section. Compare with what computed in Ex.1

34:

Iwate Collider School 2024

Exercise 2
Solution• Questions:• Generate the code for dileptonic top decay and compute thecross-section. Compare with what computed in Ex.1

• > generate p p > t t~, (t > w+ b, w+ > l+ vl), (t~ > w- b~, w- > l- vl~)
• > output myttbardecayed• > launch• What do we expect?
• Something like 505 * 1/9 = 56 pb?
• Wait: what is l+/l-?

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Iwate Collider School 2024

Exercise 2
Solution• Questions:• Generate the code for dileptonic top decay and compute thecross-section. Compare with what computed in Ex.1

• > generate p p > t t~, (t > w+ b, w+ > l+ vl), (t~ > w- b~, w- > l- vl~)
• > output myttbardecayed• > launch• What do we expect?
• Something like 505 * 1/9 = 56 pb?
• •Wait: what is l+/l-?
> display multi particles

Multiparticle labels:
all = g u c d s u~ c~ d~ s~ a ve vm vt e- mu- ve~ vm~ vt~ e+ mu+t b t~ b~ z w+ h w- ta- ta+
l- = e- muj = g u c d s u~ c~ d~ s~
vl = ve vm vt
l+ = e+ mu+
p = g u c d s u~ c~ d~ s~
vl~ = ve~ vm~ vt~

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Iwate Collider School 2024

Exercise 2
Solution• Questions:• Generate the code for dileptonic top decay and compute thecross-section. Compare with what computed in Ex.1

• > generate p p > t t~, (t > w+ b, w+ > l+ vl), (t~ > w- b~, w- > l- vl~)
• > output myttbardecayed• > launch• What do we expect?4/81 = 25
• Something like 505 * 1/9 = 56 pb?
• •Wait: what is l+/l-?
> display multi particles

Multiparticle labels:
all = g u c d s u~ c~ d~ s~ a ve vm vt e- mu- ve~ vm~ vt~ e+ mu+t b t~ b~ z w+ h w- ta- ta+
l- = e- muj = g u c d s u~ c~ d~ s~
vl = ve vm vt
l+ = e+ mu+
p = g u c d s u~ c~ d~ s~
vl~ = ve~ vm~ vt~

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Iwate Collider School 2024

Cross-section :22.63 +- 0.01553 pb
Nb of events : 10000

last bit of discrepancy comes from
more subtle thing(essentially scales)

Exercise 2
Solution• Questions• Compute the cross section for mt=170, 175 and 180 GeV. Do
you see anything strange

launch run_170
set mt 170
done
launch run_175
set mt 175
done
launch run_180
set mt 180
done• The cross section grows with mt!?!

?

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Iwate Collider School 2024

What is happening?
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Iwate Collider School 2024

36

Exercise 2
Solution• Questions• Compute the cross section for mt=170, 175 and 180 GeV. Do
you see anything strange

launch run_170_gammaok
set mt 170
set wt auto
done
launch run_175_gammaok
set mt 175
set wt auto
done
launch run_180_gammaok
set mt 180
set wt auto
done

• With “set wt auto” the top width is re-computed from theparam_card parameters

?

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Exercise 2
Solution• Questions:• What is the difference with p p > l+ l- vl vl~ b
b~?

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Iwate Collider School 2024

Exercise 2
Solution• Questions:• What is the difference with p p > l+ l- vl vl~ bb~?

• It is a much more complex process (will not run in 10s on a laptop)• Each subprocess has O(100) diagrams rather than O(1)38:

Iwate Collider School 2024

6
ve~
e-

6

4

b~
w-

4

7
b

b

t

5
g

5

vm

w+

mu+

page 9/9

mu+
1

3

Exercise 2
Solution3• Questions:• What is the difference with p p > l+ l- vl vl~ b
diagram 81

QCD=2, QED=4

2

2

2

g

8

b~
b~

g

g

8

vm

b~?

