Download [a,b]! - Nikhef

1
Particle Physics
(experimentalists view)
2004/2005
Particle and Astroparticle Physics Master
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 ee and  colliders, neutrino factories, …)
2
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), [email protected]
 S. Bentvelsen, Tel. 020-5925140 (NIKHEF-H241), [email protected]
 G. Raven, Tel. 020-5925107 (NIKHEF-N327), [email protected]
 Your coordinates:
 Room H222b at NIKHEF
3
4
Biertje?
The social side: Friday’s between 17:00 and 18:00
“happy hour” at few locations at NIKHEF
Particle Physics I
I.
II.
III.
IV.
•
•
•
•
•
•
•
•
•
•
•
Introduction, history & overview (1)
Concepts (3):
Units (h=c=1)
Symmetries (quark model, …)
Relativistic kinematics
Cross section, lifetime, decay width, …
Quantum Electro Dynamics: QED (6-7)
Spin 0 electrodynamics (Klein-Gordon)
Spin ½ electrodynamics (Dirac)
Experimental highlights: “g-2”, ee, …
Quantum Chromo Dynamics: QCD (3-4)
Colour concept and partons
High q2 strong interaction
Structure functions
Experimental highlights: s, ep, …
Particle Physics II
V.
VI.
VII.
VIII.
•
•
•
•
•
•
•
•
•
Quantum Flavour Dynamics: QFD (4)
Low q2 weak interaction
High q2 weak interaction
Electro-weak interaction
Experimental highlights: LEP
Origin of mass? (2)
Symmetry breaking
Higgs particle: in ee and in pp
Origin of matter? (6)
K0-K0, oscillations
B0-B0 oscillations
Neutrino oscillations
Fantasy land (2)
Lecturers:
I. Introduction, history & overview
Particle Physics 2004/2005
Thomas Peitzmann
Stan Bentvelsen
Paul Kooijman
Marcel Merk
Part of the “Particle and Astroparticle Physics” Master’s Curriculum
5
6
Introduction
Particle physics: particles & forces
7
me = 0.9210-30 kg
electron
e
qelectron = 1.61019 C  1
mp = 1.710-27 kg
proton
p
u
u
d
qproton = 1 = 2x(2/3)  1x(1/3)
neutron
mn = 1.710-27 kg
n
d
u
d
qneutron = 0 = 1x(2/3)  2x(1/3)
8
9
Particles: masses & history
1e family
m
e
1956
e
1897
u
[MeV]
0
\
© 1998
0.511
3
2e family


1937
[MeV]
0
© 1998
106
\
1250


s
m
2000
1975
t
1974
6
1963
1961
c
1963
d
m
3e family
1995
120
1963
(1 MeV 1.810-30 kg)
b
[MeV]
0
© 1998
1777
\
174300
178000
4200
1976
10
Forces: masses & history
Electromagnetic
interaction
Weak
interaction
1900-1910

0 MeV
W
W+
80419 MeV
80419 MeV
1983
Strong
interaction
1983
g g g g g g g g
1979
Z0
91188 MeV
1983
0 MeV
How do we get particles?
I. From outer space: cosmic rays
11
How do we get particles?
II. Nuclear reactions: powerplants & sun
e
H  H D e  e
12
How do we get particles?
III. Particle accelerators
13
Particle
accelerator:
example
LEP:
14
e e 
27 km circumference
87-209 GeV Ecm
1989-2000
Experiment at particle accelerator: schematic
15
Particle accelerator
experiment:
example
16
L3:
magnetic-field: 0.5 T
e & : E/E1.5%
muons: p/p3.0%
“jets”: E/E15%
17
What do we measure?
I. Bound state energy levels
Atomic energy levels
ee energy levels
Electromagnetic force
cc energy levels
Strong force
What do we measure?

