Lecture 16 – Tools of the trade

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Lecture 16 – Tools of the trade

The final three lectures focus on how we produce particles and measure them in the laboratory.

Use practical units for this section unless otherwise stated.

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Tools of the trade

● ”Production” of particles in collisions

Accelerators ● Beam energies/configurations● Accelerator design ● LHC

● Measurement of particles produced from collisions (next lecture)

Interactions of particles in material Detectors to identify and measure

the momentum and energy of produced particles

Detector

x

xx

x x

x

x

x

x

x

Important to understand both particle properties themselves and the experimental techniques which are used to measure them.

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Collider or fixed target.● Collide two beam or scatter one beam off a stationary (fixed) target.

Collide high energy beams

● Usually head-on for maximum centre-of-mass energy and,eg, discovery potential for ”new” heavy particles (eg LEP-1; e+ + e- : 45+45 GeV)

● Sometimes asymmetric beam energies. (HERA: e-+p: 27.5 + 820 GeV), (KEK-B e-+ e+:8.+3.5 GeV).

Collide high energy beam with a stationary target (fixed target experiments).

Advantage- can easily change target material

Disadvantage – hard to achieve high c.m. energy (lec 10 and later in lecture)

Head-on collisions

Fixed target interaction

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An collider at which the electron and positron beams have the same energy

operates at 10.58 GeV centre-of-mass energy, which allows the production of the -meson

at rest. It decays into

e e

a mesons. The mass of a -meson is 5.28 GeV and its lifetime

(in its rest frame) is 1.5ps.

(a) Calculate the average decay length of the -mesons (i.e. distance they travel before decaying).

(b)

B B B

B

Instead of symmetric beam energies consider the experiment at KEKB at which the electrons

have energy 8 GeV and the positrons have energy 3.5 GeV. Again a -meson is produced but this

time its not at rest. If the energy is shared equally amongst the -mesons estimate the decay length

of a -meson. ( Experimentally, a -decay can be measured more efficienciently if the decay length

> 0.2mm (n

B

B B

12

28 12 5

2

1.5 10

10.59 5.2955.295 1.002

2 5.28

1 5.281 1 0.06 0.06 3 10 1.002 1.5 10 2.7 10

5.295

ext lecture). )

Decay length: = s

GeV

m=0.027mm

Energy of a

lab rest restl v v

EE

m

l

B

2 2

12 12 8 12 4

8 3.55.8

22.4

5.8 5.28 2.45.28

2.41.5 10 1.5 10 3 10 1.5 10 2 10 0.2

5.28

-meson in asymmetric beam energy experiment GeV.

Momentum GeV ;

Decay length m= mm

E

pp p m

m

l v c

Question

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History of accelerators in particle physics

Now 2009! ...

Traditionally collide hadron-hadron

(eg , ) and electron-positron.

+ (HERA)

Colliders are successful tools

for discovering fundamental

particles and measuring their

properties.

pp pp

ep

Top quark

W+-,Z0

3 light

gluon jets

Charm (J/

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The world’s major colliders

Name Colliding Particles

Approximate beam energies

(GeV)

Location Status

SLC e-e+ 50+50 Stanford, USA

Ended

LEP e-e+ 100+100 CERN, Geneva

Ended

Tevatron pp 1000+1000 Fermilab, USA

Current

HERA e-p 27.5 (e-) + 920 (p)

DESY, Hamburg

Ended

PEP-II e-e+ 9 (e-) +3.1 (e+) Stanford, USA

Current

KEKB e-e+ 8 (e-) +3.5 (e+) Tsukuba, Japan

Current

LHC pp 7000+7000 CERN, Geneva

Start 2009

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Designing a collider: e++e- or hadron-hadron ?

e++e- hadron-hadron

Clean – can study annihilation reactions with no remnants of colliding particles

Messy – remnants of interacting hadrons remain and influence measurements.

Lower energy (for same radius) due to synchrotron radiation. LEP: ECM200 GeV

Higher energy (for same radius) LHC: ECM14000 GeV

Energy of e+,e- known. Energy of q,q not known (only have pdfs)

Fixed energy of e+,e- for a given set of operator conditions

Variable energy of q,q for a given set of operatorational conditions

Best for detailed study Best for discovery

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SLC

(45 + 45 GeV).

