Particle Physics Status and Perspectives - PowerPoint Presentation

Slide1

Particle Physics

Status and Perspectives

142.095

Claudia-Elisabeth WulzInstitute of High Energy PhysicsAustrian Academy of Sciencesc/o CERN/PH, CH-1211 Geneva 23Tel. 0041 22 767 6592, GSM: 0041 75 411 0919E-mail: Claudia.Wulz@cern.chhttp: //home.cern.ch/~wulz2 May 2017

Part

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Literature

Theory:T. Morii, C.S. Lim, S.N. Mukherjee: The Physics of the Standard Model and Beyond, World Scientific Publishing Co. (2004)D. Griffiths: Introduction to Elementary Particles, J. Wiley VCH (2008)General: B.R. Martin, G. Shaw: Particle Physics, J. Wiley and Sons (3rd ed. 2008) D. H. Perkins: Introduction to High Energy Physics, Cambridge U. Press (4th edition, 2000)Detectors:W. R. Leo: Techniques for Nuclear and Particle Physics Experiments,Springer (2nd ed. 1994)Ch. Joram: Particle Detectors, http://joram.web.cern.ch/Joram/lectures.htm

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Web pages

Introductions to particle physics:http://www.cpepweb.org/http://particleadventure.orghttp://www.particlephysics.ac.ukhttp://www2.slac.stanford.edu/vvc/Default.htmhttp://www.teilchen.atFor physicists/students:http://indico.cern.ch/categoryDisplay.py?categId=70http://pdg.lbl.gov/

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High Energy Physics

=

Elementary particle physics

•

•

What is matter made of and how

does it keep together?

It deals with particles and their

interactions

3

Slide5

High energy physics

One needs higher momenta to explore smaller dimensions.Energy can be borrowed for a short time.

D

l @ 1/GeV @ 0.2 . 10-15 m

1/4

of the radius of a proton

Important units and constants

h

_

D

p

D

l ≥ , DE Dt ≥

Heisenberg’s uncertainty principle

h

_

h

_

…

Planck’s constant (action) = h/2p = 6.6 . 10-22 MeVs1 eV = 1.6 . 10-19 Ws … unit of energyProton mass: 938 MeV/c2 = 1.67 . 10-27 kg, electron mass: 0.511 MeV/c2 = 9 . 10-31 kgNote: c and ħ are often set to 1 (“natural units”), such that MeV or GeV represent energy, momentum or mass.

h

_

4

Slide6

The Standard Model of Particle Physics

The Standard Model is a theory of the strong, weak and electromagnetic forces, formulated in the language of quantum gauge field theories, and of the elementary particles that take part in these interactions. It does, however, not include gravity. Interactions are mediated by the exchange of virtual particles.Fundamental forces

FORCERELATIVE STRENGTHRANGECARRIERStrong1 10-15 mGluonsWeak10-610-18 mW, ZElectromagnetica (10-2)infinitePhotonGravitational10-38 infiniteGraviton ?

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Slide7

Particle Content of the Standard Model

Matter particles: Fermions (half-integer spin, s = ½ħ) and their antiparticles.There are 3 families (generations) of fermion fields, which are identical except for their masses. Fermions come as leptons and quarks. Mediator particles:Gauge bosons (integer spin, s = 1ħ).There are 3 types of gauge bosons, corresponding to the 3 interactions described by the Standard Model. Higgs particle:Needed to explain that the symmetries of the electroweak theory are broken to the residual gauge symmetry of QED. Particles that interact with the Higgs field cannot propagate at the speed of light and acquire masses through coupling to the Higgs boson (s = 0ħ).

