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1
Particle Physics(experimentalists view)
2004/2005
Particle and Astroparticle Physics Master
2
Overview
Aim: To make current experimental frontline research in particle physics
accessible to you. I.e. publications, seminars, conference talks, etc. To get an idea: look at recent conference talks, e.g. on
http://www.ichep02.nl
Program: The theoretical framework:
Quantum Electro Dynamics (QED): electro-magnetic interaction Quantum Flavor Dynamics (QFD): weak interaction Quantum Color Dynamics (QCD): strong interaction
The experiments: History Large-Electron/Positron-Project (LEP): “standard” electro-weak interaction
physics Probing the proton: “standard” strong interaction physics K0-K0, B0-B0 and neutrino oscillations: CP violation (origin of matter!) Large-Hadron-Collider (LHC): electro-weak symmetry breaking (origin of mass!) Fantasy land (order TeV ee and colliders, neutrino factories, …)
3
Administration Literature:
“Introduction to Elementary Particles” D. Griffiths “Quarks & Leptons” F. Halzen & A. Martin “The Experimental Foundations of Particle Physics” R. Cahn & G. Goldhaber “Gauge Theories in Particle Physics” I.J.R. Aitchison & A.J.G. Hey “Introduction to High Energy Phyics” D.H. Perkins “Facts and Mysteries in Elementary Particle Physics” (M. Veltman) “Review of Particle Properties” http://pdg.lbl.gov
Exam: Course participation & exercises Written exam (probably one at each semester’s end)
Our coordinates: F. Linde, Tel. 020-5925134 (NIKHEF-H250), f.linde@nikhef.nl S. Bentvelsen, Tel. 020-5925140 (NIKHEF-H241), s.bentvelsen@nikhef.nl G. Raven, Tel. 020-5925107 (NIKHEF-N327), g.raven@nikhef.nl
Your coordinates: Room H222b at NIKHEF
4
The social side: Friday’s between 17:00 and 18:00 “happy hour” at few locations at NIKHEF
Biertje?
Particle Physics 2004/2005 Part of the “Particle and Astroparticle Physics” Master’s Curriculum
5
Particle Physics II
V. Quantum Flavour Dynamics: QFD (4)• Low q2 weak interaction• High q2 weak interaction• Electro-weak interaction• Experimental highlights: LEP
VI. Origin of mass? (2)• Symmetry breaking• Higgs particle: in ee and in pp
VII. Origin of matter? (6)• K0-K0, oscillations• B0-B0 oscillations• Neutrino oscillations
VIII. Fantasy land (2)
Particle Physics I
I. Introduction, history & overview (1)II. Concepts (3):
• Units (h=c=1)• Symmetries (quark model, …)• Relativistic kinematics• Cross section, lifetime, decay width, …
III. Quantum Electro Dynamics: QED (6-7)• Spin 0 electrodynamics (Klein-Gordon)• Spin ½ electrodynamics (Dirac)• Experimental highlights: “g-2”, ee, …
IV. Quantum Chromo Dynamics: QCD (3-4)• Colour concept and partons• High q2 strong interaction• Structure functions• Experimental highlights: s, ep, …
I. Introduction, history & overview
Lecturers: Thomas PeitzmannStan BentvelsenPaul KooijmanMarcel Merk
6
Introduction
7Particle physics: particles & forces
8
eelectron
p
proton
n
qelectron = 1.61019 C 1
neutron
me = 0.9210-30 kg
mp = 1.710-27 kg
mn = 1.710-27 kg
udu
ddu
qproton = 1 = 2x(2/3) 1x(1/3)
qneutron = 0 = 1x(2/3) 2x(1/3)
9
e
e
u
d
1e family 2e family
c
s
t
b
3e family
Particles: masses & history
(1 MeV 1.810-30 kg)
m [MeV]
0
0.511
3
6
m [MeV]
0
106
1250
120
m [MeV]
0
1777
174300
4200
\© 1998
\© 1998
\© 1998
19951974
1976
1975
1956
1897
1963
19631963
1937
19612000
178000
10
Forces: masses & history
Weakinteraction
Z0
91188 MeVW
80419 MeVW+
80419 MeV
Stronginteraction g g g g g g g g 0 MeV
Electro-magnetic
interaction 0 MeV
1900-1910
1983 19831983
1979
11
How do we get particles? I. From outer space: cosmic rays
12
How do we get particles? II. Nuclear reactions: powerplants & sun
eeDHH e
13
How do we get particles? III. Particle accelerators
14LEP:ee
27 km circumference87-209 GeV Ecm
1989-2000
Particleaccelerator:
example
15 Experiment at particle accelerator:
schematic
16
Particle accelerator experiment:
example
L3:magnetic-field: 0.5
Te & : E/E1.5%muons: p/p3.0%“jets”: E/E15%
17
Atomic energy levels
What do we measure? I. Bound state energy levels
ee energy levels cc energy levels
Electromagnetic force Strong force
18
What do we measure? II. Particle mass, lifetime and decay width
e
e
19
What do we measure? III. Particle scattering
20
How do we observe particles? I. Tracking
track reconstruction & particle identification
charged particles ionize material
2
d
E/d
x
0.7
21
Track reconstruction: an example
time measurement
space measurement
time
s
igna
l
t
time
s
igna
l
t
Real life: in magnetic field B; curvature gives particle momentum p; p/p p (you check!)