II. Particle mass, lifetime and decay width


e

e
18

What do we measure?
III. Particle scattering



19
20
How do we observe particles?
I. Tracking
 dE/dx
charged particles
ionize material
2


0.7
track reconstruction & particle identification


21
Track reconstruction: an example

 signal
t
 time

 signal
t
 time
time measurement

space measurement
Real life: in magnetic field B; curvature gives particle momentum p; p/p  p (you check!)
How do we observe particles?
22
II. Calorimetry
“shower”
charged particles:
• ionization
• Bremstrahlung
neutral particles:
• photo-electric effect
• pair creation: ee
• Compton scattering: e e
Characteristics:
Simple Model:
ee
ee
1 XRL
2 XRL
3 XRL
with: E’=1/2E
with: E’=1/2E
Interactions after a
“radiation length (XRL)
E0
X=1
1/2
E0
X=2
1/4
E0
Etc.
4 XRL
5 XRL
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)  size  ln(E0)
T(Xmin)  XRL E0/Emin  E0  E/E  1/E
Energy reconstruction: an example
Measured energy
distribution
Fitted energy
distributions
Find the expected
energy density
distribution (X,Y; X0,Y0)
(X0,Y0) is shower center
X0
 X0
N=11
Eseen = 38 GeV
(X0,Y0)=(0.4,0.2)
tot = 0.85
2/DF=0.92
Efit = Eseen/tot=45 GeV
N=10
Eseen = 31 GeV
(X0,Y0)=(0.4,0.2)
tot = 0.68
2/DF=0.94
Efit = Eseen/tot=46 GeV


N


i
;
,

2
E
X
Y


i
0
0

Minimize:  

channels i 1   E   i ; X ,Y  
i
0 0


i
i
This gives you:
2
• 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
23
Real detectors: many sub-systems
 
Z e e
 



Z
Z  qq
24
LEP I events: ee  Z  ff




ee



qq

25
LEP I
results
cross sections
asymmetries
26
LEP II events: ee  WW  ….
W  W   q' qq' q
W  W   q ' q 
27
W  W   e e  
How best to determine W-boson mass from these events?
LEP II
results
cross sections
W-boson mass
28
29
Fit all available data to the “Standard Model”
30
Real life: resolution, inefficiency, breakdown, …
Ideal world:
Real world:
Real world:
Real world:
Everything works fine!
Resolution:
bad fits
Inefficiencies:
missing/noise hits
Breakdown:
broken channels
Solution, simulate your data sample in great detail i.e.:
 the underlying physics of interests (event generator e.g. ee  Z  
 detector response (GEANT; software package for particle passage through material)
 specific detector reconstruction software and your own event selection/analysis code
31
Monte Carlo integration technique
b
f(x)
 f ( x ) dx
Use your math knowledge:
a
a
b x
Use your computer with
N equidistant points on [a,b]
1
b a N  (b a )(i  2 ) 
 f a


N i 1 
N


Use your computer with
N randomly choosen points on [0,1]
ba N
 f a  (b  a ) R 

i
N i 1
f(x)
a
b x
f(x)
a
b x
fmax
f(x)
a
b x
Hit/Miss Monte-Carlo method
Use your computer with
N randomly choosen pairs on [0,1]
Increment Nacc if:
f a (ba ) Ri 
R
f max
 (b  a ) f max
N acc
N
i 1
Last method yields N “event” i.e. x values distributed according to f(x) on interval [a,b]!
32
History
Historical overview
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
IX.
X.
XI.
XII.
XIII.
XIV.
XV.
XVI.
Periodic system of elements (Mendeleev)
Electron discovery (Thomson 1897)
Photon as a particle (Einstein, Compton, …: 1900-1924)
Atomic structure (Rutherford 1911)
Positron discovery (First anti-particle, Anderson 1931)
Anti-proton discovery (1955)
Cosmic rays  muon, pion, … (1937, 1946, …)
Strange particles (1946, 1951, …)
Neutrino’s “observed” (1958)
Charmed particles (1974)
Gluon discovery (1979)
W and Z bosons (1983)
t-quark discovery (1995)
Neutrino oscillations (atmospheric (1998) and solar (2000))
-neutrino discovery (2000)
Higgs boson discovery?
33
Mendeleev: periodic system of elements
Chaos
 order
 better understanding
 predictions (new elements)
34
 new insights
35
Thompson (1897): electron
E
BE
E,B0  v=Ec/B
B0  R=vmc/qB
No deflection in EB configuration:




Ec
 
 v 

0  F  q E  B  v  
B
c
 Measured q/m much larger than for
 (with electron charge) me31026 g
Circle with radius R with only B0:
mc
q vc
R v
 
qB
m RB
1H-atom
“Plum”-model
of the atom
atom
Joseph Thomson
Nobel Prize 1906
In recognition of the great
merits of his theoretical and
experimental investigations
on the conduction of
electricity by gases
(1856-1940)
36
37
Rutherford (1911): 4He-Au scattering experiment
observation:
unexpected large number of alpha particles
deflected over large angles!
 all positive charge at center!
R+<10-12 cm “Solar system”-model
nucleus
of the atom
note:
compare shooting bullets at bag of sand

