The art of collider physics
Fabio Maltoni
Università di Bologna & Université catholique de Louvain

Iwate Collider School 2023

1

Fabio Maltoni

Introduction
1 μν(4)ℒSM = − F Fμν + ψ̄i/Dψ + (yijψ̄ iLϕψRj + h . c.) + | Dμϕ |2 − V(ϕ)
4
• SU(3)c x SU(2)L x U(1)Y gauge symmetries.
• Matter is organised in chiral multiplets of the fund.
representation.
• The SU(2) x U(1) symmetry is spontaneously broken toU(1)EM.
• Yukawa interactions lead to fermion masses, mixing and
CP violation.
• Matter+gauge group => Anomaly free
• Renormalisable = valid to “arbitrary” high scales.
• A number of accidental symmetries seen in Nature.
• Neutrino masses can be accommodated in two distinct
ways.

Iwate Collider School 2023

2

Fabio Maltoni𝛶𝛕

Experimental point of view
The story of collider physics in the last 60 years is marked by the accelerators
eras and punctuated by key discoveriest

W/Z

246 GeV
100 GeV

10 GeV

c

H

v

b

J/ψ

1 GeV

1960

1970

Iwate Collider School 2023

1980

1990
3

2000

2010

2020
Fabio Maltoni𝛶𝛕

Experimental point of view
The story of collider physics in the last 60 years is marked by the accelerators
eras and punctuated by key discoveriest

W/Z

246 GeV
100 GeV

10 GeV

c

H

v

b

J/ψ

1 GeV

SppS
PETRA 20+20 GeV

1960

LEP I and II

PEP &KEKSPEAR 3+3 GeV
Adone

Ada

1970

Iwate Collider School 2023

1980

LHC

Tevatron
HERA

Daphne

1990
3

2000

2010

2020
Fabio Maltoni𝛶𝛕(A) theorist’s point of view
The story of collider physics in the last 60 years is the slow yet steady turning of theStandard Model into a Standard Theory for Strong and EW interactions.

t

W/Z

246 GeV
100 GeV

10 GeV

c

H

v

b

J/ψ

1 GeV

1967

1970

Iwate Collider School 2023

1980

1990
4

2000

2010

2020
Fabio Maltoni𝛶𝛕(A) theorist’s point of view
The story of collider physics in the last 60 years is the slow yet steady turning of theStandard Model into a Standard Theory for Strong and EW interactions.

t

W/Z

246 GeV
100 GeV

10 GeV

c

H

v

b

J/ψ

1 GeV

1 μν
ℒ(4)
=
−
F Fμν + ψ̄ iDψ
/SM
4Strong and electroweak gauge interactions+(yij ψ̄ iL ϕψ Rj + h . c.)+ | Dμϕ |2 − V(ϕ)
1967

1970

Iwate Collider School 2023

1980

1990
4

2000

Flavour structure

Yukawa couplings

EWSB mechanism

Higgs potential

2010

2020
Fabio Maltoni

Present• Tangible results of an amazing
experimental effort over a 10+ year
span, accessing a wide range of final
states, each with very different
challenges.
• So many processes test very different
sectors of the SM.

Iwate Collider School 2023

5

Fabio Maltoni

Present• Tangible results of an amazing
experimental effort over a 10+ year
span, accessing a wide range of final
states, each with very different
challenges.
• So many processes test very different
sectors of the SM.
• Comparison with SM predictions
shows that we have the necessary
theoretical and experimental control
to move onto the next phase.

Iwate Collider School 2023

5

Fabio Maltoni

Present• Tangible results of an amazing
experimental effort over a 10+ year
span, accessing a wide range of final
states, each with very different
challenges.
• So many processes test very different
sectors of the SM.
• Comparison with SM predictions
shows that we have the necessary
theoretical and experimental control
to move onto the next phase.

Iwate Collider School 2023

5

Fabio Maltoni

Present
Higgs couplings
H

Unique mass generation mechanism for fermions/vectors
and the scalar.

}+ 4 point interactions.

V (H) =
V

SM

m2H 2
H +
2

( )=

2

µ (

†

3 vH

3

4

+

)+ (

4
†

H4 + . . .

)

2

)

{

v 2 = µ2 /m2H = 2 v 2

{

SM
=
3
SM
=
4

In the SM gauge invariance + SSB => constrained system. Two-point functions(propagators/masses) x the 3-point and 4-point interactions!

fi

Iwate Collider School 2023

6

🔒

Fabio Maltoni

Present
Higgs couplings

Since its discovery, impressive advances in our understanding of the Higgs
boson's properties have been achieved. At this moment, the new scalar seems
consistent with the expectations of the SM, with different degrees of precision
yet order 10%, in all measured channels.
Need to explore 2nd and 1st fermion generation and Higgs potential.
Iwate Collider School 2023

7

Fabio Maltoni

The future
The LHC reference frame and unit of time
today

LHC
Run 1

Run 2
LS1

7 TeV

HL-LHC

8 TeV

Run 3
LS2

EYETS

13 TeV

splice consolidation
button collimators
R2E project

cryolimit
interaction
regions

Run 4 - 5...
LS3

13 - 14 TeV EYETS

Diodes Consolidation
LIU Installation

inner triplet
radiation limit

Civil Eng. P1-P5

14 TeV

HL-LHC
installation
2027

ATLAS - CMS
upgrade phase 1

experimentbeam pipes
nominal Lumi

2 x nominal Lumi

ALICE - LHCb

2040
5 to 7.5 x nominal Lumi

ATLAS - CMS
HL upgrade

2 x nominal Lumi

upgrade75% nominal Lumi

30 fb-1-1
integrated 3000 fb
luminosity 4000 fb-1

350 fb-1

190 fb-1

HL-LHC TECHNICAL EQUIPMENT:
DESIGN STUDYPROTOTYPESCONSTRUCTIONINSTALLATION & COMM.

