Physics at the Large Hadron Collider: Luminosity ... · Physics at the Large Hadron Collider: Luminosity Measurements at the LHC Introduction about the LHC as rpoton colliding machine

Physics at the Large Hadron Collider: Luminosity Measurements at the LHC

Physics at the Large Hadron Collider:Luminosity Measurements at the LHC

Christian [email protected]

28. Januar 2009

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Introduction about the LHC as proton colliding machine

Luminosity in HE collider experimentsSome basicsMethods for absolute luminosity determination at LHC

Instruments for absolute luminosity calibrationAbsolute Luminosity measurement For Atlas (ALFA)Zero Degree Calorimeter (ZDC)

Instruments for relative luminosity monitoringLUminosity measuring using Cherenkov Integrating Detector(LUCID)

Summary

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Summary

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Most important features of a collider ring

I The actual accelerator: a RFcavity

I Dipole magnets to bend thebeam around the circle

I Quadrupol magnets to keepthe beamsize small

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The LHC RF cavity

I A f ≈ 400MHz RF �eld isgenerated inside the 8cavities per beam

I The accelerating �eld is5MVm−1

I Frequency and phase areadjusted in a way, so thatthe protons are quasiwaveriding

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The dipole magnets

I 1232 dipole magnets createa peak magnetic �eld of8,33T in the beampipe

I The superconducting NbTiwire is kept at 1,9K whilecooled with super�uid helium

I The current inside the coilsis 11,7 kA

I Each dipole magnet weighsabout 35 t

I Here physics are rather easy:

~p = e · ~v × ~B6 / 46



The quadrupole magnets

I The trajectories, because ofthe impulse distribution,would occupy to muchvolume

I focusing with quadrupolemagnets

I 392 main quadrupolemagnets installed along thering

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Strong focusing (FODO structures)

I The quadrupole magnetshave a focusing e�ect in onedirection and a defocusing inthe other

I Therefore one uses a latticeof Focusing, freepropagation, Defocusing,free propagation and so on...(FODO)

I The equation of motion in this case is the so-called HillsequationBut sorry, here physics are a bit more complicated

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Hill's equation

I Maxwell's equations for our case (vacuum no electric �elds):

~∇ · ~B = 0, ~∇× ~B = µ0 ~j + ε0µ0∂~E

∂t= 0 ⇒ ∂Bx

∂y=∂By

∂x

I Taylor expansion of B

By (x) = B0y (x)︸︷︷︸dipole

+∂By

∂xx︸︷︷︸

quadrupole

+ ...

Bx(y) = B0x(y) +∂Bx

∂yy + ...

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Hill's equation

I The equations of motion (only const. quadrupole �eld):

px = −e vz∂By

∂xx , py = e vz

∂Bx

∂yy

I Harmonic oszillation on one axis and exponential increase onthe other

x = −Kx , y = Ky , K = vze

m

∂Bx

∂y

I This discussion only accounts to small de�ections or an idealquadrupole �eld!

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Hill's equation

I Quadrupole �eld changes over time t or distance z along theaccelerator circle

I Use independent variable s[m]

x ′′(s) = K (s) x(s)

this is the so-called Hill's equation

I The solution can only be derived numerically and is in theform:

x(s) =√ε√β(s) cos (ψ(s) + φ)

I initial conditions → ε, φ

I ε is the so-called beam emittance (πε is the area the trajectoryencloses in 2D phase space)

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The β-function

I The β-function issome sort ofenveloping functionfor the particletrajectories with alimited beamemittance

I Beamsize assuming agaussian distribution:

σ =√εβ

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Beam optics near the interaction point

I Goal: minimal β at IP ⇒ maximal luminosity!13 / 46



Some facts - the LHC in numbers

Circumfrence 26 659mNominal energy, protons 7TeVNominal energy, ions 2,76TeV/uDesign luminosity 1034 cm−2s−1

Peak magnetic dipole �eld 8,33TNumber of magnets 9 593Number of main dipoles 1 232Number of quadrupoles 392Number of RF cavities 8 per beamNo. of proton bunches 2 808 per beamNo. of protons per bunch 1,1 · 1011Distance between bunches 7mProton velocity 99,999 999 1%c

Number of turns per second 11 245Number of collisions per second 6 · 108

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Luminosity in HE collider experiments

Some basics





Summary

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Some basics

What is luminosity?

I Luminosity links counting rates in detectors to the crossection

σ =N

L

I It is in a center of mass system collider experiment:The product of the number of particles per unit area from bothsides times the overlapping area of the beames per unit time

I Or in a collider, that like the LHC works with bunches ofparticles:

L =n1n2f

4πσxσy

with n1, n2 number of particles per bunch, σx , σy the beamdimensions and f the bunch crossing frequency

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Some basics

Why is knowing it with high precision so important?

I For collider experiments: theory predicts crossections

I The detectors measure production rates

I Precise knowledge of luminosity ⇔ Precise measurement ofcrossections

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Some basics

How can one determine and monitor it?

