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Inleiding Subatomaire FysicaFrank Filthaut
http://www.hef.ru.nl/~filthaut/teach/isaf/welcome.php:course information, including lecture notes
Tuesday, March 27, 2012
Course Contents1.Introduction
2.Quantum Electrodynamics
heuristic derivation of Feynman diagrams
3.Strong Interaction and Quantum Chromodynamics
hadrons and the static quark model
dynamics: deep-inelastic scattering
QCD
4.Weak Interaction
leptons: unitarity, gauge bosons
Higgs mechanism
quarks: CKM-matrix, discrete symmetries, CP violation
(neutrino oscillations)
2
Tuesday, March 27, 2012
Course StrategyMain aim: explain how the Standard Model “works”
Emphasis on theoretical aspects
but information from experiment is indispensable! Wherever relevant or useful, experimental results will be discussed
No time for aspects of instrumentation
but see next pages for generally relevant properties
3
Tuesday, March 27, 2012
Current Research
The Higgs boson has not been found yet
an important research topic
There are theoretical problems (“fine tuning” / “hierarchy”) related to the Higgs boson, and the Standard Model cannot describe gravitation
searches for experimental evidence for models for “beyond the Standard Model” physics
The Standard Model does not explain the existence of dark matter and dark energy
interaction with astrophysics (cosmology, ...)
The Standard Model is extraordinarily successful in describing elementary particles and their EM, weak, and strong interactions... but it is incomplete!
5
Tuesday, March 27, 2012
But: which particles are measured?
Typical functionality of a multi-purpose collider detector (see animation):charged particles are identified and and their momenta measured intracking detectors
electrons, positrons, and photons are absorbed, identified, and their energy measured in the electromagnetic calorimeter
strongly interacting particles (hadrons) are absorbed and their energy measured in the hadronic calorimeter
muons are identified (and, in some experiments, their momentum measured) in the muon system
short-lived particles are reconstructed through their decay products
(high-energy) quarks/gluons manifest themselves as hadron jets
neutrinos escape undetected
We will also encounter examples of detectors with more specific measurement purposes
7
Tuesday, March 27, 2012
Example: Event Display
hadron jets
charged particletrajectories
identified electron or positron
neutrino hypothesis(apparent lack of
momentum conservation)
9
identified muon
Tuesday, March 27, 2012
Non-relativistic: Schrödinger equation
Continuity equation:
i∂∂ t
ψ(x) =
−∇2
2m+V (x)
ψ(x) −i
∂∂ t
ψ∗(x) =
−∇2
2m+V (x)
ψ∗(x)
i
ψ∗(x)∂∂ t
ψ(x)+ψ(x)∂∂ t
ψ∗=− 1
2m
ψ∗(x)∇2ψ(x)−ψ(x)∇2ψ∗(x)
i∂∂ t
|ψ(x)|2 =− 12m
∇ ·
ψ∗(x)∇ψ(x)−ψ(x)∇ψ∗(x).
ρ(x) = |ψ(x)|2,
j(x) =−i2m
ψ∗(x)∇ψ(x)−ψ(x)∇ψ∗(x)
∂∂ t
ρ(x)+∇ ·j(x) = 0
multiply by ψ* multiply by ψ
10
Tuesday, March 27, 2012
Negative-energy solutions
Identical effect on “the system” (quantum numbers):
emission of an anti-particle
absorption of a (E<0) particle
V
V
t
x
≅
e+ (E>0) e- (-E<0)
2nd order process: scattering of a particle off of two potentials
12
Tuesday, March 27, 2012
Discovery of the positron
Larger curvature above than below the Pb plate:
particle travels upward
Path length much longer thanexpected for protons: a light particle
Sign of the curvature in the B-field:positively charged particle
13
Tuesday, March 27, 2012
Perturbation theoryAdd perturbation term V to system H0 which can be solved completely:
Expand wavefunction in terms of unperturbed basis:
This yields an equation describing the time evolution of the respective coefficients:
ψ(x , t) =
n
an(t)φn(x)e−iEnt .