6

mue-

54

z

3
mu+

b

3

g
1

1

e+

a

b

b

g

6

mu+
ve~

7

7

ve~

7

4

b

3

e-

4

vm

5

w-

b

mu+

a

w+

g

g g > mu+ e- vm ve~ b b~ WEIGHTED=10mu+

1

diagram 78

b

8

t

b
55

t~

8

b~
wz

ww+

g g

4

b

ve~
vm

5

w+

g

11

w+

b

t

6

4

1

QCD=2,
QED=4
QCD=2,
QED=4

diagram 81

2
g
8

2

vm
vm

Iwate Collider School 2024:b~vm~ w-

6

ve~
e-

b~

QCD=2, QED=4

g

7

b

8

b~
5

8

1
diagram 46

g
b~

3

b~

QCD=2, QED=4

2

5
mu+

g

3

vm

b

5

vm
mu+

3

38

4

a

7
b

e-

w-

w-

4

6

ve~

ve~
e-

3

mu+
e-

diagram8087
diagram

7

b

b~

e-

b

g

6

ve~

7

4

8

b~

vm
mu+ 6

t

2

g

5

6
4
b~

QCD=2, QED=4

2

7

g g
b~

3

QCD=2, QED=4
QCD=2, QED=4

w+

33

b~

5

22

mu+
u+

6

e-

3 vm
w+

b

diagram 84
diagram 77

6

6

4 w- ve~• It is a much more complex process (will not run in 10s on a laptop)• Each subprocess has O(100) diagrams rather than O(1)• This process ‘contains’ tt ̄ decayed, but also other things
b~
b~

e-

8

b~

5

mu-

e-

vm

b
w+

6

w- ve~
mu+

5

5

t

mu+

3

Exercise 2
Solution• Questions:• What is the difference with p p > l+ l- vl vl~ bb~?

• It is a much more complex process (will not run in 10s on a laptop)• Each subprocess has O(100) diagrams rather than O(1)• This process ‘contains’ tt ̄ decayed, but also other things• Which one is correct?

38:

Iwate Collider School 2024

Exercise 2
Solution• Questions:• What is the difference with p p > l+ l- vl vl~ bb~?

• It is a much more complex process (will not run in 10s on a laptop)• Each subprocess has O(100) diagrams rather than O(1)• This process ‘contains’ tt ̄ decayed, but also other things• Which one is correct?

• Strictly speaking tt ̄ decayed, is correct only in the limit Γt=0 i.e. whentops are on-shell

38:

Iwate Collider School 2024

Exercise 2
Solution• Questions:• What is the difference with p p > l+ l- vl vl~ bb~?

• It is a much more complex process (will not run in 10s on a laptop)• Each subprocess has O(100) diagrams rather than O(1)• This process ‘contains’ tt ̄ decayed, but also other things• Which one is correct?

• Strictly speaking tt ̄ decayed, is correct only in the limit Γt=0 i.e. whentops are on-shell• If one searches for (on-shell) top-pair production (e.g.imposing cuts on
l, v, b mass), the full process will give little extra contribution

38:

Iwate Collider School 2024

Exercise 2
Solution• Questions:• What is the difference with p p > l+ l- vl vl~ bb~?

• It is a much more complex process (will not run in 10s on a laptop)• Each subprocess has O(100) diagrams rather than O(1)• This process ‘contains’ tt ̄ decayed, but also other things• Which one is correct?