38
Cross section calculation
Nodig: b ( )
Z
1
2 E tan / 2 
opstelling: dichtheid alpha deeltjes ; snelheid alpha deeltjes v
flux: v [#/cm2/s]
# over hoek  verstrooide alpha deeltjes:  2bb
2
2


N
1
Z   cos
1
 Z 

  v 2 
 v 2bb  v 2 
 


t
 2 E  tan / 2   tan / 2  
 2 E  4sin 4 / 2 
Z 
1
 d  
d  2 E  4sin 4 / 2 
2
Earnest Rutherford (1871-1937)
Nobel Prize 1908 (Chemistry!)
For his investigations into the
disintegration of the elements and the
chemistry of radioactive substances
39
Bohr (1914): energy levels in atoms
40
Experiment showed emission (absorption) of specific, element dependent, wavelengths!
Example:
Balmer series in hydrogen
1
1 1
 R 2  2
n 3, 4,5,...

2 n
 
410
434
486
Discreteness of energy levels hard to
reconcile with the classical atomic model
Bohr:
v
p+
e
r
Hydrogen: 1 proton with 1 electron
Electron angular momentum quantized!
Discrete lines: transitions between states
1
L  mvr  nh  E  2
n
n
656 nm
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"
41
Chadwick (1932): the neutron discovery
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.
Be
Solution:
Chadwick postulated the existing
of a neutral particle inside the
atomic nucleus: the neutron!
paraffine
e-
-radiation
Thompson
42
protonen
1H
p+
Rutherford
e-
4He
2 p+
2n
Chadwick/Bohr
14C
atom
“Plum”-model
of the atom
nucleus
“Solar system”-model
of the atom
nucleus:
14 protons
7 electrons

spin ½
experiment: spin 1
nucleus
“modern”-model
of the atomic nucleus
James Chadwick 1891 - 1974
Nobel Prize 1935
For the discovery of the neutron
43
The photon (1900-1924) as a particle
Einstein/Millikan
observation:
electron emission stops abruptly as soon as
wavelength exceeds a certain (material
dependent) value.
explanation: Ee  h-W
Compton
observation:
deflected photon wavelength shifted from incident
photon wavelength according to: f= i + (1-cos) h/mc
Planck
Klassiek:  (  , T ) 
Planck:
8
4
kT
Raleigh - Jeans 

tot
   (  ,T ) d 
1
 (,T )  8hc

5 exp hc

KT  1

lim  ( ,T )  0 lim  ( ,T )  Planck  RJ
 0
 
0
44
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”
45
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
46
Robert Andres Millikan (1868-1953)
Nobel price 1923
For his work on the
elementary charge of
electricity and on the
photo-electric effect
47
Arthur Holly Compton (1892-1962)
Charles Thomson Rees Wilson (1969-1959)
48
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"
Electro - magnetisme
In de quantum-velden theorie is een Zwakke wisselwer king
interactie (of kracht) het gevolg van
Sterke wisselwer king
uitwisseling van veld-quanta
Gravitatie

W  , Z 0 ,W 
gluonen
?
10 2
10 13
1
10 38
49
Anti-matter
1927: Dirac equation with two energy solutions:
2
2 2
2 4
E p c m c
E   p 2c 2  m 2c 4
E   p 2c 2  m 2c 4
How do you avoid that all particles tumble into the negative energy levels?
Simple: assume that all negative energy levels are
filled (possible thanks to Pauli exclusion principle!)
E=0
-
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!
e
n
p



e
n
p
50
The anti-particles: e and p
anti-particles: predicted to exist by Dirac
lead plate
first anti-electron (e+) observation
bubble
chamber
p p  p p p p
p
p  6.3 GeV
p
p
p
p
p
Werner Schrodinger (1887 – 1961)
Paul Dirac (1902 – 1984)
Nobel Prize 1933
For the discovery of
new productive forms
of atomic theory
51
Anderson (1905 – 1991)
Nobel Prize 1936
For his discovery of the positron
52
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)
53
The pion () and the muon ()
-decay
-decay


    


  e    e
54
Strange particles
55










0
1232 MeV

0


1385 MeV



1533 MeV
?
Production of particles with a very long lifetime!
Typically in pairs 
production mechanism  decay mechanism
(strong interaction)
(weak interaction)
1680 MeV
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
1232 MeV

