Chapter3
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3.1WhyDoWeNeedAccelerators?
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3.2.1LinearAccelerators 3.2.2CircularAccelerators 3.3CollidersandLuminosity
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3.1.1TheCenter-of-Mass(c.m.)System 3.1.2TheLaboratorySystem
3.1.3FixedTargetAcceleratorandCollid
3.2LinearandCircularAccelerators
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3.3.1Example:theCERNAcceleratorComplex
3.4ConversionofEnergyintoMass
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3.4.1UseofFixedTargetAccelerators 3.4.2BaryonicNumberConservation ¡
3.5ParticleProductioninaSecondaryBeam
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F. Ould-Saada
3.5.1Time-of-FlightSpectrometer
3.6.1ConservationLaws 3.6.2TheElectron“Spiral” 3.6.3Electron-PositronPair
3.6.4AnElectron-Positron“Tree”
3.6.5ChargedParticleDecays
3.6BubbleChambersinChargedParticleBeams §
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LikeLightwave,Matterwave
- carries kinetic energy p²/2m
- has a wavelength λ = h/p=2πh c/pc
λ (fm)=1.24/p(GeV/c)
Possibilitytostudysmallerobjectspossessingfinerdetails
- the higher the energy, the smaller the distance
- optical microscope: λγ ~ 200 nm
(1 nm = 10-9m)
- electron microscope: λe ~ 0.001 nm
- high energy accelerator resolves distances down to 10-20m!
h 2π !c
2π !c
λ= =
⇔ pc =
p
pc
λ
6.28 × 0.197GeV ⋅ fm
λ = 1 fm ⇒ pc =
~ 1.2GeV
1 fm
6.28 × 0.197GeV ⋅ fm
pc = 1TeV ⇒ λ =
~1.2 × 10 −18 m ~ am
1000GeV
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Uncertaintyprinciple
§  ΔxΔpx~h/2
§  ΔxΔE~hc/2
§  Toexploredimensions
oforderΔxenergyof
E=2ΔE~hc/Δxneeded
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“Creationofparticles.”
§  aprocessofconvertingenergyintomassbasedonE=mc2
§  80GeV(W±),91GeV(Z0),125GeV(Higgs),174GeV(topquark),…
§  Creationandstudyofnew,shortleavedparticlesthatonlyexistedjust
aftertheBigbang.
§  Accelerator+Detector=Large,”time-travelmicroscope”
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Combinationofaccelerator,detectorsandcomputersactsasa”timetravel
microscope”whereresearchershopetoshedlightonnewphenomena
àMainComponentsofanaccelerator:
-Magnetstobendandfocusparticlebeams
-Radiofrequency,RF,devicestoacceleratethem.
-Vacuumchamber.
àWhenparticlescollide,
energyisreleasedthat
istransformedintoa
showerofnewparticles.
àParticlecollision
productsare
“photographed”by
Detectors
àComputers,coupled
togetherinaGrid
network,process
andanalysethe
data…
¡
Linearprotonaccelerator
§  (1)ionsource;(2)acceleratingcylindricalelectrodes;(3)radio-frequency;(4)
vacuumpipe
▪  Whydoestubelengthincreaseforprotonsandnotforelectrons?
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Proton-synchrotron.
§  Pre-accelerator:electrostaticaccelerator(1)
followedbyalinearaccelerator(2).