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7

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Slide9

Gravitational interaction

Long-range forceOnly attractiveGravity is currently described by General RelativityDifferent assumptions about the Universe at the macroscopic scale than those made by quantum mechanics at the microscopic scaleQuantum gravity: theories that attempt to unify gravity with the other forces (e.g. string theory, loop quantum gravity)Examples of systemsBlack holesUniverse

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Electromagnetic interaction

Long-range force

Much stronger than gravity but effectively shielded over long distances

Repulsive or attractiveUnified description of electricity and magnetism.Examples of systems:Atoms (electrons and nuclei)Electromagnetic waves (light, radio waves)

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Slide11

Weak interaction

Short-range forceVery weakOnly force that can change the flavor of quarks (e.g. d -> u) Unified with electromagnetic forceCP violation (charge conjugation, parity not conserved)Examples of systemsNeutrino interactionsBeta decaysNuclear fusion

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Slide12

Particles without strong interactions are called

LEPTONS

(e.g. electron, muon, neutrino). The weak interaction is mediated by the INTERMEDIATE VECTOR BOSONS (W±, Z). They are about 100 times heavier than the proton and were discovered in 1983 at the experiments UA1 and UA2 of the CERN SppS collider entdeckt. Carlo Rubbia and Simon van der Meer received the Nobel Prize for their decisive contributions.

It occurs for example in radioactive

b

-decay (e.g. 3H  3He):

1

2

11

The weak interaction

Slide13

“…for their decisive contributions to the large project which led to the discovery of the field particles

W

and Z, communicators of weak interaction”

Nobel prize 1984

C. Rubbia S. van der Meer

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Slide14

C.-E. Wulz

13

W -> en at the UA1 experiment

13

13

Slide15

C.-E. Wulz

14

ino

Z -> e+e- at the UA1 experiment

14

14

Slide16

Strong interaction

Short-range forceVery strongHolds quarks (and nuclei) togetherMediated by gluonsNeither gluons nor quarks are free particles (“Confinement”)Particles that experience the strong force are called hadronsExamples of systemsProton and other atomic nuclei

Slide17

Gluons and quarks carry a

color charge (“COLOR”) Quantumchromodynamics (QCD)Visible particles are colorless, however.

u

d

Þ

Proton

u

Ü

d

u

d

Þ

u

Ü

»»

»»

u

d

u

d

d

p

+

Neutron

d

16

The strong interaction

Slide18

Yukawa theory

Protons and neutrons in nuclei are attracted through a field. The field quantum must reflect the properties of the strong interaction, which means it must be relatively heavy due to the short reach of the nuclear force. Yukawa claimed that its mass should be about 300 me. He called it meson (mass between me and mp).

Particles with corresponding properties were indeed found in cosmic rays. Nevertheless, discrepancies appeared in mass and lifetime measurements, and only a weak interaction with atomic nuclei was found. The particles found were actually

muons.

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Slide19

Marietta Blau

Marietta Blau at the Vienna Institute for Radium Research (Radiuminstitut), about 1925

She developed a photographic method for the study of cosmic rays, which led to the discovery of new particles. With her method the pion was discovered in 1947 by Cecil Powell et al. and much later, in

Jahr

2000, the tau neutrino. Powell received the Nobel prize in 1950, which

Blau should probably have shared owing to her decisive contributions. She was twice nominated by Erwin Schrödinger for the Nobel prize.

1894 - 1970

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Slide20

+  + + 

Lattes, Powell, Occhialini, Muirhead (1947)Pic du Midi Observatory

Marshak

, Bethe: Muons could be decay products of heavier particles, which could in turn be Yukawa’s mesons.Indeed, p mesons (now called pions) where identified as Yukawa’s field quanta. Their decay products, the muons, have nothing to do with the strong interaction. They mostly decay before reaching the surface of the Earth to electrons and two neutrinos (the electron’s energy is not constant – 3-body decay): +  e++e+m -  e-+e+m

-

-

p

600

m

m

m

e

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Slide21

1947 it looked as if the greatest problems in elementary particle physics were more or less understood, apart from the role of the muons (I. Rabi: “Who ordered that?”). Then came the dioscovery of “strange particles” …

K

+

m

+

3 cm lead

}

Charged V event: K+  m + + nm

Rochester, Butler:K0 K+ K+  etc.Anderson et al.:L 

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The “strange particles” were strange insofar as they were produced in large quantities (time scale typically 10-23 s), but decayed relatively slowly (time scale 10-10 s). This meant that their production and decay mechanisms were different. Strange particles are produced through the strong interaction, but they decay through the weak interaction. Gell-Mann and Nijishima attributed a property named “strangeness” to each particle, which is conserved in strong interactions, but violated in weak interactions. Therefore strange particles are only produced in pairs, such as p- + p+  K0 + L When they decay, strangeness is not conserved, e.g.   p + p- .