H = H0 +V (x , t), H0φn = Enφn with
d3xφ∗n(x)φm(x) = δnm.
i∂ψ(x , t)
∂t=
n
φn(x)e−iEnt
Enan(t) +
dan(t)dt
= (H0 + V (x , t))ψ =
n
(H0 + V (x , t))an(t)φn(x)e−iEnt
=
n
(En + V (x , t))an(t)φn(x)e−iEnt
⇒ i
n
dan(t)dt
φn(x)e−iEnt =
n
V (x , t)an(t)φn(x)e−iEnt
14
Tuesday, March 27, 2012
Perturbation theory (2)
Multiply by ϕ*f eiE
ft and integrate over space:
Integrate (formally) over time, assuming initial state i:
Make Lorentz-covariant:
This yields:
NB: in the last two equations only first-order terms were retained
daf (t)dt
= −i
n
an(t)e−i(En − Ef )t · Vfn(t), with Vfn(t) =
d3xφ∗f (x)V (x , t)φn(x)
af (t) = δfi
+ (−i) t
−Tdt Vfi (t )e−i(Ei − Ef )t
+ (−i)2
n
t
−Tdt Vfn(t )e−i(En − Ef )t ·
t
−Tdt Vni (t )e−i(Ei − En)t + ...
φn(x) ≡ φn(x)e−iEnt ⇒ af (t) = −i t
−Tdt
d3xφ∗
f (x)V (x)φi (x).
t → ∞ : Tfi → −i
d4xφ∗f (x)V (x)φi (x)
15
Tuesday, March 27, 2012
Delbrück scatteringObserved (1973, G. Jarlskog et al.) in scattering of high-energy (E ~ 7 GeV) photons off uranium
effect ~ Z4
Small scattering angles (~ mrad)!
Tuesday, March 27, 2012
Electron Magnetic MomentDirac equation reduced to two-component spinors:
Spatial (LHS) part:
RHS, non-relativistic limit:
Conclusion:
σ · (p + eA)
2uA = ((E + eA0)2 − m2)uA
σ · (p + eA)
2= σiσj
pipj + e2AiAj + e(piAj + Aipj )
= (δij + iijkσk )
pipj + e2AiAj + e(piAj + Aipj )
= pipi + e2AiAi + e(piAi + Aipi ) + ie(piAj + Aipj )ijkσk
= (p + eA)2 + e(∇× A) · σ= (p + eA)2 + eσ · B
((E + eA0)2 − m2) = ((m + (E + eA0 − m))2 − m2) ≈ 2m(E + eA0 − m)
(E − m)uA =
(p + eA)2
2m− eA0 +
e2m
σ · B
uA
18
Tuesday, March 27, 2012
Discovery of the charged pion(and of the muon...)
π±
μ±
e±
1.charged pion is stopped2.pion decays3.resulting muon is stopped4.muon decays5.electron/positron escapes
20
Tuesday, March 27, 2012
Discovery of “strange” particles
charged kaon:angle and energy e-
V0 (KS, Λ): “vertices”,momenta of outgoing particles
Tuesday, March 27, 2012
Lifetimes of “strange” particles
particle mass (MeV) lifetime (s) (main) decay modesspin 0
K− 494 1.2 · 10−8 µ−νµ, π−π0
K0S 498 9 · 10−11 π+π−, π0π0
K0L 498 5 · 10−8 π±e∓νe, π±µ∓νµ, π+π−π0, π0π0π0
spin 1/2Λ 1116 2.6 · 10−10 pπ−, nπ0
Σ+ 1189 8 · 10−11 pπ0, nπ+
Σ0 1193 7 · 10−20 ΛγΣ− 1197 1.5 · 10−10 nπ−
Ξ− 1322 1.6 · 10−10 Λπ−
Ξ0 1315 3 · 10−10 Λπ0
Σ+, Σ- are not antiparticles!