§  Mainring:(3)magnets,(4)acceleratingcavity
and(5)the“straightsections”
§  (6)targets,(7)secondarybeamlinesfor
experiments
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¡
Collisionswithdifferent
particlesleadto
complementaryinformation:
§  pN,
§  e+e-, ep
§  pp, ppbar,
§  pb pb,
§  νN, νe-, µN,
¡
¡
Previousacceleratorsaspreaccelerators
CollidervsFixedTarget
experiments
§  Collider:LHCppandPbPb
collisions
§  FixedTarget:neutrinobeamsent
fromCERNtoGranSassoinItaly
730kmaway
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¡
Hadroncolliders
§  Discoverymachines
▪  Fractionofproton
momentumcarriedby
quarksandgluons,x,varies
▪  largedomainofenergies
investigatedsimultaneously
▪  Potentialsourceofdiscovery
andsurprises
¡
Electroncolliders
§  Precisionmachines
▪  Linearcollidersasasolution
tothesynchrotronradiation
problemofcircularcolliders
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ep-colliders
§  Explorationandprecision
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§  Measurementofstructurefunctions
9
¡  N=L.σ
§  N:Distributionofnumberofevents
▪  Distributionmeasuredbydetector
§  L:Luminosity
▪  GivenbyAccelerator
§  σ:Cross-section
▪  Theory
¡
Feynmandiagramsà
processprobabilitybya
setofmathematicalrules
(Feynmanrules),derived
fromunderlyingquantum
fieldtheory
▪  Fermi’sgoldenrule
▪  M:matrixelement–transitionprobabilityiàfcalculableusingFeynman
diagramrules
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M (i1, i2 → f1, f2 ,..., fn ) %
d3 pf (
dσ =
'∏
*(2π )4 δ 4
3
4 ( p1 ⋅ p2 )2 − m12 ⋅ m22 '& n (2π ) 2E f *)
F. Ould-Saada
(∑ p −∑ p ) S
i
f
10
n. of protons
per bunch
Numberofcollisions
N=L.σ (pp→X)
LuminosityL
n. of bunches
N 2k b f
L=
4πσ xσ y
n. of turns
per second
beam size at IP
(σx,y = 16 µm)
€
Cross-section
σ
Verysmall
fornew
processes
LargeHadronCollider
27kmincircumference,100munderground
protonbuncheswith1000billionprotonscirculatenearly
atthespeedoflight:
v=0.99999991c
protonbunchescollideevery25/50ns:
100µsperround…10000roundspersecond
energyreleasedenablescreationofnewparticles
q  Particlecollisions
atLHC
Ø  Simulated
proton+proton
àblackhole
candidate
Ø  LHCcollides
alsoheavyions:
pb-pbandp-pb
q  Sensitivitytorare
phenomena–with
smallcross
sections–
dependsonthe
luminosity
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45 m
ATLAS superimposed to
the 5 floors of building 40
24 m
7000 Tons
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Let’s
build
ATLAS
in~1
minute…
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Arealeventinadetector…
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CMS: 2900 physicists
184 Institutions
38 countries
550 MCHF
LHCB 700 physicists
52 Institutions
15 countries
75 MCHF
ALICE; 1000 physicists
105 Institutions
30 countries
150 MCHF
and 3 smaller experiments
TOTEM
LHCf
MoEDAL
ATLAS : 3030 Physicists
174 Institutions
38 countries
550 MCHF
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Pb
Pb
Heavyioncollisions
p
π-
π+
ALICE activities in Oslo
ALICE
QCD phase
diagram
Exploding QGP
with initial-state
fluctuations
Tomographic QCD probes
Mission of ALICE: Investigating the QGP in
the LHC energy regime. Comparison of
Pb+Pb to p+p collisions (also p+Pb).
- Tomographic studies using selected hard
probes (e.g. neutral mesons, direct photons,
charged hadrons), medium modifications of
spectra (RAA) and correlations due to parton
energy loss in QGP. Jet-flow separation.
- Collective properties and dynamics explored
through anisotropic flow and thermal photon
spectra.
Nuclear modification,
p0 RAA
0
I p RAA
Di-hadron correlations – jets + flow
Thermal
PHOS module
(g-calorimeter)
p0 conversion
in the TPC
Prompt (pQCD)
Direct photon
spectrum
Detection of electromagnetic signals
https://www.youtube.com/watch?feature=player_embedded&v=zEX5qKvFZSs
21
¡
Particleidentification
throughdE/dx
§  measuredde/dxsignalversus
magneticrigidity,together
withtheexpectedcurvesfor
negatively-chargedparticles
(Bethe-Blockformula).
§  insetpanel:TimeOfFlight
massmeasurementwhich
providesadditionalseparation
between3Heand4Hefortracks
withp/Z>2.3GeV/c.