22How do we observe particles? II. Calorimetry
charged particles:• ionization• Bremstrahlung
neutral particles:• photo-electric effect• pair creation: ee
• Compton scattering: e e
“shower”
hom
ogen
eous
sam
plin
g
active (red)
passive (black)
Simple Model:
ee with: E’=1/2E ee with: E’=1/2E
Interactions after a “radiation length (XRL)
Characteristics:
After X radiation lengths:
Multiplicity: N(X)=2X Energy/particle: E(X)=E0/2X
Charged track length: T(X)XRL2X
Particle energy equal Emin:
Xmin = ln(E0/Emin) / ln(2) T(Xmin) XRL E0/Emin E0
1 XRL 2 XRL 3 XRL 4 XRL 5 XRL
X=1 X=2 Etc.
E0 1/2 E0 1/4 E0
size ln(E0) E/E 1/E
23Energy reconstruction: an
exampleMeasured energy
distribution
Minimize:
N
ichannelsii
i
i
YXiYXi
E
E1 00
00
2
2
,;
,;
This gives you:
• shower center coordinates (X0,Y0)
• observed energy fraction tot (i;X0,Y0) 1
Efit Ei /tot Eseen /tot
• quality of fit (figure of merit)• possibility to correct for dead channels
Fitted energy
distributions
N=11Eseen = 38 GeV(X0,Y0)=(0.4,0.2)tot = 0.852/DF=0.92Efit = Eseen/tot=45 GeV
Find the expected energy density
distribution (X,Y; X0,Y0)
(X0,Y0) is shower center
X0 X0
N=10Eseen = 31 GeV(X0,Y0)=(0.4,0.2)tot = 0.682/DF=0.94Efit = Eseen/tot=46 GeV
24Real detectors: many sub-systems
eeZ
Z
qqZ
25
LEP I events: ee Z ff
ee
26
LEP I results
cross sections
asymmetries
27
LEP II events: ee WW ….
qqqqWW '' qqWW ' eeWW
How best to determine W-boson mass from these events?
28
LEP II results
cross sections
W-boson mass
29
Fit all available data to the “Standard Model”
30Real life: resolution, inefficiency,
breakdown, …
Ideal world:
Everything works fine!
Real world:
Resolution: bad fits
Real world:
Inefficiencies: missing/noise hits
Real world:
Breakdown: broken channels
Solution, simulate your data sample in great detail i.e.:
the underlying physics of interests (event generator e.g. ee Z detector response (GEANT; software package for particle passage through material) specific detector reconstruction software and your own event selection/analysis code
31Monte Carlo integration
technique
a b
f(x)
x
b
adxxf )(Use your math knowledge:
a b
f(x)
x
N
i iRabafN
ab1
)(Use your computer withN randomly choosen points on [0,1]
a b
f(x)
x
fmax
NNfab acc
max)( Use your computer withN randomly choosen pairs on [0,1]
Increment Nacc if:
R
f
Rabafi
i1
max
)(
N
i N
iabaf
N
ab1
2
1))((Use your computer withN equidistant points on [a,b]
a b
f(x)
x
Last method yields N “event” i.e. x values distributed according to f(x) on interval [a,b]!