KS and KL are “mixtures” of K0 and K0
will be covered in context of weak interaction
—
Tuesday, March 27, 2012
Meson octets
,_ +0
K K
KK
π π πη
_
0 +
_0
S = 0
Q = −1 Q = 1Q = 0
S = 1
S = −1
,_ +0
K
K_
S = 0
Q = −1 Q = 1Q = 0
ρ ρ ρω
K_* *0
0* K *+
S = 1
S = −1
JP=0- JP=1-
24
Tuesday, March 27, 2012
Baryon octet and decuplet
ΣΣΣ
n p
Ξ Ξ
Λ,
_
_ +
0
0
Q = −1 Q = 0 Q = 1
S = 0
S = −1
S = −2
ΣΣΣ
Ξ Ξ
Δ Δ Δ Δ
Ω_
_0* *
*_ 0* *
_ 0 + ++
+
Q = −1
Q = 0
Q = 1
Q = 2
S = 0
S = −1
S = −2
S = −3
JP=1/2+ JP=3/2+
25
Tuesday, March 27, 2012
Discovery of the Ω- particle
Photographed using a “bubble chamber” nearly boiling fluid, charged particles cause bubbles
26
Tuesday, March 27, 2012
Baryon masses in the spin interaction model
Particle Predicted mass (GeV) Measured mass (GeV)n, p 0.89 0.939Λ 1.08 1.116Σ 1.15 1.193Ξ 1.32 1.318∆ 1.07 1.232Σ∗ 1.34 1.385Ξ∗ 1.50 1.533Ω− 1.68 1.673
M = m1 + m2 + m3 + A
S1 · S2
m1m2+
S1 · S3
m1m3+
S2 · S3
m2m3
Tuesday, March 27, 2012
Meson masses in the spin interaction model
Particle Predicted mass (GeV) Measured mass (GeV)π 0.15 0.137K 0.46 0.496η 0.57 0.549ρ 0.77 0.770ω 0.77 0.782K∗ 0.87 0.892φ 1.03 1.020
M = mq + mq + ASq · Sq
mqmq
Tuesday, March 27, 2012
Spectroscopy of heavy mesons
2
4
6
8
10
12
ME
SO
N M
AS
S (
GE
V)
c J/
’c
’
hc c0
c1
c2
b
’b
’
’’
b0b1(1P)b2
b0b1(2P)b2
(1D)
hb(1P)
hb(2P)
Bc
BsB
B*
s
B*
DsD
exptfix parameters
postdictionspredictions
30
Tuesday, March 27, 2012
Inelastic electron-proton scatteringExperiments by Friedman, Kendall, Taylor et al., 1969:
Ee ≲ 20 GeV
measurement of inclusive cross sections (i.e., not only e-p final states are being considered)
First indication of the proton’s composite nature
Tuesday, March 27, 2012
Bjørken scaling
Q2
2mpx W2(x , Q2)
Experiment: deep-inelastic electron-proton scattering,
Ee ≲ 20 GeV
x=0.25
Tuesday, March 27, 2012
Gell-Mann matrices
λ1 =
0 1 01 0 00 0 0
λ2 =
0 −i 0i 0 00 0 0
λ3 =
1 0 00 −1 00 0 0
λ4 =
0 0 10 0 01 0 0
λ5 =
0 0 −i0 0 0i 0 0
λ6 =
0 0 00 0 10 1 0
λ7 =
0 0 00 0 −i0 i 0
λ8 = 1√3
1 0 00 1 00 0 −2
34
Tuesday, March 27, 2012
Measurements of F2(x,Q2)
log-log scale!
data for different values of x moved by a factor 2i (for readability)
Q2 (GeV
2)
F2(x
,Q2)
* 2
i x
H1ZEUSBCDMS
E665NMCSLAC
10-3
10-2
10-1
1
10
102
103
104
105
106
107
108
109
10-1
1 10 102
103
104
105
106
(source: PDG)
Tuesday, March 27, 2012
Measurements of F2(x,Q2)
same data versus x
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
10-6
10-5
10-4
10-3
10-2
10-1
1x
F2(x
,Q2)
ZEUS
H1
SLAC
BCDMS
NMC
0
1
2
3
4
5
6
7
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1x
F2 c
c(x
,Q2)
+ c
(Q)
H1
ZEUS
EMC
0
0.025
0.05
0.075
0.1
0.125
0.15
0.175
0.2
10-6
10-5
10-4
10-3
10-2
10-1
x
F2 b
b(x
,Q2)
+ k
(Q)
(source: PDG)
Tuesday, March 27, 2012
e+e- ⟶hadrons: jets
Events with 3 jets: first direct evidence for the existence of the gluon
Tuesday, March 27, 2012
e+e-⟶hadrons: cross section
10-1
1
10
102
0.5 1 1.5 2 2.5 3
Sum of exclusivemeasurements
Inclusivemeasurements
3 loop pQCD
Naive quark model
u, d, s
!
"
#
!!
