lecture 7 mod.ppt - physics · proportional to z2/a of the material. proportional to z 1 4 of the...
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General Information
Muon Lifetime Update The next steps
Organize your results Analyze, prepare plots, fit lifetime distribution Prepare report using the Latex templates from the web site
Reports due May 14
Today’s Agenda Interaction of Particles with Matter (Summary) Cherenkov and Transition Radiation Interaction of Photons with Matter
The concept of cross sectionsCross sections or differential cross sections ddare used to express the probability of interactions between elementary particles.
Example: 2 colliding particle beams beam spot area A
= N1/t = N2/t
What is the interaction rate Rint. ?
Rint · t) = · L
Luminosity L [cm-2 s-1]
has dimension area !Practical unit: 1 barn (b) = 10-24 cm2
incident beam
solid angle element d
scattered beam
target
.nA = area density of scattering centers in target
Nscat() Ninc· nA · d= dd() · Ninc·nA· d
dE/dx ReviewHow do charged particles loose energy in matter ? Discrete collisions with the atomic electrons of the absorber material.
Collisions with nuclei not important (me<<mN).
If are big enough ionization (Bethe Bloch Equation)
Instead of ionizing an atom, under certain conditions the photon can also escape from the medium. Cherenkov and Transition Radiation
densityelectron :
0
N
ddEdNE
dxdE
e-
k ,
0,mv
k ,
Average Energy Loss <dE/dx>
22ln14 2max
2
222
21
2222
T
Icm
AZzcmrN
dxdE e
eeA
dE/dx in [MeV g-1 cm2]
Bethe-Bloch formula only valid for “heavy” particles (mm).
dE/dx depends only on independent of m !
First approximation: medium simply characterized by Z/A (~ electron density)
Z/A~0.5
Z/A = 1
2
1
dxdE
22ln dxdE
“relativistic rise”
“kinematical term” 3-4minimum ionizing particles, MIPs
“Fermi plateau”
Minimum Ionizing Particles (MIPs)
-1 -1 2
min min
-3
Absorber MeVcm MeVg cm( )
Water 2.03 2.03Xenon (gaseous) 7.3 10
dE dEdx d x
1.24Iron 11.7 1.48Lead 12.8 1.13Hy -4drogen (gaseous) 3.7 10 4.12
Energy loss of minimum ionising particles
<dE/dx> has broad minimum around = 0.96 or ~ 4Relativistic particles with an energy loss corresponding to this minimum are calledMinimum Ionizing Particles or MIPs.For a light absorber with Z/A ~ 0.5
-dE/dxmin ~ 2 MeV/(g/cm2)
Example
Bremsstrahlung Electrons and positrons lose energy via ionization just like other charged particles.
Small changes to calculation (identical particles, m(target) = m(projectile))
BUT dominant energy loss mechanism for high energy electrons is electromagnetic radiation
Circular acceleration: Synchrotron Radiation Motion through matter: Bremsstrahlung
ln522
122
1
22
41
2
kMv
kr
Mvcm
ZZc
edkd ee
Semi-classical calculation yields:
Cross section depends on•Incident particle’s mass (1/M2)•Medium (Z2)
Proportional to Z2/A of the Material.
Proportional to Z14 of the incoming
particle.
Proportional to of the material.
Proportional 1/M2 of the incoming particle.
Proportional to the Energy of the Incoming particle
E(x)=Eo e(-x/X0) – ‘Radiation Length’
X0 M2A/ ( Z14 Z2)
X0: Distance where the Energy E0 of the incoming particle decreases E = E0e-1 = 0.37E0 .
Bremsstrahlung, QM
Radiation Length (Lr)The radiation length is a very important quantity describing energy loss of electronstraveling through material. We will also see Lr when we discuss the mean free path forpair production (i.e. e+e-) and multiple scattering.