Hit/Miss Monte-Carlo method
32
History
33
Historical overviewI. Periodic system of elements (Mendeleev)II. Electron discovery (Thomson 1897)III. Photon as a particle (Einstein, Compton, …: 1900-1924)IV. Atomic structure (Rutherford 1911)V. Positron discovery (First anti-particle, Anderson 1931)VI. Anti-proton discovery (1955)VII. Cosmic rays muon, pion, … (1937, 1946, …)VIII. Strange particles (1946, 1951, …)IX. Neutrino’s “observed” (1958)X. Charmed particles (1974)XI. Gluon discovery (1979)XII. W and Z bosons (1983)XIII. t-quark discovery (1995)XIV. Neutrino oscillations (atmospheric (1998) and solar (2000)) XV. -neutrino discovery (2000)XVI. Higgs boson discovery?
34Mendeleev: periodic system of elements
Chaos order better understanding predictions (new elements) new insights
35
Thompson (1897): electron
No deflection in EB configuration:
B
cEvB
cv
EqF
0
E,B0 v=Ec/B
Circle with radius R with only B0:
RBvc
mq
qBmcvR
B0 R=vmc/qB
EBE
Measured q/m much larger than for 1H-atom (with electron charge) me31026 g
“Plum”-modelof the atom
atom
36
Joseph Thomson (1856-1940)
Nobel Prize 1906
In recognition of the great merits of his theoretical and experimental investigations on the conduction of electricity by gases
37Rutherford (1911): 4He-Au scattering experiment
observation: unexpected large number of alpha particles deflected over large angles!
all positive charge at center!
note:compare shooting bullets at bag of sand
“Solar system”-modelof the atom
R+<10-12 cmnucleus
38
Cross section calculation
opstelling: dichtheid alpha deeltjes ; snelheid alpha deeltjes v flux: v [#/cm2/s]
# over hoek verstrooide alpha deeltjes: 2bb
2/sin4
12
2/sin4
cos2
22/tan
12/tan
12
22
4
2
4
22
EZ
dd
EZ
vEZ
vbbvtN
2/tan1
2)( :Nodig
EZ
b
39Earnest Rutherford (1871-1937)
Nobel Prize 1908 (Chemistry!)
For his investigations into the disintegration of the elements and the chemistry of radioactive substances
40Bohr (1914): energy levels in atoms
Experiment showed emission (absorption) of specific, element dependent, wavelengths!
,...5,4,31
2
1122
nn
R
Example: Balmer series in hydrogen
656 nm486434410
Discreteness of energy levels hard to reconcile with the classical atomic model
Bohr:Hydrogen: 1 proton with 1 electron
Electron angular momentum quantized!
Discrete lines: transitions between states
2
1
nEhnmvrLn
p+
ev
r
41
Niels Bohr (1885-1962)
Nobel prize 1922
For his services in the investigation of the structure of atoms and of the radiation emanating from them"
42Chadwick (1932): the neutron discovery
protonen
paraffineBe
-radiation
Chadwick observed protons emerging from paraffine (lots of 1H) when bombarded by neutral radiation. The proton recoil energy was way too high for this process to be due
to photons.
Solution:
Chadwick postulated the existing of a neutral particle inside the atomic nucleus: the neutron!
p+
e-
1H 2 p+
2 n
e-
4He
“Solar system”-modelof the atom
Rutherford
nucleus
“Plum”-modelof the atom
Thompson
atom
14C nucleus: 14 protons 7 electrons
spin ½experiment: spin 1
“modern”-modelof the atomic nucleus
Chadwick/Bohr
nucleus
43
James Chadwick 1891 - 1974
Nobel Prize 1935
For the discovery of the neutron
44
The photon (1900-1924) as a particle
observation: electron emission stops abruptly as soon as wavelength exceeds a certain (material dependent) value.explanation: Ee h-W
Einstein/Millikan
observation: deflected photon wavelength shifted from incident photon wavelength according to: f= i + (1-cos) h/mc
Compton
Klassiek:
Planck:
0tot4 ),(Jeans-Raleigh 8
),(
dTkTT
RJPlanck0
5
),(lim0),(lim
1exp
18),(
TTKT
hchcT
Planck
45
Max Planck (1858-1947)
Nobel prize 1918
In recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta
In 1916 Millikan stated on the foto-electric effect:
“Einstein’s photo electric equation … appears in every case to predict exactly the observed results…. Yet the semi-corpuscular theory by which Einstein arrived at this equation seems at present wholly untenable”
46
Albert Einstein (1879-1955)
Nobel prize 1921
For his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect
47Robert Andres Millikan (1868-1953)
Nobel price 1923
For his work on the elementary charge of electricity and on the photo-electric effect
48Arthur Holly Compton (1892-1962) Charles Thomson Rees Wilson (1969-1959)
Nobel prize 1927
"for his discovery of the effect named after him"
"for his method of making the paths of electrically charged particles visible by condensation of vapour"
In de quantum-velden theorie is een interactie (of kracht) het gevolg van uitwisseling van
veld-quanta 38
130
2
10?Gravitatie
1king wisselwerSterke
10,,king wisselwerZwakke
10magnetisme-Electro
gluonen
WZW
49
Anti-matter
1927: Dirac equation with two energy solutions:
4222
422242222
cmcpE
cmcpEcmcpE
How do you avoid that all particles tumble into the negative energy levels?
