particle physics: introduction to the standard model ... · particle physics: introduction to the...

39
Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert [email protected] Laboratoire de l’accélérateur linéaire (CNRS) Cours de l’École Normale Supérieure 24, rue Lhomond, Paris January 19th, 2017 1 / 39

Upload: trannguyet

Post on 16-Aug-2018

254 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Particle Physics: Introduction to the Standard ModelQuantum Electrodynamics (I)

Frédéric [email protected]

Laboratoire de l’accélérateur linéaire (CNRS)

Cours de l’École Normale Supérieure24, rue Lhomond, Paris

January 19th, 2017

1 / 39

Page 2: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Part II

Quantum Electrodynamics (I)

2 / 39

Page 3: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

1 Quantum Field TheoryWhy do we need quantum field theory ?Special relativity and quantum field theoryDiagram ordersA brief recipe...

2 The Lagrangian

3 The Feynman Rules

4 Example of processesMoeller ScatteringBhabha

5 Acceleration and DetectionAccelerationDetection

3 / 39

Page 4: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Why do we need quantum field theory ?Special relativity and quantum field theoryDiagram ordersA brief recipe...

The History

The history

Introduction of particles (ατoµoς)

Particle-Wave dualism (deBroglie wave length)

Particles are fields in a quantum field theory

1941: Stueckelberg proposes to interpret electron lines going back intime as positrons

end of 1940s: Feynman, Tomonaga, Schwinger et al developrenormalization theory

anomalous magnetic moment predicted (not today)

4 / 39

Page 5: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Why do we need quantum field theory ?Special relativity and quantum field theoryDiagram ordersA brief recipe...

Why do we need quantum field theory ?

from E = mc2 to quantum field theory

The Einstein equation makes a relation between energy and mass

E = mc2

This means that if there is enough energy, we can create a particle with agiven mass m.However, due to conservation laws, it will most probably be necessary toproduce twice the particle’s mass (particle and antiparticle).Hence

Particle number is not fixed

The types of particles present is not fixed

This is in direct conflict with nonrelativistic quantum mechanics and forexample the Schrödinger equation that treats a constant number of particlesof a certain type.

5 / 39

Page 6: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Why do we need quantum field theory ?Special relativity and quantum field theoryDiagram ordersA brief recipe...

Attempts to incorporate special relativity in Quantum mechanics

Quantum mechanics and special relativity

Schrödinger equation contained first order time derivative and second orderspace derivatives

− ~2

2m

∂2ψ

∂x2+ Vψ = i~

∂φ

∂t

Not compatible with special relativity (E2 = p2 + m2).First attempt consisted to promote the time derivative to the second order.This resulted in the Klein Gordon equation :

1c2

∂2ψ

∂t2− ∂2ψ

∂x2=

m2c2

~2ψ

But this leads to funny features:

Negative presence probabilities,

negative energy solutions

Dirac solved the problems by reducing the spatial derivative power.Resulted in the Dirac equation.

6 / 39

Page 7: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Why do we need quantum field theory ?Special relativity and quantum field theoryDiagram ordersA brief recipe...

Quantum Field Theory in a nutshell

e−

t

Leading Order (LO) diagram isthe simplest diagram

The electron is on-shell(p2 = m2

e), no interactions

7 / 39

Page 8: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Why do we need quantum field theory ?Special relativity and quantum field theoryDiagram ordersA brief recipe...

e−

γ

t

NLO (next-to-leading order)diagram

Process not allowed in classicalmechanics

Heisenberg: ∆E∆t ≥ 1 →process allowed for reabsorptionafter ∆t ∼ 1/∆E

Quantum mechanics: add alldiagrams, but that would alsoinclude Nγ = ∞Each vertex is an interaction andeach interaction has a strength(|M|2 ∼ α = 1/137)

Perturbation theory withSommerfeld convergence

8 / 39

Page 9: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Why do we need quantum field theory ?Special relativity and quantum field theoryDiagram ordersA brief recipe...