There are several expressions for Lr in the literature, differing in their complexity.The simplest expression is:
)/)(183ln(4 23/121 AZZNrL aer
Leo and the PDG have more complicated expressions:
)/)1()](()183[ln(4 3/121 AZZZfZNrL aer Leo, P41
)]))(([4 21221
radradaer ZLZfLZNrL PDGLrad1 is approximately the “simplest expression” and Lrad2 uses 1194Z-2/3 instead of 183Z-1/3, f(z) is an infinite sum.Both Leo and PDG give an expression that fits the data to a few %:
)()/287ln()1(
4.716 2
cmgZZZ
ALr
The PDG lists the radiation length of lots of materials including: Air: 30420cm, 36.66g/cm2 teflon: 15.8cm, 34.8g/cm2
H2O: 36.1cm, 36.1g/cm2 CsI: 1.85cm, 8.39g/cm2
Pb: 0.56cm, 6.37g/cm2 Be: 35.3cm, 65.2g/cm2
Leo also has a table ofradiation lengths on P42but the PDG list is more up to date and larger.
Critical Energy: If dE/dx (Ionization) = dE/dx (Bremsstrahlung)
Muon in Copper: p 400 GeVElectron in Copper: p 25 MeV
W. Riegler/CERN 10
For the muon, the second lightest particle after the electron, the critical energy is at 400GeV.
The EM Bremsstrahlung is therefore only relevant for electrons at energies of past and present detectors.
Critical Energy
Z2 electrons, q=‐e0
W. Riegler, Particle Detectors
Interaction with the atomic electrons. The incoming particle looses energy and the atoms are excited or ionized.
Interaction with the atomic nucleus. The particle is deflected (scattered) resulting in multiple scattering of the particle in the material. During these scattering events a Bremsstrahlung photons can be emitted.
In case the particle’s velocity is larger than the velocity of light in the medium, the resulting EM shockwave manifests itself as Cherenkov Radiation. When the particle crosses the boundary between two media, there is a probability of the order of 1% to produce an X ray photon, called Transition radiation.
Electromagnetic Interaction of Particles with Matter
M, q=Z1 e0
Cherenkov Radiation
A charged particle travels through a medium at a speed larger than the local speed of light
Roger Forty Particle ID (Lecture I) 13
Cherenkov light
• Named after the Russian scientist P. Cherenkov who was the first to study the effect in depth (he won the Nobel Prize for it in 1958)
• From Relativity, nothing can go faster than the speed of light c (in vacuum)
• However, due to the refractive index n of a material, a particle can go faster than the local speed of light in the medium cp = c/n
• This is analogous to the bow wave of a boat travelling over wateror the sonic boom of an aeroplane travelling faster than the speed of sound
Roger Forty Particle ID (Lecture I) 14
Propagating waves
A stationary boat bobbing up and down on a lake, producing waves
Roger Forty Particle ID (Lecture I) 15
Propagating waves
Now the boat starts to move, but slower than the waves
• No coherent wavefront is formed
Roger Forty Particle ID (Lecture I) 16
Propagating waves
Next the boat moves faster than the waves• A coherent wavefront is formed
Roger Forty Particle ID (Lecture I) 17
Propagating waves
Finally the boat moves even faster• The angle of the coherent wavefront changes
cos = vwavevboat
Roger Forty Particle ID (Lecture I) 18
Speed calculation
• Using this construction, we can determine (roughly) the boat speed:
70º, vwave = 2 knots on water→ vboat = vwave/cos 6 knots
• Cherenkov light is produced when charged particle (vboat= c) goes faster than the speed of light (vwave= c/n)
→ cos C = 1 / n
• Produced in three dimensions, so the wavefront forms a cone of light around the particle direction
• Measuring the opening angle of cone → particle velocity can be determined
º
For Ne gas (n = 1.000067)
Nov 2004 19
Wave front comes out at certain angle
Cherenkov Radiation (2)
1cos c n
Threshold: > 1/n
Threshold Momentum for Cherenkov RadiationExample: Threshold momentum for Cherenkov light:
nt1
1
111
1222
nn
n
tt
t
)1)(1(1
112
nnn
tt
Example: Thresholds for different particles in He
)2(1
tt
The momentum (pt) at which we get Cherenkov radiation is:
)2(
mmp ttt
For a gas +2 so the threshold momentum can be approximated by:
2mmp ttt
For helium =3.3x10-5 so we find the following thresholds:electrons 63 MeV/c kaons 61 GeV/cpions 17 GeV/c protons 115GeV/c
Medium =n-1 thelium 3.3x10-5 123CO2 4.3x10-4 34H2O 0.33 1.52glass 0.46-0.75 1.37-1.22
For gases it is useful to set = n-1
Nov 2004 21
Cherenkov Radiation (3)
How many Cherenkov photons are detected?