E=0
-
Simple: assume that all negative energy levels are filled (possible thanks to Pauli exclusion principle!)
Excitation of an electron with negative energy to one with positive energy yields:- a real electron with positive energy- “hole” in the sea i.e. presence of a + charge with positive energy!
1940-1950: Feynman Stuckelberg interpretation: negative energy solutions correspond to positive energy solutions of an other particle: the anti-particle! pp
nn
ee
50
The anti-particles: e and p
anti-particles: predicted to exist by Dirac
lead plate
bubble chamber
first anti-electron (e+) observation
p p
pppppp
p 6.3 GeV
p p p p
51Werner Schrodinger (1887 – 1961) Paul Dirac (1902 – 1984)
Nobel Prize 1933
For the discovery of new productive forms of atomic theory
52
Anderson (1905 – 1991)
Nobel Prize 1936
For his discovery of the positron
53
Sin-Itiro Tomonaga (1906 – 1979) Julian Schwinger (1918 – 1994) Richard Feynman (1918 – 1988)
Nobel prize 1965
For their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles
Mathematische consistente theorie voor electro-magnetische kracht: Quantum-Electro-Dynamica (QED)
54
The pion () and the muon ()
-decay
ee
-decay
55
Production of particles with a very long lifetime!
Typically in pairs
production mechanism decay mechanism (strong interaction) (weak interaction)
Strange particles 0
0
X X
?
1232 MeV
1385 MeV
1533 MeV
1680 MeV
56
Murray Gell-Mann (1929)Nobel prize 1969
For his fundamental contributions to our knowledge of mesons and baryons and their interactions
Also for having developed new algebraic methods which have led to a far-reaching classification of these particles according to their symmetry properties. The methods introduced by you are among the most powerful tools for further research in particle physics.
0
0
X X
1232 MeV
1385 MeV
1533 MeV
1680 MeVFundamental
particles: u-, d- & s-quarks!
duudduddd
sdd
uuu
sud suu
ssd ssu
sss
57
Neutrino’s
existence of the neutrino postulated by Pauli:
eepn
Ee
#
even
ts
mn-mp-me 17 keV
epn
Ee
#
even
ts
not this but this
experiment to demonstrate neutrino’s existence: Cowan & Reines
ee
enpe
by followed e+e
annihilation
n-capture
e
n
e+
58Martin Perl (1927) Frederick Reines (1918 – 1998)(Cowan had died)
Nobel Prize 1995
For pioneering experimental contributions to lepton physics:
for the discovery of the tau leptonfor the detection of the neutrino
59
101
101
011
011
###
e
e
muonelectronleptonLepton
Anti-particles count as “1”
Leptongetal1962: Experiment shows that there exists something like “conservation of lepton number”
101
101
011
011
###
e
e
muonelectronleptonLepton
Particles count as “+1”
Nonep
Yesnp
Noe
Noepne
Yesepne
Lederman, Schwartz, Steinberger
( )( )
( )( )Later:We will see that these particles can be organized in doublets; much alike e.g. the electron spin states:
Spin-up: Spin-down:
60
Leon M. Lederman (1922)Melvin Schwartz (1932)Jack Steinberger (1921)
Nobel Prize 1988
For the neutrino beam method and the demonstration of the doublet structure of the leptons through the discovery of the muon neutrino
61
Charmed particles (1974)
SLAC:excess events @ s 3.1 GeV
ee hadrons
Burt Richter
interpretation:new quark: ee cc hadrons
Brookhaven:excess events @ Mee 3.1 GeV
p+Be ee
Sam Ting
interpretation:new bound state: cc ee
62
Burton Richter (1931)Samuel Ting (1936)
Nobel Prize 1976
For their pioneering work in the discovery of a heavy elementary particle of a new kind
10
10
01
01
#/#/#
3
13
13
13
1
s
c
d
u
scdubaryonquark
( )( )
Later:We will see that these particles can be organized in doublets; much alike e.g. the electron spin states:
Spin-up: Spin-down:
63And many many more particles ………
64Sheldon Lee Glashow (1932) Abdus Salam (1926 – 1996)Steven Weinberg (1933)
Nobel Prize 1979
For their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles, including, inter alia, the prediction of the weak neutral current
65
Gerardus 't Hooft (1946)Martinus Veltman (1931)
Nobel Prize 1999
For elucidating the quantum structure of electroweak interactions in physics
66The W and Z bosons: SppS collider
WeWWXpp e or with ZeeZZXpp or with
67
Carlo Rubbia (1934) Simon van der Meer (1925)
Nobel Prize 1984
For their decisive contributions to the large project, which led to the discovery of the field particles W and Z, communicators of weak interaction
68
Gluon discovery
q
qg
e-e+q
q
e+ e-
69
The t-quark: Tevatron collider
)(difficult
(clean)or
qqW
eW
WbWbtt
tXtpp
e
70
Higgs discovered @ LEP?