PHYSICS

HL-LHC CIVIL ENGINEERING:
DEFINITION

Iwate Collider School 2023

EXCAVATIONBUILDINGS

8

Fabio Maltoni

The future
The LHC reference frame and unit of time
today

LHC
Run 1

Run 2
LS1

7 TeV

8 TeV

Run 1
LS2

EYETS

13 TeV

splice consolidation
button collimators
R2E project

cryolimit
interaction
regionsLS3

13 - 14 TeV EYETSLS1

Diodes Consolidation
LIU Installation
Civil Eng. P1-P5

Run 3

7 TeV

8 TeV

13 TeV

splice consolidation
innercollimators
tripletbuttonradiation limit
R2E project

HL-LHC

LHC

Run 2

Run 4 - 5...

EYETS

14 TeVupgrade phase 1
nominal Lumi

ALICE - LHCb
upgrade75% nominal Lumi

30 fb-1

190 fb-1

2 x nominal Lumi

experimentbeam pipes

inner triplet
radiation limit

Civil Eng. P1-P5

LS3

14 TeV

HL-LHC
installation

2040

2027

upgrade phase 12 x nominal Lumi

ALICE - LHCb

2040
5 to 7.5 x nominal Lumi

ATLAS - CMS

ATLAS - CMS
HL upgrade
nominal Lumi

Run 4 - 5...

13 - 14 TeV EYETS

Diodes Consolidation
LIU Installation

ATLAS - CMS
HL upgrade

2 x nominal Lumi

upgrade75% nominal Lumi

30 fb-1

HL-LHC TECHNICAL EQUIPMENT:LS2

5 to 7.5 x nominal Lumi

ATLAS - CMS
2 x nominal Lumi

Run 3cryolimit
interaction
regions

HL-LHC
installation
2027

experimentbeam pipes

HL-LHC-1

integrated -13000 fb
190 fbluminosity 4000 fb-1

350 fb-1-1
integrated 3000 fb
luminosity 4000 fb-1

350 fb-1

HL-LHC TECHNICAL EQUIPMENT:

DESIGN STUDYPROTOTYPESDESIGN STUDYCONSTRUCTION

HL-LHC CIVIL ENGINEERING:
DEFINITION

Iwate Collider School 2023

INSTALLATION & COMM.

PHYSICS
PROTOTYPESCONSTRUCTIONINSTALLATION & COMM.

PHYSICS

HL-LHC CIVIL ENGINEERING:EXCAVATIONBUILDINGSDEFINITION

8EXCAVATIONBUILDINGS

Fabio Maltoni

The future
The LHC reference frame and unit of timetHL-LHC

t0

LHC
Run 1

Run 2
LS1

7 TeV

cryolimit
interaction
regions

Diodes Consolidation
LIU Installation
Civil Eng. P1-P5

Run 3
LS3

13 - 14 TeV EYETSLS1

LS2

EYETS

13 TeV

splice consolidation
button collimators
R2E project

8 TeV

Run 1

7 TeV

8 TeV

13 TeV

splice consolidation
inner collimators
tripletbuttonradiationlimit
R2E project

HL-LHC

LHC

Run 2

Run 4 - 5...

EYETS

14 TeVupgrade phase 1
nominal Lumi

ALICE - LHCb
upgrade75% nominal Lumi

30 fb-1

2 x nominal Lumi

HL-LHC TECHNICAL EQUIPMENT:HL upgrade
nominal Lumi

| 2031| 2032| 2033| 2034| 2035| 2036 2027
| 2037

ALICE - LHCb

| 20402038

ATLAS - CMS
HL upgrade

2 x nominal Lumi

upgrade-1

3000 fb
integrated
190 fb-1
luminosity 4000 fb-1

350 fb-1-1
integrated 3000 fb
luminosity 4000 fb-1

350 fb-1

HL-LHC TECHNICAL EQUIPMENT:

DESIGN STUDYPROTOTYPESDESIGN STUDYCONSTRUCTION

HL-LHC CIVIL ENGINEERING:
DEFINITIONINSTALLATION & COMM.

PROTOTYPESPHYSICS

CONSTRUCTIONINSTALLATION & COMM.

PHYSICS

HL-LHC CIVIL ENGINEERING:EXCAVATIONBUILDINGSDEFINITIONEXCAVATIONBUILDINGS

We are at 1/3 of our adventure with 1/20 of the expected data
Iwate Collider School 2023

| 20395 to 7.5 x nominal Lumi

upgrade phase 12 x nominal Lumi

14 TeV

HL-LHC
installation

ATLAS - CMS

ATLAS - CMS

experimentbeam pipes| 2030LS3

inner triplet
radiation limit

Civil Eng. P1-P5

2028 2040| 2029Run 4 - 5...

13 - 14 TeV EYETS

Diodes Consolidation
LIU Installation

75% nominal Lumi

30 fb-1

190 fb-1

LS2

5 to 7.5 x nominal Lumi

ATLAS - CMS
2 x nominal Lumi

Run 3cryolimit
interaction
regions

HL-LHC
installation
2027

experimentbeam pipes

HL-LHC

9

Fabio Maltoni

Where do we stand?
The LHC reference frame and unit of time

Iwate Collider School 2023

10

Fabio Maltoni

HL-LHC projections
Higgs self-coupling

Now[ATLAS, 2022]

Iwate Collider School 2023

11

Fabio Maltoni

HL-LHC projections
Higgs self-coupling

Now[ATLAS, 2022]

Currently limits on

Future[De Blas et al., 2020]

kλ from H and HH are comparable and will stay so at the HL-LHC.