SLAC National Accelerator

Laboratory (Stanford, California).

(1990-1998)

e e

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Cyclic accelerators”Bending” dipole magnets keep a particle in a circular trajectory. Cyclical accelerators are also called storage rings.

(16.01)

(16.02)

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Synchrotron

0r 0R B A C

Technology used for modern day cyclic accelerators, eg LHC, HERA, Tevatron...

Principles of a synchrotron:

(1) Acceleration performed in RF-cavities

(2) Accelerated by time-varying electric field.

(3) Bending magnetic field increased after particles pass through cavity

Synchronised to keep same radius:

(16.02) increases and increases

Out of time particle orbits corrected b

pr p B

qB

y form of time-varying -field.

Eg Particle arrives in time (synchronised).

Particle arrives behind and gets smaller momentum kick.

Particle arrives ahead of and gets bigger momentu

E

A

B A

C A

.

m kick

All particles move with After "momentum kick" in rf cavity.

Particle radius (16.03)

Particle radius (16.04) Similarly, (16.05)

AA

CBB A C A

v c

pA r

qB

ppB r r r r

qB qB

Time at fixed point in rf cavity.

A

B

EC

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Time at fixed point in rf cavity.

A

B

EC

2 1

2 2

1

2 2

angular frequency of increases

; = > (16.06)

Similarly angular frequency of decreases

= < (16.07)

and arrive "on time" next tim

BB B A

B B A

C AC C A

B

r c cT

c T r r

C

c c

T r r

C B

e.

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Question

Consider a charged particle accelerrated in a cyclical

acclerator. Explain why it is not possible to use an electronstatic

field around the ring to accomplish the acceleration.

Maxwell equation for el

0

0

ectrostatic fields.

(16.08) Work done per unit charge in moving a

charged particle around a closed loop=0.

Need time varying fields i.e.

(16.09)S

E dl

E dl B dSt

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Focus in horizontal plane.

Quadrupole focusing magnets

Force on +ve particles coming out or -ve particles going in plane.

Need beam to be sharply focused and not diffuse. Alternately placed to focus and defocus in horizontal and vertical planes.

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From lecture 10 - Luminosity

.

For colliding beams of particles and .

particle bunches, each of or in a ring of circumference

Particles move with speed and are steered by a magnetic field.

Collide at a collision point

a b

a b

j N N U

v

2100

times per unit time.

=beam cross section at collision point. (10.25)

Typical beam sizes mm

LHC: for nominal running conditions (i.e. when it works as planned)

2808 bunches

a b

jv

Ujv

N NUL A

A

11

34 2 110

per beam, 1.18 10 protons per bunch,

Bunch crossing/collision every 25ns.

Luminosity: L cm s

Collision point+detector

Na

Na

Nb

Nb

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Integrated luminosity and total number of events

00

0

0

'

'

(10.24) gives rate of reactions.

An experiment can run over a time .

Total number of interactions/"events"

Integrated luminosity

(10.26)

LHC will provide

tt

t

t

R L

t

Rdt Ldt

N Rdt

L Ldt

N L

1' 10 fb per year.L

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Cross sections for processes at the LHC and Tevatron

Total cross section

Total cross section

14 TeV

810

For LHC:

Total cross section

, mostly

"uninteresting" interactions

such as

nbtot

pp

pp pp

anything

210

Cross section for:

Higgs (150 GeV mass) +

nb <<<<<<<<<Higgs tot

pp

anything

1 interaction/"event" per bunch crossing.

Mostly "soft" interactions. Small rate for

"interesting" physics.

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QuestionFor "nominal" LHC running. Estimate how long will it take the LHC to

accumulate 10000 events containing a Higgs boson if the Higgs boson

has mass of (a) 150 GeV and (b) 500 GeV.

From earlier: expect 10 1

2

6 1 12

10

'

10000' 10 1

10

fb per annum

(a) For 150 GeV mass: nb.