• Strictly speaking tt ̄ decayed, is correct only in the limit Γt=0 i.e. whentops are on-shell• If one searches for (on-shell) top-pair production (e.g.imposing cuts on
l, v, b mass), the full process will give little extra contribution• If one wants to look away from the resonant region, then the full38:

Iwate Collider School 2024

Exercise 2
Solutionby terms of O( t /mt ) for inclusive observables. Indeed, similar small-sized di↵erences are observed for di↵erential observables either inclusive in, or insensitive to,the invariant mass of the (W + , Jb )-system. As an illustrative example we present
in Figure 4 the transverse momentum distribution of the light jet, pT (Jlight ). The
lower panel reveals that the NWA and ET NLO results di↵er by 1-2% in all binsfrom the o↵-shell NLO results. In the upper panel it can be seen that both the
NWA and ET results are actually contained within the scale variation band of the
NLO o↵-shell result, indicating that for this observable the size of o↵-shell e↵ects
is smaller than the scale uncertainty.

• Questions• What is the difference with p p > l+ l- vl vl~ bb~• Have a look at single-top production (Papanastasiou et al.
arXiv:1305.7088)



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Iwate Collider School 2024



Exercise 3
Unitarity in gauge theories• Consider the process e+e-→W+W• Which diagrams contribute• Generate the full process, the process with no ZWWvertex and the process with only the neutrino diagra• Use the / x y syntax in the generate command to vetospeci c particles (see also help generate• Calculate the cross section at √s=165, 175, …, 205, 400 GeV(script it!) and comment the behaviour
Hint: set ebeam 200 sets both beams’ energies to 200

m

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Exercise 3
Unitarity in gauge theories
Feynman Diagrams:

page 1/1

2

generate e+ e- > w+ wgenerate e+ e- > w+ w- / z
generate e+ e- > w+ w- / z a

2

3
e-

e-

w+

a

w-

e+

diagram 2

4
w-

e-

ve~

e+

w+

1

3
diagram 3:

41

QCD=0, QED=2

41

QCD=0, QED=2

2

w-

e+

4
diagram 1

w+

z

1

Iwate Collider School 2024

3

QCD=0, QED=2

Exercise 3
Unitarity in gauge theories• Script to calculate the cross sections
generate_events run_165
set ebeam 82.5
generate_events run_175
set ebeam 87.5
generate_events run_185
set ebeam 92.5
generate_events run_195
set ebeam 97.5
generate_events run_205
set ebeam 102.5
generate_events run_400
set ebeam 200
42:

Iwate Collider School 2024

Exercise 3
Unitarity in gauge theories• Results

>w
e
e+

43
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Iwate Collider School 2024

+ w-

a
z
z
/
/
w
w
+
+
w
w
>
>
e
e
+
+
e
e

16

0

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160

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40

σWW (pb)√s (GeV)Full
no Z
no Z gam

35
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arXiv:1302.3415
LEP

20

25
20
15

10

10

YFSWW/RacoonWW
no ZWW vertex (Gentle)
only νe exchange (Gentle)

5
0
200

250

300

350

400

0

160

180

200

√s (GeV)

Iwate Collider School 2024

44
Figure 5.1: Measurementsof the W-pair production cross-section, compared to t

g

u
g

u

u

What’s going on?

3

1

u u~ > g g WEIGHTED=2

1

page 1/1

diagram 1

2

4

2

4

u~
u~

diagram 2

QCD=2, QED=0

3

2

g

u~

g

g
g

u

u

g

u

u
3

1
diagram 1

g

u

1

1

3
diagram 2

QCD=2, QED=0g

QCD=2, QED=04
diagram 3

QCD=2, QED=0

̄ gg in QCD• Consider a simpler case uū→• In a non-abelian gauge theory, in order to ful l the Ward
3