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Willis Lamb in his Nobel lecture 1955:When the Nobel Prizes were first awarded in 1901, physicists knew something of just two objects which are now called « elementary particles »: the electron and the proton. A deluge of other « elementary » particles appeared after 1930; neutron, neutrino, μ meson, π meson, heavier mesons, and various hyperons. I have heard it said that « the finder of a new elementary particle used to be rewarded by a Nobel Prize, but such a discovery now ought to be punished by a $10,000 fine ». A similar thing was said in 1963 by Enrico Fermi (to Leon Lederman) in connection with hadron spectroscopy, which resulted from the quark model that was subsequently presented:Young man, if I could remember the names of all these particles, I would have been a botanist.

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The quark model

Elementary building blocks of matter:

Materie:

1964: Gell-Mann, Zweig

23

Slide25

The quark model

24

Slide26

Mesons, Baryons

Each baryon consists of

3

quarks.

Each meson consists of

1

quark and 1 antiquark.

25

Slide27

Mesonen octet

-

-

p + (ud)

K0 (sd)

K

0

(ds)

K+ (us)

p - (du)

p0, h

(uu,dd,ss)

K- (su)

-

-

-

-

-

-

-

-

Gell-Mann,

Ne’eman (1961)

26

The eightfold way

Slide28

n (udd)

p (uud)

S

- (dds)

S+ (uus)

S0 (uds)

L (uds)

X- (dss)

X0 (uss)

Baryon octet

27

The eightfold way

Slide29

L+ has the same quark content as the proton, but a different energy level, analogous to a hydrogen atom in different states of excitation.

Baryon decuplet

L

- (ddd)

L0 (udd)

L+ (uud)

L++ (uuu)

S*- (dds)

X*- (dss)

W- (sss)

X*0 (uss)

S* (uus)

S

*0

(uds)

Quarks: s

pin

1/2!

Pauli

- principle

-> COLOR(O.W. Greenberg)

28

The eightfold way

Slide30

The Omega Minus

Brookhaven, 1964

29

Slide31

Glashow, Salam, Weinberg (1978)3 families (generations) of quarks and leptons:

e

n

e

(

)

m

nm

(

)

t

nt

(

)

+ antiparticles 12 leptons

u

d

(

)

c

s

(

)

t

b

(

)

[

+ antiparticles

]

x 3 colors 36 quarks

4

mediator particles of the electroweak interaction:3 intermediate vector bosons (W±, Z) + 1 photon (g)8 mediator particles of the strong interaction:8 gluons (g)1 particle to generate mass (for W, Z and fermions):Higgs boson (H)

Summary of the Standard Model

30

Slide32

Practically all existing data (except neutrino masses) are very well described by the standard model. But the question of particle masses is not yet fully understood! In the standard model there is a particle associated with the mechanism through which most (or all?) particles obtain mass - the Higgs boson.It was found at the Large Hadron Collider (LHC)Design beam energy: 14 TeV p-p (2012 8 TeV, since 2014 13 TeV) It was not possible to establish a discovery at Fermilab‘s Tevatron near Chicago. Previously, at LEP at CERN compatible events were also found, but their statistical significance was not high enough. In the framework of supersymmetry there could be more Higgs particles as well as supersymmetric partners of known particles (squarks, sleptons, gluinos etc.).