Borderline sensitivity to say something about EW baryogenesis…
Iwate Collider School 2023

11

Fabio Maltoni

Our leptonic future(s)Extensive studies with ESU & Snowmass and now in ECFA w/ 106 Higgs bosons
Iwate Collider School 2023

12

Fabio Maltoni

Our leptonic future(s)Iwate Collider School 2023

13

Fabio Maltoni

Collider Physics
The purpose of colliders is to explore physics at small scales
in a controllable environmentΔt ⋅ ΔE ∼ ℏ

Iwate Collider School 2023

14

Fabio Maltoni

Collider Physics
The purpose of colliders is to explore physics at small scales
in a controllable environmentΔt ⋅ ΔE ∼ ℏ⇒

cΔt ⋅ ΔE ∼ ℏc

Iwate Collider School 2023

14

Fabio Maltoni

Collider Physics
The purpose of colliders is to explore physics at small scales
in a controllable environmentΔt ⋅ ΔE ∼ ℏ⇒

cΔt ⋅ ΔE ∼ ℏc
⇒

ℏc
Δx ∼
ΔE
Iwate Collider School 2023

14

Fabio Maltoni

Collider Physics
The purpose of colliders is to explore physics at small scales
in a controllable environmentΔt ⋅ ΔE ∼ ℏ⇒

cΔt ⋅ ΔE ∼ ℏc
⇒

ℏc
Δx ∼
ΔE
Iwate Collider School 2023

14

QFT

Fabio Maltoni

Collider Physics
The purpose of colliders is to explore physics at small scales
in a controllable environment
TheoryCollider(Accelerator)

Experiment• Lagrangian• Measurement ofproperties physicalobjects• Models:- SM- SUSY- ...

- momentum- energy- angles
- ...

• QFT

• Cross Sections

Interpretation• Signal/Background• Assess systematic
uncertainties• Statistics

Iwate Collider School 2023

15

Fabio Maltoni

pA
MM
(p(m,
)0,
=
(p+1!p0,
+
p20)
)
p
+
B
2==
1
2M
p
M
'
2mE
2
M = (p + p )2
pp2
M '1 2mE

(185)
(183)
p1 ' (E, 0, 0, E) (183)(182)(186) (183)
(186)
(181)

A+B !M(186)
The reach of collider
facilities
(186)
(184)
p = (m,0, 0, 0)
p
p
2
pM
'2M
(E,
0,
0,
E)
1M
=
(p
+
p
)
'
2mE
1 0, 0,2E)
2mE
p1 '
'
(E,
E
kin

A+B !M

fixed target:

M 2 = (p1 + p2 )22

p1 ' (E,E0, 0, E)
kinproduction in 2-particle collisions:(182)
p2p ='(m,
0,0,
0,0,
0)E)
(E,
Ekin0, 0, 0)
p12 =
(m,
E
Ekin

p2 = (m,E0, 0, 0)p

before

M'

p

(183)

(184)
(183)
(187)

(184)
(187)
2
M = (p1 + p2 )2

2mE

(185)
(184)
after
(185)
(188) (187)
(187)

(185)
(188)
p1 ' (E, 0, 0, E)

root increase in M
M ' 2mE
(186)
p
p
=
(m,
0, 0)
(185)
2
E0,
(188)
p1 = M
(E,'
0, 0,
E)
(189)
2mE
(186)
E
E
(188)
root
law:
large
energy
loss
in
kin
p
=
(E,
0,
0,
E)
(189)
dense
target:large
collision
rate/luminosity
1
p1 ' (E, 0, 0, E)(184) p2 = (m, 0, 0, 0)

0, 0,E)0, E)
collider target: p2 =p(E,1 =0,(E,Ekinp2 = (E, 0, 0, E)
p2 = (m, 0, 0, 0)

before

(185)

M
'
2E
p2 = (E, 0, 0, E)- linearE law: no energy loss
- less dense bunches: small collision rates
Iwate Collider School 2023

13

16

(190)
after(189)

(187)
(190)

(191) (190)(188)

Fabio MaltoniM ' 2E

p2 = (E, 0, 0, E)
p2 = (E, 0, 0, E)

A=
p2 = (E, 0, 0, E)f=' 35%A =(191)
L =Collider characteristics

(1
(
(1

M
'
2E
Event rate for process with cross section σInteraction
M 'P
(1
p
f 2E
=
(
L
=2
n
2
) (192)+( iregionNi =n! R = i=1 ET,i (⌘i P⌘cluster
cluster )f=emnBunch 1
Bunch 2 (1M'
2E
EEnergy:T,iranges from a few GeV to several TeV (LHC)i=1
Ni =Luminosity from bunch
Ni = in(1
NN
2
Luminosity:crossings
1P
measuresthecollidingbunches
at frequency
f =ratefrev ofnb particles
L=(
Effectivearea
AA=
ET,i(193)
12i
ET =34P 2 1
N1 N2 fnumber
Ni for=Gaussian
Ein
Ljrms
=
with
sizes
σx σy A = 4 π σx(1σT,jLbunches=of10particles
cm
sbunches
A=
f= A
(194)
A = transverse bunch area
(1
34
2
1
X
L
=
10
cm
s
High Luminosity : N↑ collide many ~particles, A↓ squeezed in small bunches(

large aperture quadrupoles
LHC (targeted):
L = 1034 cm(

p/T =collisionp~Trate(observed)
f = bunch
13 ( f↑ crossings
LHC 1.15 x 1011 protons, nb = 2808
300 atfb25 1ns intervals)
observed
rate
forprocesswithcrosssectionL =(195)
Beams squeezed using strong13
2

1
4 1 in 3 years
300
fb
s E
⇠ (E/m) /R

13
around the interaction points
4
Circular vs linear collider:
E
=
c
E
/⇢
from ~ 0.2 mm to
13!IP =->0.5 m< ! > = 80 m
charged particles in circularmotion:towards centerσx = σy =17 µm permanently acceleratedarc
emitting photons Rareas synchrotronlight
E ⇠very
E 4 small/R cross section,
new processes,
like Higgs production can have

-39cm2 .
34 cm-2s-1
like
1fb
=
10
LHC
designed
for
very
high
LuminosityL=10- large loss of energy [hypothetical TeV collider at LEP: E ' E per turn]
Event rate
forenergy
such rare processes : ~ 1 new particle every 28h.
state
- no-more sharp initial
Instead pp σtot ≈ 0.1 barn 30 / crossing