2

u~

g

µ3 µ4

pµ 3 " µ 4 = 0
identity M
one must include the diagram with the 3-gauge verte<latexit sha1_base64="x/CKvycgurr21iY7Pvjqnib4lqM=">AAACJHicbVDLSgMxFM3UV62vUZdugkVwVWZsUUGUghs3QgX7gM44ZNK0Dc1khiRTKMN8jBt/xY0LH7hw47eYaWehrRcSTs65h5t7/IhRqSzryygsLa+srhXXSxubW9s75u5eS4axwKSJQxaKjo8kYZSTpqKKkU4kCAp8Rtr+6DrT22MiJA35vZpExA3QgNM+xUhpyjMvnACpIUYM3sKHxAlirwqzu5bCyJu9U+iMkSCRpEw7kly9hJZnlq2KNS24COwclEFeDc98d3ohjgPCFWZIyq5tRcpNkFAUM5KWnFiSCOERGpCuhhwFRLrJdMkUHmmmB/uh0IcrOGV/OxIUSDkJfN2ZrSTntYz8T+vGqn/uJpRHsSIczwb1YwZVCLPEYI8KghWbaICwoPqvEA+RQFjpXEs6BHt+5UXQOqnYp5XqXa1cv8rjKIIDcAiOgQ3OQB3cgAZoAgwewTN4BW/Gk/FifBifs9aCkXv2wZ8yvn8AkcCkIg==</latexit>

u

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g

1

<latexit sha1_base64="40BTL3XizpATtwFI6FkXqMX+m4Y=">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</latexit>

4

µ3 µ4
M2
⇠ g 2 ta 3 t a 4
diagram 3

QCD=2, QED=0

µ3 µ4
M3
⇠

2 a4 a3g t t• Otherwise, the Ward identity is violated

µ3 µ4
M1
⇠ g 2 f a 3 a 4 b tb
Diagrams made by MadGraph5_aMC@NLO→ no gauge invariance→ possible violation of unitarity at high energies: in the case with theW’s, the longitudinal component has terms ~E/mW, whose contribution
cancels in a gauge invariant amplitude
Diagrams made by MadGraph5_aMC@NLO

x

fi

45
:

Iwate Collider School 2024g

QCD=2, Q

Exercise 4
Initial-state radiation in lepton collisions• Consider muon-pair production at an electron-positron colliderof 500 GeV.
• Set pdlabel=isronlyll and lpp1(2)=-3(+3) in the
run_card. This will tell the code to include ISR effects for theelectron• Plot the invariant mass of the muon pair (MadAnalysis5 does it
automatically). What do you see? How do you explain the
double peak?

46
:

 

s

Iwate Collider School 2024

ISR (at LL)

GRIBOV V. N. and LIPATOV L. N.
GRIBOVV. N.Phys.,and LIPATOV
L. 438N.
Sow.
J . Nucl.
15 (1972)
Sow. J . Nucl. Phys., 15 (1972) 438
GRIBOV V. N. and LIPATOV L. N.
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'
2α
Q 22
η = 2α log Q 2(η = π log m )π
m 22 )
(
2α
Q
η=
log 2
π
m )
(

S):
S):

S):

6
6

6

(1

1
x)1 ⌘/2~0.05 for Q=100 GeV• Hadronic PDFs vanish at large x(divergence at small-x avoided by cuts
Collinear factorisation:
Collinearfactorisation:• Leptonic PDFs diverge (but arepriority
to collinear
logarithms
priority to collinear logarithms
integrable) at large
Collinear factorisation:
While leptonic PDFs have been•priority to collinear logarithms
substantially improved since 1972, theasymptotic behaviour is unchange• A different phase space mapping isrequired wrt pp collisions
)

d

47

x

Iwate Collider School 2024

Exercise 4
Solution
Z-mass peak48:

Iwate Collider School 2024

peak corresponding to ISR with z=1

Exercise 5
Higgs production at the ILC• Try to reproduce some of the curves in this plot
top

Hi assgg o cs p iatrod educ
ti on

Higgs production in electron-positron collisions
qu

WW

fus
ion

wa
ka
Yu
ark

ZZ
&

500

on
os g
s b ling g upHi lf-cose

2501000 GeV

Higgs studies can start at 250 GeV
full set of Higgs measurements:
add ~500 & ~1000 GeV

36⇥ ⇤⌅⇧⌃⌥⌦↵⇥

From Daniel Jeans
49:

Iwate Collider School 2024