31

The Higgs boson

Slide33

Sources of highly energetic particles

1950:

Only source of highly energetic particles was cosmic radiation (“Höhenstrahlung”) discovery of positrons and pions. Today: almost exlusively particle accelerators are used. Advantage: only 1 projectile with known, selectable energy.Fixed target experiment: stationary target, one single particle beamCollider experiment: two counter-rotating particle beamsIn both cases the produced particles are detected through their interaction with matter detectors

Linear accelerator

Storage ring

32

Slide34

Electromagnetic forces are used to accelerate stable, charged particles. A source is needed, e.g. hot cathode (heated wire) or an ion source.- Linear accelerators (LINACs)- Circular accelerators (cyclotrons, synchrotrons)Synchrotrons:Energies larger than 1 GeV. “Circular” orbit through arrangement of dipole magnets (deflection magnets), acceleration through high frequency cavities. For beam focussing quadrupole- , sextupole- or more complex magnets (focussing magnets) are used.

Particle accelerators

33

Slide35

Principle of acceleration

Elektromagnetic

wave as seen from above

red

+, blue -

Electromagnetic wave is traveling, driving particles along with it

Electromagnetic wave

Positively charged particles close the the crest of the electromagnetic wave experience the largest force forward; those closer to the center experience less of a force. The result is that the particles tend to move together with the wave - stability of the orbit.

RF in phase with the particles.

34

http://

particleadventure.org/accel_ani.html

Slide36

Schematic of a synchrotron

35

Slide37

Super Proton Synchrotron of CERN

36

Slide38

HERA

at DESY

37

Ep = 920 GeV

E

e

-

= 27.5 GeV

Slide39

Sextupole magnet (LEP/CERN)

Quadrupol

magnet

(HERA/DESY)

38

Slide40

LHC test stand

with dipoles

High frequency resonator

(TESLA prototype for linear collider)

39

Slide41

Cross section of an LHC double dipole

40

Slide42

Center

-of-mass

and laboratory energies

Center

-of-mass frame):p = S pi = 0 ECM = Wc2

W

2c4 = E2 - p2c2W … invariant mass of a set of particlesE, p … Total energy and momentum

e.g. particle beam of particles with mass

m

S

,

hitting a target with mass mT and momentum pL hat. The target is at rest, therefore pT = 0.Particle energies in the laboratory frame:EL = √mS2 c4 + pL2 c2 ET = mT c2W2 c4 = (EL + mT c2 )2 - pL2 c2 = mS2 c4 + mT2 c4 + 2 mT c2 EL ECM = √mS2 c4 + mT2 c4 + 2 mT c2 EL

41

Slide43

Fixed target accelerators and colliders

Fixed target accelerator

Collider

ECM = √mS2 c4 + mT2 c4 + 2mT2 c2 EL ECM = 2 EL ECM ~ √ ELmany particles only stable, charged particleshigh luminosity lower luminosity

E

CM

…

center-of-mass energy, EL … laboratory energypCM = 0 … center-of-mass momentum,mS … mass of the beam particle, mT … mass of the target particleFixed target: Part of the energs must appear as kinetic energy of the final state particles and is therefore not available for particle production.

42

Slide44

Storage rings: acceleration and storage of particles with mit opposite charge in a single magnet ring. Linear Collider: straight beam tubes.

Acceleration up to the maximal energy, extraction onto a stationary target (solid or liquid).Primary beams: stable charged particles (e.g. p, e±)Secondary beams: neutrals or unstable particles (e.g. p, g, n).