Rough recipe for the Feynman calculations

Process calculation

Construct the Lagrangian of Free Fields

Introduce interactions via the minimal substitution scheme

Derive Feynman rules

Construct (ALL) Feynman diagrams of the process

Apply Feynman rules

Some aspects are not part of these lectures, but will sketch the ideas

9 / 39

Page 10: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Remember the particle zoo

treat only the carrier of theinteraction γ

as well as the e

(

uL

dL

) (

cL

sL

) (

tL

bL

)

(

νeL

eL

) (

νµL

µL

) (

ντL

τ L

)

uR cR tR

dR sR bR

eR µR τR

γg

W±, Z

H

10 / 39

Page 11: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Lagrangian field theory

The Lagrangian and the Action

The Lagrangian is defined by

L = T − V

The action is the time integration of the Lagrangian, S =∫

Ldt . This is afunctional: its argument is a function and it returns a number.Assuming that the Action should be minimal

S =

∫ t2

t1

L(q, q)dt with δS = 0

(the qi(t) being the generalized coordinates)leads to the Euler-Lagrange equation

d

dt

∂L

∂qi

− ∂L

∂qi

= 0

The familiar equations of motion can be obtained from this equation.

11 / 39

Page 12: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Lagrangian field theory

Lagrangian density

Lagrangian formalism is now applied to fields, which are functions ofspacetime ψ(x , t). The Lagrangian is, in the continuous case, the spaceintegration of the Lagrangian density.

L = T − V =

Ld3x

and the action becomes

S =

Ldt =

Ld4x

Typically,L = L(ψ, ∂µψ)

From a Lagrangian density and the Euler-Lagrange equation, equationsgoverning the evolution of particles (i.e. fields) can be derived.

12 / 39

Page 13: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

The photon

MAXWELL equations:

∂µFµν(x) = jν(x)ǫµνρσ∂νFρσ(x) = 0

with the photon field tensor:

Fµν(x) = ∂µA

ν(x)− ∂νAµ(x)

Aµ being the usual vector potential,A = (ψ, ~A) and jν(x) the currentdensity.

Fermions

Schrödinger equation is i~∂ψ∂t

= Hψ,

with H = − ~2

2m∇2 + V . H should be

chosen to satisfy special relativy,H = c~α× (i~∇) + βmc2.αi and β are actually 4 × 4 matrices,γ0 = β and γ i = βαi

The Dirac equation is obtained:

(iγµ∂µ − m)ψ(x) = 0

leading to: ψ(x)(iγµ∂µ − m)ψ(x) withψ = ψ†γ0 = ψT⋆

γ0

The free Lagrangian (L0)

L0 = −14

Fµν(x)Fµν(x) + ψ(x)(iγµ∂µ − m)ψ(x)

13 / 39

Page 14: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Minimal Substitution

i∂µ → i∂µ + eAµ(x)

ψ(x)γµi∂µψ(x)

→ ψ(x)γµ(i∂µ + eAµ(x))ψ(x)= ψ(x)γµi∂µψ(x) + eψ(x)γµAµ(x)ψ(x)

leads to a coupling between photon and fermion fields:

Interaction Lagrangian L′

L′ = −jµAµ = eψ(x)γµAµ(x)ψ(x)

the negative sign for jµ = −eψ(x)γµψ(x)

14 / 39

Page 15: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Dirac equation for adjoint spinor

iγµ∂µψ − mψ = 0− i(γµ)⋆∂µψ

⋆ − mψ⋆ = 0− i(∂µψ

†)(γµ)† − mψ† = 0− i(∂µψ

†)γγ(γµ)†γ − mψ†γ = 0− i(∂µψ)γ

(γµ)†γ − mψ = 0− i(∂µψ)γ

µ − mψ = 0i(∂µψ)γ

µ + mψ = 0

EM current conserved

∂µjµ = ∂µ[−eψγµψ]= −e(∂µψ)γ

µψ − eψγµ∂µψ Dirac

= −imeψψ + iemψψ Dirac adjoint

= 0

15 / 39

Page 16: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Gauge Invariance

Invariance of the Lagrangian under local U(1) transformationsor: why should physics depend on the location ?

Aµ → Aµ + ∂µΛ(x)ψ(x) → exp (ieΛ(x))ψ(x)

L0 + L′ = L → LLocal gauge invariance under a U(1) gauge symmetry (1929 Weyl)if Λ 6= f (x) it is a global U(1) symmetry.

16 / 39

Page 17: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

U(1) Gauge invariance:

Photon field

Fµν = ∂µAν − ∂νAµ

= ∂µ(Aν + ∂νΛ)− ∂ν(Aµ + ∂µΛ)

= ∂µAν − ∂νAµ + ∂µ∂νΛ− ∂ν∂µΛ ∂µ∂ν = ∂ν∂µ

= ∂µAν − ∂νAµ

= Fµν

Photon field ok

17 / 39

Page 18: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Fermion field

ψ(iγµ∂µ − m)ψ

= ψ†γ0(iγµ∂µ − m)ψ

→ ψ† exp (−ieΛ)γ0(iγµ∂µ − m)(ψ exp (ieΛ))