Iwate Collider School 2023

17

pT

Fabio Maltoni

LHC master formula

Iwate Collider School 2023

18

Fabio Maltoni

LHC master formula
+

`

x1 E

x2 E

`

p

p

Iwate Collider School 2023

18

Fabio Maltoni

LHC master formula
+

`

x1 E

x2 E

`

p

p
long distancelong distance

Iwate Collider School 2023

18

Fabio Maltoni

LHC master formula
+

`

x1 E

x2 E

`

p

p
long distancelong distance

σX =

!" 1
a,b

2
2
Q
Q
dx1 dx2 fa (x1 , µ2F )fb (x2 , µ2F ) × σ̂ab→X (x1 , x2 , αS (µ2R ), 2 , 2 )µF µR
0Iwate Collider School 2023

18

Fabio Maltoni

e+ e master formula
+

`

x1 E

x2 E

`

e-

e+
long distancelong distance

σX =

!" 1
a,b

2
2
Q
Q
dx1 dx2 fa (x1 , µ2F )fb (x2 , µ2F ) × σ̂ab→X (x1 , x2 , αS (µ2R ), 2 , 2 )µF µR
0Iwate Collider School 2023

19

Fabio Maltoni

Kinematics
We describe the collision in terms of partonenergies
E1= x1 Ebeam
E2= x2 Ebeam

Obviously the partonic c.m.s. frame will be ingeneral boosted. Let us say that the two partonsannihilate into a particle of mass M.
2
M 2 = x1 x2 S = x1 x2 4Ebeamx1
1
y = log
2
x2
M −y
M y
x1 = √ e x2 = √ e
SS
Iwate Collider School 2023

20

Fabio Maltoni

k02

2
2 ↵s
(dkT /kT ) P̂q

2⇡

@fa/p
↵s X
=
Pa
2
@ ln Q2⇡ 0
a =q,gq (z)@ ln Q2=2⇡

a0 =q,g

@fa/p
↵s X
=
Pa
2
@ ln Q2⇡ 0

Pa a0 ⌦ fa0 /p(256)

a0 ⌦ fa0 /p

LHC master formulaa0 ⌦ fa0 /p

a =q,g 2(257)

2
fa/p (x, Q0 ) ! fa/p(x,Q(257) )

fa/p (x, Q20 ) ! fa/p (x, Q2 )

(258)

XZ
More exactly
2
2 dx f=dx, µF ) ˆa,b!k (µF , µR ) ⇥(Cuts) D(kpp!X
fa/p (x, Q
)
!
f
(x,
Q
)1 2 a/p (x1 , µF )fb/p (x2(258)a/p0" Z1 a,b
!
2
2
X
Q
Q
2
2
2
)
σ
=
)f
(x
,
µ
dx
dx
f
(x
,
µ
×
σ̂
(x
,
x
,
α
(µ
, !
)X)
X
b
2
1
2
a
1
dx1 dx2 fa/p (x1 , FµF )fb/p (x2F, µF ) ˆab→X
SR ), D(kpp!X =
a,b!k (µ1F , µ2R ) ⇥(Cuts)
2
2
µF µR
a,ba,b 0"!#Z 3, µ ) ⇥(Cuts) D(kXfa/p (x1 , µF )fb/p (x2 1, µF ) ˆa,b!k
(µ
! X)
d
~qiR
F
µ
n
4
4
µ
where
the
partonic
cross
sectioniscalculatedbyˆa,b!k =
⇧i=1
(2⇡)
q
(p
+
p
)
|Mab!k (µF
1
2
i
3
"
!#
(2⇡) 2Ei
Z 2s
3
i

1
ˆa,b!k =" 2s
d3 ~qi4 4(2⇡)
2⇡)3 2Ei[flux factor]

⇧ni=1

d ~qi
(2⇡)3 2Ei

X µ
qi
xi

4 4

(2⇡)
!#

(p1 + p2 )

µ

X µ
qi

(p1 + p2 )µi|Mab!kfi/p(µF , µR )|[phase space (LiPS)]x|Mab!k (µF , µR )|2[squared matrix element]

Crucial pieces for the calculation of the hadronic cross section are the parton distributionfunctions fi/p and the squared matrix element |M|2 (259)
Iwate Collider School 2023

21

2

n

Fabio Maltoni

2

A simple example: tt
Let’s see how to calculate the cross section for a simple process such as pp → ttbar. There are
two initial states possible, gg and qqbar. For gg (which will dominate at the LHC) we obtain:

d
=
dŝ

Z 1Z 10dx1 dx2 g(x1 , µF )g(x2 , µF ) ˆ (ŝ) (ŝx1 x2 s)0

We introduce the variable tau, that is proportional to x1 and x2:ŝ⌧ ⌘ = x1 x2sand obtaind=d⌧

Z 1Z 10⇣ˆ (ŝ)
dx1 dx2 g(x1 , µF )g(x2 , µF )1⌧0Iwate Collider School 2023

⌘
x x
1 2

⌧

Fabio Maltoni 22

A simple example: ttdˆ (ŝ)
=
d⌧
⌧

Z 1
⌧

dx1
⌧
g(x1 )g( )x1x1

We define the dimensionless partonic luminosity:and calculate the total cross section as:
Z 1

dLgg
⌘
d⌧

Z 1
⌧

dL
(pp ! tt̄ + X) =d⌧ · ˆgg!tt̄ (s⌧ ) ·
d⌧
⌧min
Z 1

d⌧
⌧ dL
=
· [ŝˆgg!tt̄ (ŝ)] ·ŝd⌧⌧min ⌧
Iwate Collider School 2023

dx1⌧
g(x1 )g( )x1x1

close toa constant“cross section”

Fabio Maltoni 23

A simple example: tt

Iwate Collider School 2023

Fabio Maltoni 24

A simple example: tt
dLgg
⌘
d⌧

Z 1
⌧

dx1
⌧
g(x1 )g( )x1
x1

If we take for simplicity

g(x) =

1
x1+

dLgg
1
)
= 1+ log ⌧d⌧⌧i.e. the total “cross section” will scale as a power of 1/mt1+delta Log Mt
The short distance coefficient can be easily calculated at LO via the feynman diagrams:

Iwate Collider School 2023

Fabio Maltoni 25

A simple example: tt

3 diagrams squared + the interferences. This amplitude is integrated over the phase space atfixed shat:1
ˆgg!tt̄ =
2ŝ

2⇡

Z +1
1

d cos ✓⇤ |M |2 /256

eventually giving:

Iwate Collider School 2023

Fabio Maltoni 26

A simple example: ttdˆ (ŝ) dLgg
=
d⌧
⌧
d⌧

5

4

3

2

1

0.025

0.030

0.035

0.040

0.045

0.050

0.055

LO estimation with toy pdf (δ=0.3)

Iwate Collider School 2023

NLO result with proper MC

Fabio Maltoni 27

LHC master formula
σX =

!" 1
a,b

2
2
Q
Q
dx1 dx2 fa (x1 , µ2F )fb (x2 , µ2F ) × σ̂ab→X (x1 , x2 , αS (µ2R ), 2 , 2 )µF µR0Two ingredients necessary:
1. Parton Distribution Functions (from exp, but evolution from th).
2. Short distance coefficients as an expansion in αS (from th).
2
σ̂ab→X = σ0 + αS σ1 + αS σ2 + . . .
Leading order
Next-to-leading order
Next-to-next-to-leading order
Iwate Collider School 2023

28

Fabio Maltoni

Perturbative expansion• Leading order (LO) calculations typically give only the order of magnitude ofcross sections and distributions- the scale of αS is not defined- jets partons: jet structure starts to appear only beyond LO- Born topology might not be leading at the LHC• To obtain reliable predictions at least NLO is needed• NNLO allows to quantify uncertainties
Furthermore:• Resummation of the large logarithmic terms at phase space boundaries• NLO ElectroWeak corrections (αs2 = αW)• Fully exclusive predictions available in terms of event simulation that can beused in experimental analysis
Iwate Collider School 2023

29

Fabio Maltoni

LHC Physics = QCD +30
𝜖Iwate Collider School 2023

Fabio Maltoni

Higgs production channels
W
bW
t

tHj

b
_
b
bbH

Iwate Collider School 2023

31

Fabio Maltoni

Higgs production at the LHC

Iwate Collider School 2023

32

Fabio Maltoni

Iwate Collider School 2023

Fabio Maltoni 33

Iwate Collider School 2023

Fabio Maltoni 33

Iwate Collider School 2023

Fabio Maltoni 34

2

2. Parton Shower

1. High-Q Scattering

Sherpa artist

3. Hadronization
Iwate Collider School 2023

4. Underlying Event
35

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering

Sherpa artist

3. Hadronization
Iwate Collider School 2023

4. Underlying Event
36

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering☞ where new physics lies

Sherpa artist

3. Hadronization
Iwate Collider School 2023

4. Underlying Event
36

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering☞ where new physics lies

☞ process dependent

3. Hadronization
Iwate Collider School 2023

Sherpa artist

4. Underlying Event
36

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering☞ where new physics lies

☞ process dependent

Sherpa artist☞ rst principles description

3. Hadronizationfi

Iwate Collider School 2023

4. Underlying Event
36

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering☞ where new physics lies

☞ process dependent

Sherpa artist☞ rst principles description☞ it can be systematically improved
3. Hadronizationfi

Iwate Collider School 2023

4. Underlying Event
36

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering

Sherpa artist

3. Hadronization
Iwate Collider School 2023

4. Underlying Event
37

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering

Sherpa artist☞ QCD -”known physics”

3. Hadronization
Iwate Collider School 2023

4. Underlying Event
37

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering

Sherpa artist☞ QCD -”known physics”☞ universal/ process independent

3. Hadronization
Iwate Collider School 2023

4. Underlying Event
37

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering

Sherpa artist☞ QCD -”known physics”☞ universal/ process independent☞ rst principles description
3. Hadronizationfi

Iwate Collider School 2023

4. Underlying Event
37

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering

2☞ low Q physics

Sherpa artist

3. Hadronization
Iwate Collider School 2023

4. Underlying Event
38

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering

2☞ low Q physics☞ universal/ process
independent
Sherpa artist

3. Hadronization
Iwate Collider School 2023

4. Underlying Event
38

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering

2☞ low Q physics☞ universal/ process
independent☞ model dependent

3. Hadronization
Iwate Collider School 2023

Sherpa artist

4. Underlying Event
38

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering☞ low Q2 physics

Sherpa artist

3. Hadronization
Iwate Collider School 2023

4. Underlying Event
39

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering☞ low Q2 physics☞ energy and process dependent

Sherpa artist

3. Hadronization
Iwate Collider School 2023

4. Underlying Event
39

Fabio Maltoni
Fabio Maltoni

2

2. Parton Shower

1. High-Q Scattering☞ low Q2 physics☞ energy and process dependent☞ model dependent
Sherpa artist

3. Hadronization
Iwate Collider School 2023

4. Underlying Event
39

Fabio Maltoni
Fabio Maltoni

SM Status
accuracy [loops]

pp→ n particles

3

fully inclusive
parton-level
fully exclusive2

fully exclusive
and automatic

1
0
1

2

3

4 5 6 7 8 9 10complexity [n]Iwate Collider School 2023

40

Fabio Maltoni

Summary so far• High energy collisions allow to probe interactions at very shortdistances, but entail SM physics that has to be described with:✦ Identify observables that can be calculated and measured
reliably.
✦Accurate/Precise predictions
multi-loop, QCD, EW.

=> dif cult calculations,✦ A fully exclusive approach (associate an history to each
short distance event).

Fabio Maltoni

41
fi

Iwate Collider School 2023

Discoveries in the precision era
Question:
Precise/accurate predictions are very dif cult/expensive.
Are we sure they are really needed? For what exactly?

Fabio Maltoni

42fi

Iwate Collider School 2023

Discoveries in the precision era
Question:
Precise/accurate predictions are very dif cult/expensive.
Are we sure they are really needed? For what exactly?