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¡
Fixedtargetppcollision
§  Strongprocesses
§  Fractionofavailable
energytransformedinto
mass
§  Newparticleproduced
§  Quantumnumbers
conserved:baryonand
leptonnumbers,electric
charge,…
§  Electromagneticprocesses
§  Weakprocesses
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¡
“new”particleπ0produced
§  Electriccharge,baryonicnumberconserved
▪  4-momentum:pi=(Ei,pi)
Practice!
§  Lorentz-invariant(c=1):
▪  p2=E2-p2=m2
▪  s=(p1+p2)2=(E1+E2)2–(p1+p2)2
▪
▪
▪
▪
p*1=(E*1,p*), p*2=(E*2,-p*)
√s=Ecm=(E*1+E*2)=2Tcm+2mp
√sthr=2mp+mπ
Tcmthr=mπ/2=67.5MeV
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▪
▪
▪
▪
▪
p1=(E1,p1), p2=(m2,0)
s=(E1+m2)2-p12=m12+m22+2E1m2
s=4mp2+2Tlabmp
Tlabthr=(sthr-4mp2)/2mp=280MeV
2
2
=((2mp+mπ) -4mp )/2mp
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¡
Time-of-flightspectrometer
§  PrimaryprotonbeaminteractswithtargetB
§  chargedparticlesemittedatanangleαarecountedwithcounterC1,
separatedinmomentumwithmagnetMandagaincountedwithC 2
2
▪  Angleβdependsonp/Q(momentum/electriccharge)
§  Timeusedbyeveryparticletotraveldistancel=C1 MC2 ismeasured:t=l/v
1
2
§  m=p/v=pt/lègivenpandl,timedependsonlyonmass
¡
Specialrelativity:
§  m=0vsm#0:
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⎫
l
p2
2
m + 2
⎬⇒t=
β = v / c = l / tc⎭
c
c
p = mvγ
Work out
numerical
example p. 59!
l l l ⎛ 1 ⎞ l ⎛⎜ 1+ η 2 ⎞⎟
p
Δt = − = ⎜ −1⎟ = ⎜
−1⎟; η =
v c c⎝β ⎠ c⎝ η
mc
⎠
F. Ould-Saada
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¡
Timedistributionfore,
π,K,p
§  P=1GeV/c;l=10m;
equalproportions
¡
Massdistributionof
particlesproducedin
theforwarddirection
inpNcollisionsat26
GeV
§  analysedwithatime-of-
flightspectrometer.
§  Beamof2GeV/c
26
F=qvB=mv2/R
è  p=qBR
è  P(GeV/c)=0.30 R(m) B(T)
¡
Simulationofaparticle
trackinahydrogen
bubblechamber(B=2T)
§  Onlyionisation
§  a)330MeV/celectron
§  b)470MeV/cproton
§  c)sagitta=AB2/8R
¡
c)AB=50cm,B=2T
§  P=1GeV/càr=1.67m,
s=2cm;
§  p=10GeVàs=2mm
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¡
Electronspiraltrack
§  B=0.12T
§  P(MeV/c)=3.6R(cm)
▪  v~cveryhigh(smallnumberof
bubbles)
▪  mverysmall:smallradius
▪  econstantlyloosesE/pàradius
smaller
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¡
e+e-pair
production
§  e+(e-)àγ
§  γ+Nàe+e-+N
§  Alsopossible:γeà(e+e-)e-
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¡
Asinglebubble
chambrephoto
§  4“new”particles:
K+,π+,µ+,e+,
K + → π +π 0
π + → µ +ν µ
µ + → e+ν eν µ
§  Noteimportance
ofkinematicsand
conservationlaws
▪  a:2-bodydecay
▪  b:3bodydecay++
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K + → π +π +π −
π + → µ +ν µ ; π − → µ −ν µ
µ + → e+ν eν µ ; µ − → e−ν eν µ
¡
¡
¡
3chargedparticles
1charged+1neutral
1charged+2neutrals
§
π-outsideplane,µ-decaynot
visible
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¡  32