= exp (−ieΛ)ψ(iγµ∂µ − m)(ψ exp (ieΛ))

= exp (−ieΛ)ψiγµ(∂µψ) exp (ieΛ)

+ exp (−ieΛ)ψiγµψ∂µ exp (ieΛ))

+ exp (−ieΛ)ψ(−m)ψ exp (ieΛ)

= ψiγµ(∂µψ) + exp (−ieΛ)ψiγµψie∂µΛexp (ieΛ)− eψγµ(∂µΛ)ψ

+ ψ(−m)ψ

= ψ(iγµ∂µ − m)ψ − eψγµ(∂µΛ)ψ

18 / 39

Page 19: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Interaction

eψγµAµψ(x)= e exp (−ieΛ)ψγµ(Aµ + ∂µΛ)ψ exp (ieΛ)= eψγµ(Aµ + ∂µΛ)ψ= eψγµAµψ + eψγµ(∂µΛ)ψ

Interaction term combined with fermion field (−ieψγµ∂µΛψ) ok

gauge invariance of the fermion field cries for the introduction of a gaugeboson!

19 / 39

Page 20: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

External lines

initial state electron u(p)initial state positron v(p)initial state photon ǫµ

final state electron u(p)final state positron v(p)final state photon ǫµ⋆

Internal lines and vertex

virtual photon −igµν

k2+iǫ

virtual electron i 6p+m

p2−m2+iǫ

interaction(vertex) ieγµ

Matrix element

|M|2 =

′∑

fi

TfiT†fi

Sum over final state, average over initial state

20 / 39

Page 21: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Moeller ScatteringBhabha

Moeller Scattering e−e− → e−e−

Simplest diagram with initial and final state of two electrons

conserve electric charge and momentum at each vertex

t channel only: C(e− + e−) = −2e 6= C(γ) = 0

p conservation at each vertex → 2 diagrams qγ = p2 − p3 6= p2 − p4

e−

e−

t

e−(p1)e−(p2) → e−(p3)e

−(p4)

e−

e−

t

e−(p1)e−(p2) → e−(p4)e

−(p3)

21 / 39

Page 22: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Moeller ScatteringBhabha

e−

e−

Fermion arrow tip to end

Interaction

propagator (internal line)

second graph p3 ↔ p4

graphs fermion permutation: −k = f (pi)

Tfi = [ u(p4)(−ieγµ)u(p1)(−igµν

k2(p4−p1)2 )u(p3)(−ieγν)u(p2)

− u(p3)(−ieγρ)u(p1)(−igρσ

k2(p3−p1)2 )u(p4)(−ieγσ)u(p2)]

22 / 39

Page 23: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Moeller ScatteringBhabha

1iTfi = 1

i[ u(p4)(−ieγµ)u(p1)(

−igµν

(p4−p1)2 )u(p3)(−ieγν)u(p2)

− u(p3)(−ieγρ)u(p1)(−igρσ

(p3−p1)2 )u(p4)(−ieγσ)u(p2)]

= e2[ u(p4)γµu(p1)(

gµν

(p4−p1)2 )u(p3)γ

νu(p2)

− u(p3)γρu(p1)(

gρσ

(p3−p1)2 )u(p4)γ

σu(p2)]

|M|2 =∑′

fi TfiT †fi

= 14

fi TfiT†fi

After a certain number of steps...

|M|2 =64π2α2

t2u2[(s − 2m

2)2(t2 + u2) + ut(−4m

2s + 12m

4 + ut)]

23 / 39

Page 24: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Moeller ScatteringBhabha

dΩ= |M|2 1

64π2s

0 ≤ θ ≤ π/2 (electrons) me ≈ 0

t = −2p1p3 = −2(√

s/2√

s/2 − s/4 cos θ) = −s/2(1 − cos θ)

u = −2p1p4 = −2(s/4 − ~p1~p4) = −2(s/4 + ~p1~p3)

= −2(s/4 + s/4 cos θ) = −s/2(1 + cos θ)

dσdΩ

= α2

st2u2 [s2(t2 + u2) + u2t2]

= α2

s[ s2

u2 + s2

t2 + 1]

= α2

s

(3+cos2 θ)2

sin4 θ

s dσdΩ

is scale invariant: measure of the pointlikeness of a particle

24 / 39

Page 25: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Moeller ScatteringBhabha

Stanford-Princeton Storage ring

2e− beams√

s = 556MeV

limited detector acceptance

differential cross sectionmeasurement and prediction

25 / 39

Page 26: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Moeller ScatteringBhabha