Short answer:
The discovery potential of any collider working in the precisionphase ( xed energy, accumulating luminosity) is directly
related to our ability to make precise predictions.

Fabio Maltoni

42
fi

fi

Iwate Collider School 2023

New Physics• A new force has been discovered, the firstelementary of Yukawa type ever seen.

• Its mediator looks a lot like the SM scalar: Huniversality of the couplings• No sign of……New Physics (from the LHC)!
• We have no bullet-proof theoretical argument to argue for the existenceof New Physics between 8 and 13 TeV and even less so to prefer a NP
model with respect to another.

Iwate Collider School 2023

43

Fabio Maltoni

New Physics
The obvious imperative:

look for NP at the LHC by covering the widest range of
TH- and/or EXP-motivated searches.

Searches should aim at being sensitive to thehighest-possible scales of energy

Iwate Collider School 2023

44

Fabio Maltoni

Searching for new physics
Model-dependent

Model-independent

SUSY, 2HDM, ED,…

Search for new states

Search for new
interactions

speci c models, simpli ed models

anomalous couplings, EFT…

Exotic signatures

Standard signatures

precision measurements

rare processesfi

fi

Iwate Collider School 2023fi

simpli ed models, EFT, …

45

Fabio Maltoni

Searching for new physics

Search for new states

Search for new
interactions

SUSY, EXOTICS, BSM HIGGS

SM

Iwate Collider School 2023

46

Fabio Maltoni

Searching for new resonances

Iwate Collider School 2023

47

Fabio Maltoni

Searching for new resonances
peak
pp→H→4l“easy”
Background directly measured
from data. TH needed only forparameter extraction(Normalization, acceptance,...)
Iwate Collider School 2023

47

Fabio Maltoni

Searching for new resonances
peak

shape

pp→H→4l~~~~~~
pp→gg,gq,qq→jets+E/T“easy”

hard

Background directly measured
from data. TH needed only forparameter extraction(Normalization, acceptance,...)

Background shapes needed.
Flexible MC for both signal
and background tuned andvalidated with data.

Iwate Collider School 2023

47

Fabio Maltoni

Searching for new resonances
peak

shape

discriminant

pp→H→4l~~~~~~
pp→gg,gq,qq→jets+E/T

pp→H→W+W-“easy”

hardvery hard

Background directly measured
from data. TH needed only forparameter extraction(Normalization, acceptance,...)

Background shapes needed.
Flexible MC for both signal
and background tuned andvalidated with data.

Background normalization andshapes known very well.
Interplay with the best
theoretical predictions (via
MC) and data.

Iwate Collider School 2023

47

Fabio Maltoni

A simple example: tt
Imagine a new scalar exists which couples mostly to top quark, similar to the SM Higgs,
but it is heavier than 2mt. It would be produced as the SM Higgs via gluon fusion andthen mostly decay to top quarks:

giving rise to a peak in the invariant mass distribution of m(tt). However, this processinterferes with the QCD background:

Iwate Collider School 2023

48

Fabio Maltoni

A simple example: tt
2|Amp|ˆ2=+++

Taking our previous calculation of the SM amplitude and adding the scalar production:

ˆ (s)BW resonance

768<latexit sha1_base64="Sqpmf0I5XISs/93TsEljulJ6g4s=">AAAB9XicbVBNS8NAEJ34WetX1aOXxSLUS0lE0GPRi8cK9gOaWDbbTbt0Nwm7E6WU/g8vHhTx6n/x5r9x2+agrQ8GHu/NMDMvTKUw6Lrfzsrq2vrGZmGruL2zu7dfOjhsmiTTjDdYIhPdDqnhUsS8gQIlb6eaUxVK3gqHN1O/9ci1EUl8j6OUB4r2YxEJRtFKD/6AIvGN6CtaMWfdUtmtujOQZeLlpAw56t3Sl99LWKZ4jExSYzqem2IwphoFk3xS9DPDU8qGtM87lsZUcROMZ1dPyKlVeiRKtK0YyUz9PTGmypiRCm2nojgwi95U/M/rZBhdBWMRpxnymM0XRZkkmJBpBKQnNGcoR5ZQpoW9lbAB1ZShDapoQ/AWX14mzfOq51a9u4ty7TqPowDHcAIV8OASanALdWgAAw3P8ApvzpPz4rw7H/PWFSefOYI/cD5/AKUvkfA=</latexit><latexit sha1_base64="C5bHfZvaXk0Xq1t/RFufr3j3AGM=">AAAB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0lEbI9FLx4r2A9oQ9lsp+3S3U3Y3Qgl9C948aCIV/+QN/+NSZuDtj4YeLw3w8y8IBLcWNf9dgobm1vbO8Xd0t7+weFR+fikbcJYM2yxUIS6G1CDgitsWW4FdiONVAYCO8H0LvM7T6gND9WjnUXoSzpWfMQZtZlUu6mXBuWKW3UXIOvEy0kFcjQH5a/+MGSxRGWZoMb0PDeyfkK15UzgvNSPDUaUTekYeylVVKLxk8Wtc3KRKkMyCnVaypKF+nsiodKYmQzSTkntxKx6mfif14vtqO4nXEWxRcWWi0axIDYk2eNkyDUyK2YpoUzz9FbCJlRTZtN4shC81ZfXSfuq6rlV7+G60rjN4yjCGZzDJXhQgwbcQxNawGACz/AKb450Xpx352PZWnDymVP4A+fzB6mfjVE=</latexit>↵S2 GF m2
p48⇡ 2<latexit sha1_base64="pUjWPtGXGafuavqBVouUg9cwlCI=">AAACNnicbVDLSsNAFJ34tr6qLt0MFkEQS1IEXYqCuhEUrQpNDTfTiR2cTOLMjVBCvsqN3+HOjQtF3PoJTtssfB0YOJxzD3fuCVMpDLruszMyOjY+MTk1XZmZnZtfqC4uXZgk04w3WSITfRWC4VIo3kSBkl+lmkMcSn4Z3u73/ct7ro1I1Dn2Ut6O4UaJSDBAKwXV403qRxpY7oNMuxCcXTfoYXBA4+tGkW/t+KnwzZ3GRkH9kCNY15eqjHgbA63Ivc0hqQTVmlt3B6B/iVeSGilxElSf/E7CspgrZBKMaXluiu0cNAomeVHxM8NTYLdww1uWKoi5aeeDswu6ZpUOjRJtn0I6UL8ncoiN6cWhnYwBu+a31xf/81oZRjvtXKg0Q67YcFGUSYoJ7XdIO0JzhrJnCTAt7F8p64KtBG3T/RK83yf/JReNuufWvdOt2u5eWccUWSGrZJ14ZJvskiNyQpqEkQfyTF7Jm/PovDjvzsdwdMQpM8vkB5zPLyd/qmI=</latexit>