For He we find: 2-3 photons/meter (not a lot!)For CO2 we find: ~33 photons/meterFor H2O we find: ~34000 photons/meter
We can calculate the number of photons/dx by integrating over the wavelengths thatcan be detected by our phototube (1, 2):
]11[sin2sin221
22
22
1
ddxdN
For a highly relativistic particle going through a gas the above reduces to:
photons/cm)1(780 ndxdN
GAS
Photons are preferentially emitted at small ’s (blue)
Nov 2004 22
Different Cherenkov Detectors
Threshold Detectors Yes/No on whether the speed is β>1/n
Differential Detectors βmax > β > βmin
Ring-Imaging Detectors Measure β
Nov 2004 23
Threshold Counter
Particle travel through radiator Cherenkov radiation
Types of Cerenkov Counters
Differential Cerenkov Counter:Makes use of the angle of Cerenkov radiation and only samples light at certain angles.For fixed momentum cos is a function of mass:
Not all light will make it to phototube
nppm
Epnn
22
)/(11cos
Differential cerenkov counters typically on work over a fixed momentum range(good for beam monitors, e.g. measure or K content of beam).
Problems with differential Cerenkov counters:Optics are usually complicated.Have problems in magnetic fields since phototubes must be shielded from B-fields
above a few tenths of a gauss.
Nov 2004 25
Ring Imaging Detectors (1)
Ring Imaging Cerenkov Counters (RICH)RICH counters use the cone of the Cerenkov light.The ½ angle () of the cone is given by:
nppm
n
2211 cos1cos
The radius of the cone is: r=Ltan, with L the distance to the where the ring is imaged.L
r
For a particle with p=1GeV/c, L=1 m, and LiF as the medium (n=1.392) we find:deg r(m)
43.5 0.95K 36.7 0.75P 9.95 0.18
Thus by measuring p and r we can identify what type of particle we have.Problems with RICH:
optics very complicated (projections are not usually circles)readout system very complicated (e.g. wire chamber readout, 105-106 channels)elaborate gas systemphoton yield usually small (10-20), only a few points on “circle”
Great /K/p separation!
Super Kamiokande
SuperK
481 MeV muon neutrino produces 394 MeV muon which later decays at rest into 52 MeV electron. The ring fit to the muon is outlined. Electron ring is seen in yellow-green in lower right corner. This is perspective projection with 110 degrees opening angle, looking from a corner of the Super-Kdetector (not from the event vertex). Color corresponds to time PMT was hit by Cerenkov photon from the ring. Color scale is time from 830 to 1816 ns with 15.9 ns step. In the charge weighted time histogram to the right two peaks are clearly seen, one from the muon, and second one from the delayed electron from the muon decay. Size of PMT corresponds to amount of light seen by the PMT. From: http://www.ps.uci.edu/~tomba/sk/tscan/pictures.html
SuperK is a water RICH. It uses phototubes to measure the Cerenkov ring.Phototubes give time and pulse height information
From SuperK site
SuperK has: 50 ktons of H2OInner PMTS: 1748 (top and bottom) and 7650 (barrel)outer PMTs: 302 (top), 308 (bottom) and 1275(barrel)
For water n=1.33For =1 particle cos=1/1.33, =41o
880.P20 Winter 2006 Richard Kass 29
The BaBar DIRCHere the challenge is to separate ’s and K’s in the range: 1.7<p< 4.2 GeV
Detector of Internally Reflected Cerenkov light
DIRC uses quartz bars (490x1.7x3.5cm3) as radiator (n=1.473) and light guideThe cerenkov light is internally reflected to the end of a bar bar must be very flat <5ÅDIRC is a 3D device, measures x, y, and time of Cerenkov photonsDetect the photons with an array of phototubes “Typical” photon has:
=400 nm200 bounces 5m path in quartz bar
10-60 ns propagation time
laser light propagating in a quartz bar
880.P20 Winter 2006 Richard Kass 30
The BaBar DIRC
1.5 T Solenoid Electromagnetic Calorimeter
(EMC)Detector of Internally
Recflected Cherenkov
Light (DIRC)
Instrumented Flux Return
(IFR) Silicon Vertex Tracker (SVT)
Drift Chamber (DCH)
phototube array
880.P20 Winter 2006 Richard Kass 31
Performance of the BaBar DIRCTiming information very useful to eliminate photons not associated with a track
±300 nsec window500-1300 background hits
±8 nsec window1-2 background hits
Note: the pattern of phototubes withsignals is very complicated. Thedetection surface is toroidal and thereforethe cerenkov rings are disjoint and distorted.