Collider

Fixed target accelerator

43

Slide45

44

https://cms-docdb.cern.ch/cgi-bin/PublicDocDB/RetrieveFile?docid=4594&version=1&filename=SynchrotronCB.swf

Slide46

45

https://cms-docdb.cern.ch/cgi-bin/PublicDocDB/RetrieveFile?docid

=4173&version=1&filename=

SynchrotronFT.swf

Slide47

Production of secondary beams

Only stable charged particles are suited for acceleration. However, also neutral (e.g.

g) or instable particles (e.g. p±) are needed. These can be produced by directing a primary beam onto a metallic target. Through reactions with the nuclei of the target new particles are produced, which can then be analyzed.Example 1: p+ beam

p

+

p

+

p

X

Y

p

+

Collimator

electrostatic

and magnetic

fields

Monoenergetic

beam

Heavy

target

46

Slide48

Production

of secondary beams

Example

2:

n beamp± m± + nm m+ and undecayed p± are absorbed in a long absorber. The neutrino momenta depend on the original pion momenta. No further momentum selection is, however, possible!

p

±

n

m

Long

vacuum tube

Absorber

47

Slide49

KEK, Japan

p

12

SLAC, Stanford, Cal.

e

-

25

PS, CERN,

Geneva

p

28

AGS, Brookhaven, NY

p

32

Serpukhov,

Russia

p

76

SPS, CERN,

Geneva

p

450

Tevatron, Fermilab, Ill.

p

980

Fixed target machines

CESR, Cornell, NY

e

+

(6)

e

-

(6)

PEP, Stanford, Cal

. (till 1990)

e

+

(15)

e

-

(15)

TRISTAN,

Japan

(till

1995)

e

+

(32)

e

-

(32)

SLC, Stanford, Cal.(till 1998)

e

+

(50)

e

-

(50)

LEP-I, CERN,

Genf

(till 1995)

e

+

(55)

e

-

(55)

SppS, CERN, Genf

p(450)

p(450)

Tevatron

II,

Fermilab

(till

2011)

p(980)

p(980)

HERA, Hamburg (till 2007)

e

-

(27.5)

p(920)

LEP-200, CERN,

Genf

(till 2000)

e

+

(104)

e

-

(104)

LHC(>

2013)

, CERN,

Geneva

p

(6500

)

p

(6500

)

Collider

p

/e

–

Particle accelerators

48

Particle type

Beam energy/

GeV

Particle type

Beam energy/

GeV

Slide50

Synchrotron

Momentum

of a charged particle in a

magnetic field

:

Conventional magnets: Bmax ≈ 1.5 TSuperconducting magnets: Bmax ≈ 10 TFrom the formula above once can see why large radii are required for large beam momenta. Synchrotron radiation also plays a role. Synchrotron: During acceleration the magnetic field must be raised in synchronization with the momentum, as the orbit should stay constant.

p … Momentum in GeV/cr … Curvature radius in metersB … Magnetic flux density in Tesla

p = 0.3 B r

49

Slide51

Synchrotron

radiaton

Synchrotron radiation per orbit:

For

b

≈ 1 (v ≈ c)

with E = gmc2 DE ~ 1/m4 big loss of energy for electrons (at same momentum 1013 as high as for protons!), therefore in practice conventional electron accelerators have maximally about 100 GeV per beam.

b

= v/c, g = (1-b2)-1/2 … Curvature radius of the orbitq … Charge of the orbiting particlese0 = 8.85 pF/m

50

Slide52

European Synchrotron Radiation Facility

51

Grenoble

Slide53

Luminosity

L

… Luminosity in cm-2 s-1 , R … collision rate in s-1 s … Beam-beam cross section in cm2

R =

s

L

Example for a particle-antiparticle storage ring (pp, e+e-):1 vacuum tube with same magnetic field.N … Number of particles per bunchWith 1 bunch each there are 2 collision points. At each collision point (“interaction region”) collisions occur with a frequency f ≈ c/u, with u being the circumference of the storage ring.

52

Slide54

The luminosity at a collision point is then given by the following formula:nbunch … Number of bunches, N± … Number of particles per bunch A … Beam area for complete overlap of the beamsL A Fokussing magnets (e.g. quadrupoles) A = 4p sxsy for gaussian-distributed deviations from the ideal orbitsx, sy … horizontal and verticale beam size (rms)Particle oscillations in vertical and horizontal directions with respect to the ideal orbit : betatron oscillations. Longitudinal oscillations relative to the movement of an ideal particle (in phase with the high frequency field):synchrotron oscillations.

