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

qq

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?