I Absolute luminosity determination needs theoretically wellunderstood processes

I The rate of all interactions scales with luminosity

I So in principle every process can be calibrated and used tomonitor the luminosity

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Methods for absolute luminosity determination at LHC





Summary

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Using the LHC beam monitors

I The LHC beam monitors are sensors to monitor and to preventlosses of the beam

I It is di�cult to obtain the luminosity from this data

I To make things even more complicated the nearest beammonitors are far away from the IP

I Even so estimates range between 10 and 20% of accuracy forthis method

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Well-calculable physics processes observed by ATLAS

QED production of µ-pairs by double photon exchange:

I QED process ⇒ crossection well calculable

I experimentally clean

I but very small observable crossection

QCD production of W and Z gauge bosons:

I One of the best known QCD processes

I Still the error is dominated by the theoretical uncertainty

The estimated accuracy for this method is 5-10%

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Elastic scattering at small angles

For very small momentum transfer t, which means very smallscattering angles:

I proton-proton scattering via the strong interaction becomeselastic

I at even smaller angles, the coulomb interaction overbalancesstrong interactions

I experimental di�culty to resolve such small de�ection angles

I Goal: to reach an accuracy of arround 3%

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I Optical theorem with momentum transfer t:

σtot = 4π · =[fel (t = 0)]

for small t:−t = (p sin(θ))2 ≈ (pθ)2

I Remembering:

σ =N

L⇒

L =1

16π

R2tot(1 + ρ2)dRel

dt

∣∣t=0

, ρ ≡ <[fel (t)]

=[fel (t)]

∣∣∣∣t=0

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I Elastic rate: coulombinteraction and nuclearinteraction

dN

dt= Lπ |fC + fN |2

≈ Lπ

∣∣∣∣ −2α|t|︸︷︷︸coulomb

+σtot4π

(i + ρ)e−b|t|2︸︷︷︸

strong

∣∣∣∣2

I Strong amplitude equals EM amplitude for |t| = 0,000 65GeV2

→ scattering angle of 3,5µrad (η = 12, 56) for LHC

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Instruments for absolute luminosity calibration

Absolute Luminosity measurement For Atlas (ALFA)





Summary

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Requirements for measuring elastic scattering

I Special high β parallel-to-point optics

I To place detectors only ≈ 1,5mm from the LHC beam axis

I Detectors have to be integrated in the beam vacuum

I No signi�cant inactive edge (< 100µm)

I resolution of < 100µm× 100µm (goal 30µm× 30µm)

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The optics

I High β(s) means high x(s) but small x ′(s)

I Beam is sensitive on small t = (∆x ′)2

I Phase advance ψ(s) must allow parallel-to-point-focusing

I Luminosity strongly decreases in high-β runs

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Roman Pots

I Two roman pots are located240m from the IP

I They are integrated into thebeam vacuum

I Detectors can be broughtclose to the beam andretracted

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Roman Pots

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The ALFA detector

I Scintillating �bres of 0,5mmdiameter

I Areal resolution for the areawhere �bres are crossed

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Why scintillating �bres?I Scintillating �bres are very resistant to radiationI The �bres are cut in an angle of 45° at the end, so the active

detector area starts right at the edgeI Capability to deal with high ratesI Time resolution of 5 ns

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Tests and simulations

I Lab tests: ∆xdet. = 56µm

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I Geometrical acceptance in 3dist. to the beam

I With two roman pot stations(dist. 4,14m), the transveselocation of the vertex can bereconstructed

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Zero Degree Calorimeter (ZDC)





Summary

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I The ZDC is located 140m after the IP between the pipes ofthe just separated beam

I It could be used to determine luminosity in heavy ion runs

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I EM detector I Hadronic detector39 / 46


Instruments for relative luminosity monitoring

LUminosity measuring using Cherenkov Integrating Detector (LUCID)





Summary

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Monitoring luminosity

I The absolute luminosity measurements by ALFA need specialhigh-β runs

I In normal operation one wants to achieve the highest possibleluminosity which means minimal β

I Instrument needed that monitores luminosity with highprecision and in a wide range

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LUCID

I Stands for LUminosity measuring using Cherenkov IntegratingDetector

I Uses Cherenkov tubes with integrating radiation hard PMTs

I Is part of the ATLAS forward detectors (17m from IP)

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LUCID

I Pseudo rapidity η = 5, 6 .. 6

I This is inelastic pp scattering → mainly hadronic jets aremeasured

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Summary





Summary

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Summary

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Summary

Summary

I The �rst estimates for luminosity will come from the beammonitors

I The production rate of µ pairs, W and Z bosons will also givea good approximation

I In special high-β runs ALFA will calibrate LUCID to achieve anaccuracy of ≈ 3%

I However all three techniques will be compared

I In heavy ion runs the ZDC can determine luminosity withreasonable accuracy

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Documents

Physics at the Large Hadron Collider: Luminosity ... · Physics at the Large Hadron Collider: Luminosity Measurements at the LHC Introduction about the LHC as rpoton colliding machine