2

1+
ln
1

+ˆSM (s)<latexit sha1_base64="V6oIchF8EfVIHDYo3y21JVUa+v8=">AAACAXicbVBNS8NAEJ3Ur1q/ol4EL4tFqAglEUGPRS9ehIr2A5oQNtttu3Q3CbsboYR68a948aCIV/+FN/+N2zYHrT4YeLw3w8y8MOFMacf5sgoLi0vLK8XV0tr6xuaWvb3TVHEqCW2QmMeyHWJFOYtoQzPNaTuRFIuQ01Y4vJz4rXsqFYujOz1KqC9wP2I9RrA2UmDvHXsDrJGnWF/gIPOkQLfX44o6CuyyU3WmQH+Jm5My5KgH9qfXjUkqaKQJx0p1XCfRfoalZoTTcclLFU0wGeI+7RgaYUGVn00/GKNDo3RRL5amIo2m6s+JDAulRiI0nQLrgZr3JuJ/XifVvXM/Y1GSahqR2aJeypGO0SQO1GWSEs1HhmAimbkVkQGWmGgTWsmE4M6//Jc0T6quU3VvTsu1izyOIuzDAVTAhTOowRXUoQEEHuAJXuDVerSerTfrfdZasPKZXfgF6+MbGxSWAg==</latexit><latexit sha1_base64="yIjaPl3gEbqB1R1Dqc6Ix59zSgE=">AAAB/XicbVDLSsNAFJ3UV62v+Ni5GSyCq5KIoMuiGzdCRfuAJoTJdNIOnUnCzI1QQ/FX3LhQxK3/4c6/cdpmoa0HLhzOuZd77wlTwTU4zrdVWlpeWV0rr1c2Nre2d+zdvZZOMkVZkyYiUZ2QaCZ4zJrAQbBOqhiRoWDtcHg18dsPTGmexPcwSpkvST/mEacEjBTYB96AAPY070sS5J6S+O5mHNhVp+ZMgReJW5AqKtAI7C+vl9BMshioIFp3XScFPycKOBVsXPEyzVJCh6TPuobGRDLt59Prx/jYKD0cJcpUDHiq/p7IidR6JEPTKQkM9Lw3Ef/zuhlEF37O4zQDFtPZoigTGBI8iQL3uGIUxMgQQhU3t2I6IIpQMIFVTAju/MuLpHVac52ae3tWrV8WcZTRITpCJ8hF56iOrlEDNRFFj+gZvaI368l6sd6tj1lrySpm9tEfWJ8/AQKU6w==</latexit>

Iwate Collider School 2023

Interference

ˆSM

SM

49

Fabio Maltoni

A simple example: tt

ScalarPseudoscalar(exercise)

Peaks but also peak-dip and dip only structures. "Easy" to discover independently of the
precise knowledge of the SM. However, needs accurate theory to characterise it.
Iwate Collider School 2023

50

Fabio Maltoni

Collider reach

Increasing the energy of a collider gives a big boost to the reach of resonance searches, while
the gain due to the increase of luminosity is marginal (beware of assumptions here).
Iwate Collider School 2023

51

Fabio Maltoni

Searching for new physics

Search for new states

Search for new
interactions

SUSY, EXOTICS, BSM HIGGS

SM

Iwate Collider School 2023

52

Fabio Maltoni

Search for New Interactions
q
_
q

SM

Z’

New Physics
EnergyΛ

Iwate Collider School 2023

53

Fabio Maltoni

Search for New Interactions
q

Z’

t

q

_
t

_
q

_
q

SM

Z’

New Physics
EnergyΛ

Iwate Collider School 2023

54

Fabio Maltoni

Search for New Interactions
q

Z’

_
q

t

q

_
t

_
q

Z’

New Physics
EnergyΛ
Iwate Collider School 2023

55

Fabio Maltoni

Search for New Interactions
q
_
q

Z’

g

1
p2

M2

t
g

q

_
t

_
q

Z’

New Physics
EnergyΛ=M
Iwate Collider School 2023

56

Fabio Maltoni

Search for New Interactions
q
_
q

Z’

g

1
p2

M2

t
g

q

_
t

_
q

g2
M2

Z’

New Physics
EnergyΛ=M

Iwate Collider School 2023

57

Fabio Maltoni

Search for New Interactions

g2 ¯ ¯
Lef f = LSM + 2
M

2

g
M2

Λ is an upper bound on the scale of new physics
Iwate Collider School 2023

58

Fabio Maltoni

Search for New Interactions=c=1
dim A = 1
µ

dim

=1

dim ⇥ = 3/2

g2
M2

Lef f = LSM +

ci
i

dim=6
O
2 i

59 operators [Buchmuller, Wyler, 1986]

Iwate Collider School 2023

59

Fabio Maltoni

The way of SMEFT
The master equation of an EFT approach has three key
elements:1( Λ4 )

𝒪

1
(6)
EXP
SM
ΔObsn = Obsn
− Obsn = 2an,i(μ) ci(6)(μ) +Λ ∑i

Iwate Collider School 2023

60

Fabio Maltoni

The way of SMEFT
The master equation of an EFT approach has three key
elements:

1
(6)
EXP
SM
ΔObsn = Obsn
− Obsn = 2an,i(μ) ci(6)(μ) +Λ ∑i1( Λ4 )𝒪

Most precise/accurate experimental measurements withuncertainties and correlations

Iwate Collider School 2023

60

Fabio Maltoni

The way of SMEFT
The master equation of an EFT approach has three key
elements:

1
(6)
EXP
SM
ΔObsn = Obsn
− Obsn = 2an,i(μ) ci(6)(μ) +Λ ∑i1( Λ4 )

Most precise SM predictions forobservables: NLO, NNLO, N3LO…

𝒪

Most precise/accurate experimental measurements withuncertainties and correlations

Iwate Collider School 2023

60

Fabio Maltoni

The way of SMEFT
The master equation of an EFT approach has three key
elements:

1
(6)
EXP
SM
ΔObsn = Obsn
− Obsn = 2an,i(μ) ci(6)(μ) +Λ ∑i1( Λ4 )

Most precise EFT predictions
Most precise SM predictions forobservables: NLO, NNLO, N3LO…

𝒪

Most precise/accurate experimental measurements withuncertainties and correlations

Iwate Collider School 2023

60

Fabio Maltoni

1
(6)
EXP
SM
ΔObsn = Obsn
− Obsn = 2an,i(μ) ci(6)(μ) +Λ ∑i1( Λ4 )

Most precise EFT predictions

current measurements

The master equation of an EFT approach has three key
elements:

future measurements

The way of SMEFT⇒ increased NP Sensitivity

Most precise SM predictions forobservables: NLO, NNLO, N3LO…

𝒪

Most precise/accurate experimental measurements withuncertainties and correlations

Iwate Collider School 2023

60

Fabio Maltoni

1
(6)
EXP
SM
ΔObsn = Obsn
− Obsn = 2an,i(μ) ci(6)(μ) +Λ ∑i1( Λ4 )

Most precise EFT predictions

current measurements

The master equation of an EFT approach has three key
elements:

future measurements

The way of SMEFT⇒ increased NP Sensitivity

Most precise SM predictions forobservables: NLO, NNLO, N3LO…

𝒪

Most precise/accurate experimental measurements withuncertainties and correlations

Iwate Collider School 2023

60

Fabio Maltoni

1
(6)
EXP
SM
ΔObsn = Obsn
− Obsn = 2an,i(μ) ci(6)(μ) +Λ ∑i1( Λ4 )

Most precise EFT predictions
Most precise SM predictions forobservables: NLO, NNLO, N3LO…

⇒ increased NP Sensitivity⇒ increased UV identi cation power

UV

EFT

𝒪

Most precise/accurate experimental measurements withuncertainties and correlations

current measurements

The master equation of an EFT approach has three key
elements:

future measurements

The way of SMEFT

fi

Iwate Collider School 2023

60

Fabio Maltoni

A simple example: tt
Three operators of dim=6 that enter tt

Iwate Collider School 2023

Fabio Maltoni 61

A simple example: tt
These new interactions lead to deformations of the SM distributions.

Need to know the SM distributions extremely well as well as the EFT ones!
Iwate Collider School 2023

Fabio Maltoni 62

Search for New Physics at the LHC
Two main strategies for searching new physics

Search for new
interactions

Search for new states
102

Unitarity Bound

100
pb
dΣ
!
"
dMww GeV 10#2

cWWW
!2

0

Iwate Collider School 2023

!400 GeV"2
1

SM

10#4

“Peak” or more complicated structures
searches. Need for descriptive MC for
discovery = Discovery is data driven.
Later need precision for characterisation.

"

500

1000
Mww !GeV"

1500

2000

Deviations are expected to be small.
Intrinsically a precision measurement.
Needs for predictive MC and accurate
predictions for SM and EFT.
63

Fabio Maltoni

New generation of MC tools
TheoryLagrangian
Gauge invariance
QCD
Partons
NLO
Resummation...

Detector simulation
Pions, Kaons, ...
Reconstruction
B-tagging ef ciency
Boosted decision tree
Neural network...

Experimentfi

Iwate Collider School 2023

64

Fabio Maltoni

New generation of MC tools
TheoryLagrangian
Gauge invariance
QCD
Partons
NLO
Resummation
...

or
t
a
r
e
n
e
g
t
n
e
v
MC e

s

Detector simulation
Pions, Kaons, ...
Reconstruction
B-tagging ef ciency
Boosted decision tree
Neural network...

Experimentfi

Iwate Collider School 2023

64

Fabio Maltoni

New generation of MC tools
Idea
Lagrangian
FeynRules
ME Generator
Signal & Bkg
EventsPS+HadDetect. Sim.
Data
Iwate Collider School 2023

65

Fabio Maltoni

Aims of the week

Iwate Collider School 2023

66

Fabio Maltoni

Aims of the week

Think

Iwate Collider School 2023

66

Fabio Maltoni

Aims of the week

Think

Iwate Collider School 2023

Participate

66

Fabio Maltoni

Aims of the week

Think

Iwate Collider School 2023

Participate

66

Work

Fabio Maltoni

Aims of the week

Think

Participate

Work

❖

The morning lectures for reviewing or introducing newconcepts❖

The afternoons, the most important part of the school, will
be devoted to the tutorials
Iwate Collider School 2023

66

Fabio Maltoni

Aims of the week❖

Master the basic concepts of collider physics❖

Learn about the latest techniques that allow to makeaccurate and predictions for events at the LHC in the SM
and Beyond.

❖Install the full chain of tools on your laptop.

❖

Apply and use the tools to make your own New Physics
search, simulating signal and background.

❖At the end of the week you’ll be ready to roll

Iwate Collider School 2023

67

Fabio Maltoni

Mad Hosts

Kentarou Mawatari

Karou Hagiwara

Iwate Collider School 2023

68

Fabio Maltoni

Mad Teachers

Davide Pagani

Benjamin Fuks

Olivier Mattelaer

Iwate Collider School 2023

69

Rikkert Frederix

Fabio Maltoni

We are here for you!

Iwate Collider School 2023

70

Fabio Maltoni