bbqqZZee
bbqqZHee
:background
:signal
71
72
outstanding issues (only a selection!):
1. Why 3 families?2. Neutrino masses?3. Why matter/anti-matter balanced distorted?4. How to incorporate mass? Higgs?5. Dark matter in universe?6. Further unification of interactions?7. Gravity?
73
Overview
74
Quantum-Electro-Dynamics (QED)
The theory of electrons, positrons and photons
First and most successful Quantum Field Theory (1948: Feynman,
Tomonaga, Schwinger)
electric chargebased on a local U(1) gauge symmetry
field quantum: photon
Theory requires existence of the electron’s anti-particle: the
positron
Electron (e): arrow in + time direction
Positron (e+): arrow in time direction
By combination of vertices more complicated (and realistic!) processes can
be described:
Bhabha scattering
ee ee
Möller scattering
ee ee
e
e+
In a pictorial manner all electro-magnetic phenomena can be described
using one fundamental interaction vertex:
time
ee
Feynmandiagrams
75QED: coupling constant em & perturbation series
Feynman diagrams do not represent particle trajectories; they are just a symbolic notation to facilitate the calculation of physics quantities like cross-sections, lifetimes, …
Interaction strength (coupling constant): em
Experimentally: em1/137 em
Numerically: processes can be approximated by a perturbation series with a progressive number of vertices I.e. factors of em
Convergence excellent due to small numeric value of em
Agreement between experiment and theory is extra-ordinary as we will see later (e.g. for “g-2” at the ppb level)
higher order ee ee diagrams
e.g.: (ge-2)/2 1159.6521869 (41) 106
76
QED: ee cross-section “calculation”
With a (simple) set of rules QED allows you to calculate the ee cross-section ( scattering probability)
e-
e+
+
-
tCross-section is proportional to “square” of sum of the relevant Feynman diagrams
Dimension analysis tells you (later) that cross-sections go like [GeV]-2
At high energies (>> me) “only” relativistic invariant quantity available: (pe++pe-)2s
sem
semem
3
4 22
s
total
77
Each electron is surrounded by a “cloud” of ee pairs!
Through polarisation this cloud (partial) shields the bare electron charge. The “effective” charge (I.e. interaction strength) you experience depends on how close you get!
The running QED coupling constant: em(q2)
The strength of the interaction depends on the resolution of your
probe!energie
e
e e+
e e+
e+
e e+ e
e+ e
nearby probe:“bare” charge
far away probe:“screened” charge
e e+
e e+
78
Running of em
1/em
“energie”
em(0) =1/137.0359895(61)
79
Quantum-Chromo-Dynamics (QCD)
The theory of quarks and gluons
color chargebased on a local SU(3) gauge symmetry
field quanta: eight gluons g
baryons: multiply with:
(RGBRBGGRBBGR+BRG+GBR)/6 (anti-symmetric in color)mesons: multiply with:
(RR+BB+GG)/3 (symmetric in color)
uu
u
All bound states of quarks are colorless i.e. white
uu
u
++
Quark structure: p = uud , n = udd , ++=uuu
Problem: the ++ consists of three identical quarks and is thereby symmetric under uu permutations; its |JJz>=| > state has a symmetric intrinsic spin wave function (J=3/2). Hence violates Pauli principle!