0


1385 MeV



ddd ddu
duu
uuu
sdd sud suu
ssd
ssu
1533 MeV


1680 MeV
sss
Fundamental particles:
u-, d- & s-quarks!
56
57
Neutrino’s
existence of the neutrino postulated by Pauli:
not this
but this
 # events
 # events
n pe
n  p  e   e

mn-mp-me  17 keV
 Ee
 Ee
experiment to demonstrate neutrino’s existence: Cowan & Reines
e pne
followed by


e e  

n-capture

n
e
e+

e+ e
annihilation
Martin 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 lepton
for the detection of the neutrino
58
59
Leptongetal
1962: Experiment shows that there exists something like “conservation of lepton number”
Particles count as “+1”
Anti-particles count as “1”
Lepton lepton # electron# muon #
e
1
1
0
e
1
1
0
1
0
1


1
0
1
()
()
 e  n p  e 
 e  n p  e 
  e 
Yes
No
No
   p     n Yes
  p e   n

No
Lepton lepton # electron# muon #
e
1
1
0
e
1
1
0
1
0
1


1
0
1
()
()
Later:
We will see that these particles can be
organized in doublets; much alike e.g.
the electron spin states:
Spin-up: 
Spin-down: 
Lederman, Schwartz, Steinberger
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
60
61
Charmed particles (1974)
SLAC:
excess events @ s  3.1 GeV
ee  hadrons
Brookhaven:
excess events @ Mee  3.1 GeV
p+Be  ee
Burt Richter
Sam Ting
interpretation:
new quark: ee  cc  hadrons
interpretation:
new bound state: cc  ee
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
quark baryon # u / d # c / s #
1
u
3
1
0
( d)
c
( s)
3
1
0
3
1
0
1
3
0
1
1
1
Later:
We will see that these particles can be
organized in doublets; much alike e.g.
the electron spin states:
Spin-up: 
Spin-down: 
62
And many many more particles ………
63
Sheldon 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
64
65
Gerardus 't Hooft (1946)
Martinus Veltman (1931)
Nobel Prize 1999
For elucidating the quantum
structure of electroweak
interactions in physics
66
The W and Z bosons: SppS collider
pp  WX with W  e e or W    

pp  ZX with Z  e e or Z   

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
67
68
Gluon discovery
q
e+
q
e-
q
e+
q
g
e-
The t-quark: Tevatron collider
pp  Xtt
tt  Wb Wb
W  e  e or    (clean)
W  qq (difficult )
69
Higgs discovered @ LEP?
signal: e e  ZH  qq bb
background: e e  ZZ  qq bb
70
71
72
outstanding issues (only a selection!):
1.
2.
3.
4.
5.
6.
7.
Why 3 families?
Neutrino masses?
Why matter/anti-matter balanced distorted?
How to incorporate mass? Higgs?
Dark matter in universe?
Further unification of interactions?
Gravity?
73
Overview
Quantum-Electro-Dynamics (QED)
74
The theory of electrons, positrons and photons
electric charge
based on a local U(1) gauge symmetry
field quantum: photon 
First and most successful Quantum Field Theory
In a pictorial manner all electro-magnetic
phenomena can be described using one
fundamental interaction vertex:
Möller scattering
ee ee
Bhabha scattering
e
e

By combination of vertices more complicated
(and realistic!) processes can be described:
ee ee
(1948: Feynman, Tomonaga, Schwinger)
Feynman
diagrams
time
Theory requires existence of the
electron’s anti-particle: the positron
e
Electron (e): arrow in + time direction
Positron (e+): arrow in  time direction
e+
75
QED: coupling constant em & perturbation series
Interaction strength (coupling constant): em
Experimentally: em1/137
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
higher order ee ee diagrams
Agreement between experiment and
theory is extra-ordinary as we will see
later (e.g. for “g-2” at the ppb level)
e.g.: (ge-2)/2  1159.6521869 (41)  106
Feynman diagrams do not represent particle trajectories; they are just a symbolic
notation to facilitate the calculation of physics quantities like cross-sections, lifetimes, …
76
QED: ee  cross-section “calculation”
-
e+

With a (simple) set of rules QED allows you to calculate
the ee  cross-section ( scattering probability)

