lecture 23 hw particle detectors - michigan state universityparticle detectors. april 9, 2007 carl...
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PHY492: Nuclear & Particle Physics
Lecture 23
HWParticle Detectors
April 9, 2007 Carl Bromberg - Prof. of Physics 2
13.1
xmin
=mω 2
λ⎛
⎝⎜⎞
⎠⎟
1
2
xmin2 =
mω 2
λ; x
min3 =
mω 2
λ⎛
⎝⎜⎞
⎠⎟
3
2
; xmin4 =
m2ω 4
λ 2
V xmin
+ x, y( ) = −1
2mω 2 x
min+ x( )2
+ y2⎡⎣⎢
⎤⎦⎥+λ4
xmin
+ x( )2+ y2⎡
⎣⎢⎤⎦⎥
2
= −1
2mω 2 x
min2 + 2x
minx + x2 + y2⎡⎣ ⎤⎦ +
λ4
xmin4 + 4x
min3 x + 6x
min2 x2 + 4x
minx3 + x4
+ 2 xmin2 + 2x
minx + x2( ) y2 + y4
⎡
⎣⎢⎢
⎤
⎦⎥⎥
= −1
2
m2ω 4
λ− mω 2 mω 2
λ⎛
⎝⎜⎞
⎠⎟
1
2
x −1
2mω 2x2 +…
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
+1
4
m2ω 4
λ+ mω 2 mω 2
λ⎛
⎝⎜⎞
⎠⎟
1
2
x +3
2mω 2x2 +…
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
= −1
4
m2ω 4
λ+ mω 2x2 +… Q.E.D.
Homework
April 9, 2007 Carl Bromberg - Prof. of Physics 3
Homework
δEδt ; τ
Γ=
6.6 ×10−22 MeV ⋅ s1.5×103 MeV
= 4.4 × 0−25s
ti= 1 fm/c = 3.3×10−24s
τti
=4.4 ×10−25s
3.3×10−24s= 1.3×10−1
t →W + b
EW+ E
b= m
t; E
W2 = m
t2 − 2m
tE
b+ E
b2
EW2 − m
W2 = p2 = E
b2 − m
b2; E
W2 = E
b2 − m
b2 + m
W2
E
b= m
t2 + m
b2 − m
W2 2m
t( ) = 69 GeV; pb= E
b2 − m
b2( )1
2 = 69 GeV/c
Ea= x
a
s
2; p
a= x
a
s
2c; E
b= x
b
s
2; p
b= −x
b
s
2c
s = Ea+ E
b( )2− p
ac + p
bc( )2
= xa2 + x
b2( ) s
4+ x
ax
b
s
2− x
a2 + x
b2( ) s
4+ x
ax
b
s
2= x
ax
bs
.350( )2
= xax
b4( ); x
ax
b= 0.03; x
a x
b= .03 = 0.18 xa
xb= 0.025
14.1 a) Top lifetime b) No time to interact
c) Top quark decayEnergy Cons.:
Momentum Cons.:
d) Parton-parton collision
top mass = 0.175 TeV sTeV =(2 TeV)2 = 4 TeV2 sLHC =(14 TeV)2 = 200 TeV2
April 9, 2007 Carl Bromberg - Prof. of Physics 4
Homework
April 9, 2007 Carl Bromberg - Prof. of Physics 5
Homework
⎧
⎨⎪⎪
⎩⎪⎪ K
0d
µ+
µ−
s
Z0
d
s
⎛⎝⎜
⎞⎠⎟=
cosθC
− sinθC
sinθC
cosθC
⎛
⎝⎜
⎞
⎠⎟
′d
′s⎛⎝⎜
⎞⎠⎟
d = ′d cosθC− ′s sinθ
C
s = ′d sinθC+ ′s cosθ
C
K0 = d ,s( )
d ,s Z = ′d , ′d Z cosθC
sinθC− ′s , ′s Z cosθ
Csinθ
C
+ ′d , ′s Z cos2θC+ ′s , ′d Z sin2θ
C
′d , ′s Z and ′s , ′d Z are both ZERO
14.5 Quark mixing matrix 2nd order weak decays (u/c)
Not seen: 1st order weak decayflavor changing neutral current
Quark content
′d , ′d Z = ′s , ′s Z ≠ 0
d ,s Z = ′d , ′d Z cosθ
Csinθ
C− ′s , ′s Z cosθ
Csinθ
C= 0
Weak interaction acts on mixed states
Z couples only to the same weak flavor quarks
But 4 quark mixing matrix gives this cancellation
April 9, 2007 Carl Bromberg - Prof. of Physics 6
HomeworkDIS
Q = ′k −k( ),ν⎡⎣ ⎤⎦; P = 0,m
pc2⎡⎣ ⎤⎦
Q ⋅ P = mpc2ν (invariant)
xP +
Q( )2= 0 = x2 P2 + 2x
P ⋅
Q + Q2
x =Q2
2P ⋅
Q=
Q2
2mpνc2
for Q2 >> x2 P2 = x2mp2c4
14.7 a) 4-vector dot product (lab frame)
b) parton absorbs Q but remains massless
Q2
c4
2m
pν / c2
x = 1
x = 0.5
x = 0.1
W = 3m
p
W = 5m
p
W = m
p
(GeV2 / c4)
20 15 10 50
5
10
15
20
i)
ii)
GeV2
c4
⎛⎝⎜
⎞⎠⎟
W 2 = m
p2 +
2mpc2ν
c4−
Q2
c4
c) from 14.6
d) shaded regions
i) ν = E − ′E = 9 GeV; Q2 = 4E ′E sin2 θ / 2( )2m
pν = 17 GeV2 / c2; Q2 = 10 GeV2
ii) ν = E − ′E = 6 GeV; Q2 = 4E ′E sin2 θ / 2( )2m
pν = 11.3 GeV2 / c2; Q2 = 10.7 GeV2
e) two points on plot
infinitemomentumframe
April 9, 2007 Carl Bromberg - Prof. of Physics 7
• Particles are detected by making them ionize atoms!• Detecting charged particles
– The electric field of a moving charged particle can ionize theatoms of the material in which it moves.