Solution: Invent new (hidden) internal degree of freedom: color charge
3 32 2
80QCD: color interaction qr qb
grbFundamental interaction vertex:
Quarks carry color; anti-quarks carry anti-colorGluons carry a color and anti-color charge; eight (not nine!) possible combinations
Gluons (as opposed to photons) carry “charge” and
hence can couple to themselves!
ggg gggg
By combination of vertices more complicated (and realistic!) processes can
be described:qqqq
81The size of the strong coupling constant: s
p p
You can use the measured pp cross section to get an estimate of the strong coupling constant via:
sssSS
22
Experimentally (at s 10 GeV): pp cross section about 10 mb
ee cross-section about 1 nb
hence: s >> em
typically: s 0.1 - 10
Strong interaction
really strong
Perturbative calculations
valid?
82
Like em the strong coupling constant s
depends on how “hard you probe the interaction i.e. there are polarization effects.
However, due to the gluon self interactions, the polarization cloud surrounding a bare quark is more complicated than for a bare electron.
Calculations show the two effects (quarkgluon) to be opposite. The net effect depends on the number of quark flavors (Nf=6) and the number of colors (Nc=3):
2Nf 11Nc = 19
Quark polarization: s larger at higher energyGluon polarization: s smaller at higher energy ”Asymptotic
freedom”
The running QCD coupling constant: S(q2)
energie
83Running of s
S(MZ) =0.1190.004
84
QCD confinement and jetsWithin a proton the quarks rattle around and behave as almost free particles because at such distances the strong coupling constant s is small. This we call asymptotic freedom.
Once the distances between individual quarks becomes large; the coupling constant gets large and in the region in between the quarks new particle/anti-particle pairs can be created.This we call confinement.
85
QCD jets in e+e annihilation
The colored quarks can not exist as stable particles and “hadronize” into jets; a spray of collimated charged and neutral particles
e-
e+ q
EMS
q
In e+e annihilation quark/anti-quark pairs can be created: e+eqqElectric charge differences left aside, identical to e+e+ cross section
86
Weak interaction: introductionThe lifetime of the ++ particle, 10-23 s, corresponds to the time it takes the decay products (p+) to separate by about 1 fm, which in turn corresponds to about the proton diameter. This is typical for the strong interaction.
642
2
1010137/1
101
em
S
strong
em
The lifetime of the 0 is about 10-
16 s. Hence the typical electro-magnetic/strong lifetime ratio corresponds nicely with the ratio of the strong and electromagnetic coupling constants!The np+e+e lifetime is about 15 minutes! The e+ e + lifetime is about 2 s.Etc.
These are clearly very similar from typical strong and electro-magnetic lifetimes. This calls for an other decay mechanism: the weak interaction.
2
10
23
10
10
Ss
s
n
nW
and therefore W 106
87
Quantum-Flavor-Dynamics (QFD)
The weak interaction theory
which charge?based on a local SU(2) gauge symmetry
field quanta: W+, W and Z0 bosons
Note:
Later we will see that the weakness of the weak interaction is not due to a small coupling constant, but finds its origin in the heaviness of the W and Z0 field quanta.
Quark sector: W cause: ud, cs and tb transitions ee, and transitions
Z0 causes: uu, dd, cc, etc. transitions ee, ee, , etc. transitions
W: charged current (qelectric=1) Z0: neutral current (qelectric=0)
u
d W
e
e W
Z0
WW-
e-
e
WZ0
e
e
88
W,Z self couplings:
W,Z couplings to the :
Weak interaction vertices & diagrams
Examples:
The np+e+e decay
The e+ e + decay
89
The “skewed” weak interactionTim
e (
sorr
y)
Clearly for the p++ decay to take place, the weak interaction must be allowed to destroy s-quarks!
Conventionally the W-transitions are changed to become:
u d cosC + s sinC and c d sinC + s cosC
How to account e.g. for the p++; once you accept that the quark structure of the is (uds)?
s
u
du
u
du d
This mixing is expressed in terms an angle:the Cabibbo mixing angle C13o
u c
d s
Cabibbo favoredCabibbo suppressed
90
Interaction summary
91
The “Standard model”
Gauge symmetry based on SU(3)xSU(2)xU(1) groupsOpen question: are these interactions unified at a (very) high energy scale?
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