Typical t channelθ = 0 → dσ/dΩ → ∞Extremely good agreementbetween the measurement andthe theory prediction

e−e− colliders discontinued(1971)

26 / 39

Page 27: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Moeller ScatteringBhabha

The Bhabha Process

Homi Bhabha studied in the 1930s in Great Britain, worked in Indiaafterwards

e−

e+

e−

e+

t

e−

e+

t

dΩ=

α2

16s

(3 + cos2 θ)2

sin4 θ2

0 ≤ θ ≤ π

t channel: ∼ sin−4(θ/2)

s channel: ∼ 1 + cos2 θ

27 / 39

Page 28: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Moeller ScatteringBhabha

PETRA e+e− collider√s ≤ 35GeV

JADE, TASSO, CELLO

total cross section

differential cross section

28 / 39

Page 29: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

Moeller ScatteringBhabha

Excellent agreement with QED

Errors reflect statistics

QED deviation : s/Λ2 < 5% withs = 352GeV2

→ (~c)/Λ = (0.197GeV · fm)/Λ ≈0.13 · 10−3fm

N =∫

Ldt · σToday Bhabha is a luminositymeasurement

29 / 39

Page 30: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

AccelerationDetection

Electrical field

acceleration

charge times potential difference

typical unit: eV

Magnetic field

no acceleration

B field unit: [B] = Vs

m2

force on charged particle inmagnetic field:F = q~v × ~B = q p

mB

centrifugal force:F = mv2/r = p2/(m · r)

R = p/(qBc) (c because ofnatural units)

30 / 39

Page 31: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

AccelerationDetection

Acceleration

strong fields difficult to achieve(breakdown)

accelerate successively

linear assembly: distancebetween potential diffs mustincrease

circular assembly: severalrotations possible

Phase focussing

particle sees nominal (notmaximal) field

early particle: less field, lessacceleration

late particle: more field, strongeracceleration

31 / 39

Page 32: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

AccelerationDetection

LEP/LHC

circular tunnel 28kmcircumferenceelectron+positron: 210GeV

weak fieldstrong cavitiesenergy loss per turn: 6GeV(∼ E4/R)

LHC proton-proton (14TeV)strong field 10Tenergy loss per turn: 500keV

Lepton collider cavities

LEP: up to 10MV/m

ILC: 35-40 MV/m

supraconducting (THe)

Magnetic field LHC

R = 7000GeV

0.3·109m/s·10T ·1e

= 7000GeV

0.3·109m/s·10Vs/m2·10−9Ge

∼ 2km

Rtrue ∼ 4.5km

32 / 39

Page 33: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

AccelerationDetection

Instantaneous Luminosity

L ∼ N2kb fγF

4πǫβ∗

∼ (1011)2·2800·40MHz·γF

4π·15µm·β∗

LHC: 1034cm−2s−1

Integrated Luminosity

N =

Ldt · σ

LHC: 25fb−1 per experimentLinac Booster PS SPS50 1.4 25 450MeV GeV GeV GeV

7TeV per beam

33 / 39

Page 34: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

AccelerationDetection

LC the future?

linear: no synchrotron radiation

40km

polarization

luminosity

250GeV to 1TeV (3TeV: CLIC)

34 / 39

Page 35: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

AccelerationDetection

Detection at high energies

a + b → X → neutral + charged

particles long-lived wrt detectorvolume

Tracker: charged particlemomenta

Calorimeter: neutral and chargedparticles

Tracker

measure points in B-field

reconstruct sagitta

highest precision: silicon (dense,∼ 15µm)

lower precision: TPC (gazeous)

Electromagnetic calorimeter

e + A → e + γ + A

γ → e+e− etc

shower

35 / 39

Page 36: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

AccelerationDetection

ATLAS

Silicon tracking (100M channels2T)

Calorimeter (100k)

Muon chambers (toroid)

Experimental Challenges

bunches every 8m

25ns between crossings (fastreadout)

order 20 interactions per crossing

trigger: 40MHz to 200Hz

alignment

calibration

36 / 39

Page 37: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

AccelerationDetection

37 / 39

Page 38: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

AccelerationDetection

38 / 39

Page 39: Particle Physics: Introduction to the Standard Model ... · Particle Physics: Introduction to the Standard Model Quantum Electrodynamics (I) Frédéric Machefert ... Quantum Field

Quantum Field TheoryThe Lagrangian

The Feynman RulesExample of processes

Acceleration and Detection

AccelerationDetection

A calorimeter tracker for the future?

39 / 39