L

=

f n

bunch

N

+

N

-

A

Luminosity

53

Slide55

Ideal orbit of a beam particle: center of the ellipseActual location of a beam particle in phase space :s, … Transverse displacements’ … Angle to the beam axisUnit of e is normally mm mrad, and of b m. b* … Value of the amplitude function at the interaction point (focussing!) Emittance reflects the quality of the beam, the amplitude function the beam optics.

Emittance

, amplitude function

x’

x

Transverse

e

mittance

e =

pss’

Amplitude function

b = s/s’

54

Slide56

LHC

Quadrupole

Magnets

55

At

ATLAS

and

CMS:

b

* = 0.5 m,

s

x

=

s

y

=

16

m

m,

b

≈

80 m,

s

x

,

s

y

≈

0.2 mm

elsewhere

Slide57

Collider Particles L/cm-2s-1SLC (Stanford) e+ e- 0.35x1030LEP (CERN) e+ e- 2x1031HERA (DESY) e- p 1.6x1031SppS (CERN) p p 6x1030Tevatron (Fermilab) p p 4x1032 *)KEKB (Tsukuba) e+ e- 1x1034PEP II (Stanford) e+ e- 3x1033LHC (CERN) p p 1x1034*) with Main Injector, 2x1031 without

Typical luminosities for colliders

56

Slide58

Accelerator complex of

CERN

LHC/LEP

SPS

57

Slide59

Tevatron

Main Injector

Accelerator complex of

Fermilab

58

Slide60

Accelerator

complex of Fermilab

Tevatron

Main Injector

59

Slide61

Accelerator complex of SLAC

60

Slide62

Accelerator

complex

of SLAC

61

Slide63

Accelerator

complex of

KEK

62

Slide64

Particle detection

Particles are detected through: Interaction with the detector material (nuclei) Strong interaction for hadrons Weak interaction for neutrinos Production of new particles if energy sufficiently high Ionization of atoms (charged particles) Emission of electromagnetic radiation (charged particles) g -> e+e-

63

Slide65

Interactions with atomic nuclei

Short range. For hadrons, the strong interaction is equally important for charged and neutral particles.e.g. Interaction with the smallest nucleus, the proton:Elastic scattering:e.g. p - + p -> p - + pInelastic scattering:e.g. p - + p -> p + + p - + p 0 + n p - + p -> K0 + L nl + p -> l+ + X

64

_

Slide66

Interactions with atomic nuclei

Total cross sectionstot = sel + sinelstot = sel + sq + sinel (for larger nuclei)sinel … large at high energiesn; sum over all possible inelastic processes allowed by conservation laws.stot ≈ (10…50) mb for p or n, larger for nuclei (1 mb = 1 millibarn = 10-27 cm2)sq … cross section for quasi-elastic scattering (elastic scattering on nucleons) recoil -> nuclear recoil -> excitation or fission

65

Slide67

stot and sel for p - + p

stot = (10 … 50) mb for other incident hadrons

stot ≈ r 2p ≈ 30 mb for r ≈ 10-15 m

p (GeV/c)

s

(mb)

stot

sel

10

1

10-1

102

103

10

100

tot is of the same order as the geometric cross section.It varies only slowly with p for momenta above approximately 3 GeV/c.

66

Slide68

Interactions with atomic nuclei

Collision

lengthProbability (Pc) for a hadron-nucleus interaction in a thin layer with thickness dx.Pc = n stot dx (n = rNA/A … nuclei per unit volume)A … Molar mass (g/mol), r … Density (g/cm3),NA … Avogadro‘s number (6.022 . 1023 / mol) Mean free path length (“collision length”): lc = 1/n stotAbsorption length (“Interaction length”)la (la ) = 1/n sinelCollision- and absorption lengths are often also expressed in g/cm2 :lc’ = A/NA stot = r lc, la’ = A/NA sinel = r la

e.g. for neutrons on Pb: lc = 10.2 cm, la = 17.1 cm; lc’ = 116.2 g/cm2, la’ = 194 g/cm2

67

Slide69

Atomic and Nuclear Properties of Materials

Particle Data Group (http: //pdg.lbl.gov)

Tabelle gilt für n oder p. Für

n

ist stot extrem klein (10-47 m2!)