Required integrated luminosity: nb fb

month (if the LHC would run all the year round)

(b) For 500 GeV mass:

Higgs

H

L N

NL

3 110 ' nb 10fb 1 year.

iggs L

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Limitations in energy of a synchrotron several factors determining maximum momentum/energy.

(1) radius of curvature ; (2) magnetic field ; (3) synchrotron radiation (next slide).

Factor (1) is determined by construction costs and

p qBr

we'd obviously like it

to be big as possible but practically, accelerators have been restricted to

radii of several km. To illustrate the effects of factors (2) and (3) consider

particles accelerated around the LHC ring at CERN: 27km circumference.

Prior to LHC building for (7+7 TeV) ring was used for LEP: (45+45 GeV

and later 104+104 GeV)

p p e e

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Synchrotron radiation

2 3 4

0

4

3

An accelerating charge loses energy by radiation.

Eg a particle with charge moving around a circle of radius .

Energy radiated per turn per particle:

(16.10)

=mass, =ener

q R

qE

R

Em E

m

4

413

4

11

10

gy.

Relativistic particles of fixed energy

Synchrotron radiation losses for electron at energy (16.11)

Synchrotron radiation losses for proton at energy

Large problem for el

p

e

Em

mE

E m

11

ectrons.

LEP at 45 GeV and 4km radius - 8 bunches of 4 10 particles

0.5MW lost via synchrotron radiation.

Synchrotron radiation limits beam energies for electron synchrotrons.

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Limitation of proton beam energy in a synchrotron

10

19

.

7000 4

7000 1.602 10

1.602 10 4000

Synchotron radiation effects tiny in comparison with electron.

(16.02)

Maximum energy determined by size and magnetic field

LHC: GeV ; km

p qBr

r B

p r

pB

qr

85

3 10T (16.12)

Achieved with superconducting electromagnets.

Can't get much higher than that.

Proton energy limited by achievable size of magnetic field.

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Detection of particlesBefore discussing detectors it is first

important to establish how particles

will interact in matter following their production

at a collider.

Some observations:

(1) Particles will decay down into the

st 1010

, , , , ...

able particles s which enter a

detector. Consider the interactions of these,

eg

(2) Different classes of particles interact differently.

(neglect weak interactions).

(i) Charged le

e K n

0

,

, ,..

, ,..

ptons interact electromagnetically.

(ii) Photons interact electromagnetically

(iii) Charged hadrons interact strongly and electromagnetically.

(iv) Neutral hadrons interact strongl

e

K

K n

y.

Important to understand electromagnetic and strong interactions in matter.

Detector

x

xx

x x

x

x

x

x

xK- e-

e+

n

p

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Question1986 Examination.

In the USA a collider, the SSC (superconducting super collider) is planned. Head-on collisions

between protons, each with energy 20 TeV would take place. Calculate the machine's radius

for a magnetic field of 2.7 Tesla, the centre-of-mass energy and which energy a fixed-target

machine would need to give the same centre-of-mass energy. Which radius should an

equivalent accelerator have

20000 1.60220

to produce the high energy beam which is fired into the fixed

target. Compare the answer with the radius of the earth.

(Obs! This project was cancelled in 1993.)

TeV=p

p qBr r pqB

101

8

1019 4

8 19

10

3 10

20000 1.602 101.602 10 2.7 2.47 10 24.7

3 10 1.602 10 2.7

20 20 4

kgms ;

= C B= T m= km.

Centre-of-mass energy= 0 TeV

Fixed target (stationary proton) where beam energy

Fixed t

q r

E

22 2 2 2 2

25

56

,0,0, ,0,0,0 ,0,0,

2 2 40

400.001 8.0 10

2 0.001

8.0 1024.7 10 6400

20

arget:

TeV

TeV TeV.

km >> Earth radius= km.

p p

cm p p p p

p

P E E m E m E

E P P E m E Em m Em

m E

r

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Summary

● Accelerators and Colliders Symmetric and asymmetric beam energies chosen

depending on the physics under study Linear and cyclic accelerators Synchrotron beam energies restricted by

synchotron radiation (electron) and magnetic field (protons)