– Ionization electrons are small and low mass, and can be collectedby an electric field. Positive ions are big and heavy, and sluggish.
– A charged particle accelerated by a magnetic or electric fieldradiates photons that can ionize atoms and release electrons
• Detecting neutral particles– Interact the neutral particle with matter and in the process
release ionization electrons.– Sometimes you must completely destroy the neutral particle, but
its energy has been used to create ionization.• Must study Ionization to understand detectors
How to detect particles
April 9, 2007 Carl Bromberg - Prof. of Physics 8
Ionization
• Ionization potential minimum energy to ionize (outer e shell)– Hydrogen 13.5 eV– Helium 25 eV– Lithium 5 eV– Neon 22 eV
• Average ionization potential, includes inner shells– reaction dependent– for charged particles (e.g., electrons)
• ~16Z0.9 (eV) for Z>1• Low Z Nobel Gases (He, Ne, Ar, a little higher)
April 9, 2007 Carl Bromberg - Prof. of Physics 9
Photon induced ionization• Photon (<20 eV) induced ionization
– Only valence electrons (a few)– Non-penetrating– Gases & surfaces
• high temperature– thermionic emission
• high electric fields• ultraviolet light
– photoelectric effect– ozone
• photo-cathodes (Cs)• silicon photodiodes
• X-ray (<1 MeV) induced– All electrons (Z)– Penetrating– Gases & solid interiors
E = hν =
hc
λ=
1200 eV ⋅ nm( )λ
• Useful conversion
λ − wavelength, ν − frequency
hc = 2π c( ) = 2π 200 MeV ⋅ fm( )= 1.2 ×103 eV ⋅ nm( )
• Photon energies
April 9, 2007 Carl Bromberg - Prof. of Physics 10
Particle Physics Booklet• Particle Data Group - http://pdg.lbl.gov/• Products
– Order booklet http://pdg.lbl.gov/receive_our_products.htmlhttp://pdg.lbl.gov/2005/reviews/contents_sports.html#expmethetc
http://teachers.web.cern.ch/teachers/archiv/HST2002/
• Detector Lectures for Students/Teachers
April 9, 2007 Carl Bromberg - Prof. of Physics 11
Charged particle induced ionization
• nion is particle velocity and charge dependent (Bethe and Bloch)
S(T ) = −
dT
dx= n
ionI
T : kinetic energy of moving particle
nion
: number of electron-ion pairs unit path length
I : average energy electron-ion pair
• Moving particle, mass M, ionizes atoms in medium
S(T ) =4πQ2e2nZ
meβ 2c2
ln2m
ec2γ 2β 2
I
⎛
⎝⎜
⎞
⎠⎟ − β 2
⎡
⎣⎢⎢
⎤
⎦⎥⎥
γ =E
Mc2; β =
pc
E; γβ =
p
Mc
S(T ) ∝
1
β 2c2=
1
v2 S minimizes, γβ 3
β = v/c = < 0.8heavy ionization
S ∝ lnγ
when β ~ 0.95minimum ionization
ultra relativisticrise of ionization
Stopping power
April 9, 2007 Carl Bromberg - Prof. of Physics 12
Ionization in gases (relevant to all particles)
Normalized Ionization vs γβIonization vs momentumfor various particle masses
γβ =
pc
Mc2
Argon Gas
April 9, 2007 Carl Bromberg - Prof. of Physics 13
Saturation of ionization in solids• Relativistic rise of ionization is due to electric field
concentration perpendicular to direction of motion
• Solids polarize and shieldfar electrons from field
• Atoms along the line of motionsee a stronger field as v -> c.
• Effect is largest in large Zgases, e.g., Xe
effect saturates at only afew % above the minimum
April 9, 2007 Carl Bromberg - Prof. of Physics 14
Minimum ionization in thin solids
• Units for energy loss– Z/A ~ 0.4 at large A, energy loss proportional to density S~ρ,– Divided by the density -> value nearly independent of material.
• (dE/dx) min tabularized for various materials in MeV/(g/cm2)
– Polystyrene scintillator: 1.95
– Iron (steel) : 1.45
S(T ) = −
dT
dx∝ nZ = ρA
0
Z
A
Z : atomic number of medium
n : number of atoms/unit volume
n =ρA
0
A; A : atomic number of medium
ρiron
= 7.87 g/cm3
−dT
dxmin
= 1.45 MeV
g/cm2
⎛⎝⎜
⎞⎠⎟ρ
iron= 11.4 MeV/cm
ρscintillator
= 1.03 g/cm3
−dT
dxmin
= 1.95 MeV
g/cm2
⎛⎝⎜
⎞⎠⎟ρ
Scintillator= 2.0 MeV/cm
Relativistic muon loses ~2 MeV/cm in plastic, ~11.4 MeV/cm in Iron