68

Slide70

Ionization

dE

Dq

2

2m

e

c

2

b

2

g

2

d

(

g

)

dx

=

b

2

n

e

[

ln

I

-

b

2

-

2

]

All charged particles are concerned. For medium

enerrgies

(200

GeV

max.)

ionization losses through Coulomb scattering on atomic electrons dominate. The

Bethe-

Bloch formula (here for particles with spin 0 and charge q = ±e) describes the mean energy loss:x … distance traveled through the mediumme … electron massZ … atomic numberI … mean ionization potential ( I ~ 10 Z eV for Z > 20 )d(g) … dielectric screening factor (only important for highly relativistic particles)ne … electron density of the medium (ne = r NAZ/A)D … 4pa2ħ2 / me = 5.1.10-25 MeVcm2 (a = e2 / 4pe0ħc)

69

Slide71

Ionization energy loss for

p ± and p on lead

-(dE/dx)min ~ q2 Search for free qarks!

20

15

0.1

1

10

100

p (GeV/c)

-dE/dx (MeV/cm)

Minimal ionization

(

bg

≈ 3-4)

1/b

2

Relativistic rise

(

logarithmic factor

)

70

Slide72

Radiation losses

- dE/dx = E/Xo E = Eo exp(-x/Xo)

Charged

particles are decelerated or accelerated in the field of a nucleus Emission of photons energy loss (bremsstrahlung). Mainly important for electrons and positrons. (for relativistic elctrons with E >> mc2 / aZ1/3).X0 … radiation length – mean energy is reduced by a factor e (important for the design of von electromagnetic calorimeters!)

1

X

o

»

[

4Z(Z+1)

r

N

A

A

]

a

[ln(183Z

-1/3

)]

e

2

m

e

c

2

[

]

2

71

Slide73

Radiation losses

At

high

energies radiation losses are proportional to E/m2. On the other hand it follows from the Bethe-Bloch formula that ionization losses depend only weakly on the mass and energy of the projectile (at high energies). Radiation losses dominate for electrons and positrons.Ec … critical energy = energy, at which radiation losses and ionization losses for electrons are equal

Element Z X

o

/cm Ec/MeVH (26 K) 1 1000 340C 6 18.8 103Al 13 8.9 47Fe 26 1.8 24Pb 82 0.56 7

600

Ec ≈ MeV Z

72

Slide74

Interaction of photons with matter

Assumption

: Monoenergetic photon beam with I photons per second, which traverses a material with thickness x. The energy loss is then given by: dI = - I dx/l I = I0 exp (-x/l) l = 1/nsg ... mean free path length before absorption or scattering (similar to collision length for hadronic reactions)sg … total photon interaction cross section with an atomn … nuclei per cm3

Photons have high probability to be absorbed or scattered by atoms.

73

Slide75

Interaction of photons with matter

Contributions

to sg: Photoelectric effect (absorption by atom, emission of an electron) (~ Z5/Eg)Comptoneffekt(photon scattering on electrons in the atomic shell) (~ Z/Eg)Pair production (in the fields of nuclei or electrons) (~ Z2)

7 1

9

n

X

o

s

Pair

production

≈

9 X0/7 … Conversion length

7 x 9 X0

At high energies photon absorption

is

characterized by the radiation length, just as radiation loss for electrons.

I = I

0 exp ( )

74

Slide76

Photon interaction cross sections

for lead atoms

a)

Photoelectric effectb) Compton scatteringc) Pair production in the field of atomic electronsd) Pair production in the field of nuclei … dominant at high energies

d

a

b

c

sg

10- 4

10- 2

1

102

102

10

1

10- 2

E / GeV

s / b

75