+
e- t
Cross-section is proportional to “square” of
sum of the relevant Feynman diagrams
total
Dimension analysis tells you (later) that
cross-sections go like [GeV]-2
At high energies (>> me) “only” relativistic
invariant quantity available: (pe++pe-)2s


 em  em 
2
s
2
4

  em 
 3s 


s
77
The running QED coupling constant: em(q2)
Each electron is surrounded by a “cloud” of ee 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!
e
e+
e
e+
nearby probe:
“bare” charge
e
e
e+
e+
e
e
e+
far away probe:
“screened” charge
e + e
e+
e
The strength of the interaction depends
on the resolution of your probe!
energie
78
Running of em
1/em
“energie”
em(0) =1/137.0359895(61)
Quantum-Chromo-Dynamics (QCD)
79
The theory of quarks and gluons
color charge
based on a local SU(3) gauge symmetry
field quanta: eight gluons g
u
Quark structure: p = uud , n = udd , ++=uuu
u
u
Problem: the ++ consists of three identical quarks and is thereby
33
symmetric under uu permutations; its |JJz>=|2 2> 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
u
All bound states of quarks are colorless i.e. white
baryons: multiply with:
(RGBRBGGRBBGR+BRG+GBR)/6
mesons: multiply with:
(RR+BB+GG)/3 (symmetric in color)
(anti-symmetric in color)
u
u
80
QCD: color interaction
qr
Fundamental interaction vertex:
qb
grb
Quarks carry color; anti-quarks carry anti-color
Gluons 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!
ggg
By combination of vertices more complicated
(and realistic!) processes can be described:
gggg
qqqq
81
The size of the strong coupling constant: s

p

p
You can use the measured pp cross section to
get an estimate of the strong coupling constant via:


Experimentally (at s  10 GeV):
 S  S   2s

2
s
s
pp cross section about 10 mb
ee  cross-section about 1 nb
hence: s >> em
typically: s  0.1 - 10
Strong interaction
really strong
Perturbative
calculations valid?
82
The running QCD coupling constant: S(q2)
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 (quarkgluon)
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 energy
Gluon polarization: s smaller at higher energy
energie
”Asymptotic freedom”
Running of s
S(MZ) =0.1190.004
83
QCD confinement and jets
Within 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.
84
85
QCD jets in e+e annihilation
e+
q
 EM
e-
q
S
In e+e annihilation quark/anti-quark pairs can be created: e+eqq
Electric charge differences left aside, identical to e+e+ cross section
The colored quarks can not exist as stable particles and “hadronize” into jets;
a spray of collimated charged and neutral particles
86
Weak interaction: introduction
The 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.
0
10-16
The lifetime of the
is about
s.
Hence the typical electro-magnetic/strong
lifetime ratio corresponds nicely with the
ratio of the strong and electromagnetic
coupling constants!
 em
 strong
The np+e+e lifetime is about 15 minutes!
The  e+ e + lifetime is about 2 s.
Etc.
S 



  em 
2
4
6
 110 

  10  10
 1 / 137 
2
  n  10 s   W 



  n   1010 s

 S
 23
These are clearly very similar from typical
strong and electro-magnetic lifetimes.
This calls for an other decay mechanism:
the weak interaction.
and therefore W  106
2
Quantum-Flavor-Dynamics (QFD)
The weak interaction theory
Z0
which charge?
based on a local SU(2) gauge symmetry
field quanta: W+, W and Z0 bosons
Quark sector:
W cause: ud, cs and tb transitions
ee,  and  transitions
Z0
causes: uu, dd, cc, etc. transitions
ee, ee, , etc. transitions
W: charged current (qelectric=1)
e
e
e
u
d
W
W
Z0: neutral current (qelectric=0)
e
W
e-
87
W-
W
Z0
e
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.
Weak interaction vertices & diagrams
W,Z self couplings:
W,Z couplings to the :
Examples:
The np+e+e decay
The  e+ e + decay
88
89
The “skewed” weak interaction
s
d
u
u
d
u
d
u
Time (sorry)
How to account e.g. for the p++;
once you accept that the quark structure of the  is (uds)?
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 cosC + s sinC and c  d sinC + s cosC
u
c




This mixing is expressed in terms an angle:
   
the Cabibbo mixing angle  13
d   s
C
o
Cabibbo favored
Cabibbo suppressed
Interaction summary
90
The “Standard model”
Gauge symmetry based on SU(3)xSU(2)xU(1) groups
Open question: are these interactions unified at a (very) high energy scale?
91