2
3
4
5
6
7
3 3.5 4 4.5 5
Mark-IMark-I + LGWMark-IIPLUTODASPCrystal BallBES
J/$ $(2S)
$3770
$4040
$4160
$4415
c
2
3
4
5
6
7
8
9.5 10 10.5 11
MD-1 ARGUS CLEO CUSB DHHM
Crystal Ball CLEO II DASP LENA
!(1S)!(2S)
!(3S)
!(4S)
b
R
!s [GeV]
(source: PDG)
normalised to σ(e+e-→μ+μ -)
Tuesday, March 27, 2012
Neutrino-nucleon scattering
in both cases: muon neutrinos
shown: σ/E
(source: PDG)
Tuesday, March 27, 2012
Evidence for the Z boson
Gargamelle experiment (bubble chamber), 1973
atomic electron
γ conversion
γ conversion
(source: CERN)
Tuesday, March 27, 2012
Number of neutrino generationsTotale Z boson decay width ΓZ: width of the resonance
Partial decay width Γhad: cross section at the peak of the resonance
same for the decay to lepton pairs
more complicated for decay to e+e-: interference
Radiative corrections need to be applied!
in particular, initial state photon radiation Ecm [GeV]
! had [
nb]
! from fitQED unfolded
measurements, error barsincreased by factor 10
ALEPHDELPHIL3OPAL
!0
"Z
MZ
10
20
30
40
86 88 90 92 94
ΓZ = Γhad + Γ + Γνν
Tuesday, March 27, 2012
Parity violation as a tool
τ-→π-ντ decays
Eπ in the lab frame directly related to decay angle θ in the τ rest frame
Used at LEP 1 to measureτ polarisation
this too arises from parity violation, but in the production and decay of the Z boson 0
500
1000
0 0.5 1E! / E
beam
Nu
mb
er
of
De
ca
ys
!
"#
$_
#_
(source: CERN)
Tuesday, March 27, 2012
Evidence for the decay KL→π+π-
Consider large decay times (so that only KL remain)
Reconstruct π+π-
invariant mass (m*) and direction with respect to the beam (cosθ)
other particles: combinatorial backgrounds
Kaons from the beam clearly visible
Tuesday, March 27, 2012
CP violation in other decays
Volume 52B, number 1 PHYSICS LETTERS 16 September 1974
Their charge asymmetry is evaluated as a function of T' and p ' in bins of width At ' = 0.5 ! 10-10s and p ' = f
2 GeV/c starting at rmi n = 2.25 ! 10 -10 s and Pmin = 7 GeV/c.
The mass difference Am is determined by a comparison of the time dependence of the measured charge asym-
metry with the theoretical expectation fi(r', Am, y) for the set of parameters to be determined. The theoretical
function ~ and its derivatives are calculated by Monte Carlo techniques from eq. (2). This treatment accounts for
the following:
- The K~3 matrix elements according to V - A theory with linear formfactors for the hadronic current [3] and
radiative corrections [4].
- The observed beam profile, and the experimental resolution and acceptance.
- Transformation from the true kaon momentum p and lifetime r to the measured quantities p ' and r ' .
- The shape of the kaon momentum spectrum and the dilution factor A(p) as obtained in the K~2 analysis [1 ]
The influence of the actual form of the matrix element on the charge asymmetry is weak. The shape of the
momentum spectrum enters only indirectly in the transformation from r to r ' . The K S lifetime and the K L charge
asymmetries are taken from previous results of the same experiment [ 1 ,2 ] . The results of the best fits to the
measured charge asymmetries are shown in figs. 1 and 2. The A S - A Q fac tory is left free in the fits. The uncor-
rected values for the KL-K S mass difference are:
Am(Ke3 ) = (0.5287 -+ 0.0040) ! 1010 s -1 , A m ( K 3 ) = (0.526 + 0.0085) ! 1010 s -1 .
0 0 8 -
008 -
0.04 -
0.02 -
Z
4. +
Z
o i
Z
i
v
- 0 0 2 -
B
-0.04
-01)6
-0 .08
CHARGE ASYMMETRY IN THE DECAYS K°----~Tc;e'*v
+~,~- + + i L
i
"I .
dl I • I l I • a t
I I I I I i
20
K ° DECAY TIME x ' (lO'l°sec)
Fig. 1. The charge asymmetry as a function of the reconstructed decay time r' for the Ke3 decays. The experimental data are compared to the best fit as indicated by the solid line.
116
~ 10 τ(KS)
dΓ(K0 → π+e−νe, t)− dΓ(K0 → π−e+νe, t)dΓ(K0 → π+e−νe, t) + dΓ(K0 → π−e+νe, t)
Tuesday, March 27, 2012
Oscillations: Super-Kamiokande
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
1 10 102
103
104
L/E (km/GeV)
Data
/Pre
dic
tion (
nu
ll osc.)!
relation between zenith angle and path length
Tuesday, March 27, 2012
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