Use a maximum likelihood analysis to separate /K/p: L=L(c, t, n)DIRC works very well!
Z2 electrons, q=‐e0
4/18/201232
Transition Radiation
M, q=Z1 e0
When the particle crosses the boundary between two media, there is a probability of the order of 1% to produced and X ray photon, called Transition radiation.
Transition RadiationProduced by relativistic charged particles when they cross the interface of two media of different dielectric constants (Note that n ~ sqrt())
Qualitative Explanation:Since the electric field of the particle is different in the two media, the particle has to “shake off” the difference when it crosses the boundary. The total energy loss depends on the Lorentz factor= E/mc2
Mostly forward directed
Intensity roughly proportional to the energy E
Typically X-ray photons with energies between 5 –15 keV
The number of photons produced is very small. About 0.8 photons per transition for a particle with = 2000 (highly relativistic)
Stack foils to increase number of transitions
Interactions of Photons with Matter
There are three main contributions to photon interactions:Photoelectric effect (E < hundreds of keV)Compton scattering (Medium energies ~ MeV)Pair production (dominates at energies > few MeV)
A beam of ’s with initial intensity N0 passing through a medium is attenuated in number (but not energy) according to:
dN=-Ndx or N(x)=N0e-x
With = linear attenuation coefficient which depends on the total interaction cross section (total= coh+ incoh + +).
Intensity:
Interaction of photons
...0
pairComptonphoto
xeII
: mass attenuation coefficient
gcmA
Ni
Ai /2
1 M
eV
photo effect
Rayleigh scattering(no energy loss !)
Compton scattering
pair production
Interaction of Photons
Thomson and Rayleigh Scattering No energy transfer (just change in photon direction) Low energies Rayleigh scattering off the atom as a whole (coherent effect)
Photo Effect Low energy (~ binding energy of electrons in atoms) Higher cross section for high Z material (~ Z4-5)
Compton Scattering Medium energies Klein Nishina formula
Compton edge (maximum recoil energy)
Pair Production E > 1.022 MeV
21
2max hT
2
222
22
cos11cos1cos1
cos1112
cmhwithr
dd
ee
Photon Conversions
Otherwise known as pair production.
Threshold: 2mec2 (nucleus) 4mec2 (atomic electron)
Total cross section increases rapidly with photon energy, approximately proportional to Z2.
Comparing pair production with bremsstrahlung:
Or for the mean free path:
pair 79 brem
Electromagnetic Showers
• a beam of electrons impinging on solid matter will have a linear absorption coefficient of 1/X0
• this process repeats, giving rise to an e.m. shower:
• the process continues until the resulting photons and electrons fall below threshold
• so how do we get some sort of signal out?• ultimately we need ionizationWill discuss more when we talk about calorimetry…
Basic EM Interactions
e+ / e-
IonizationdE/dx ~ 1/2, z2
BremsstrahlungdE/dx ~ 1/m2, z4
Photoelectric effect
Compton effect
Pair production
E
E
dE/d
x
E
dE/d
x
E
E