H

QuarksQuarks – – “the building “the building blocks of the Universe”blocks of the Universe”

The number of quarks increased with discoveries of new particles and have reached 6

For unknown reasons Nature created 3 copies (generations) of quarks and leptons

Charm came as surprise but completed the picture

Discovery HistoryDiscovery History

u

d

tc

s b

six quarks

1947

1974 1995

1977e

e

six leptons

1956

1895

1963

1936 1975

Now we have a beautiful pattern of three pairs of quarks and three pairs of leptons. They are shown here with their year of discovery.

2000

Matter and AntimatterMatter and Antimatter

The first generation is what we are made of

Antimatter was created together with matter during the “Big bang”

Antiparticles are created at accelerators in ensemble with particles but the visible Universe does not contain antimatter

Quark’s ColourQuark’s Colour

( )

( )

( )

d d d

s s s

u u u

Baryons are “made” of quarks

To avoid Pauli principle veto one can antisymmetrize the wave function introducing a new quantum number - “colour”, so that

( )ijki j kd d d

?

The Number of ColoursThe Number of Colours

The x-section of The x-section of electron-positron electron-positron annihilation into annihilation into hadrons is proportional hadrons is proportional to the number of quark to the number of quark colours. The fit to colours. The fit to experimental data at experimental data at various colliders at various colliders at different energies givesdifferent energies gives

Nc = 3.06 0.10

The Number of GenerationsThe Number of Generations Z-line shape Z-line shape

obtained at LEP obtained at LEP depends on the depends on the number of flavours number of flavours and gives the and gives the number of (light) number of (light) neutrinos or neutrinos or (generations) of the (generations) of the Standard ModelStandard Model

Ng = 2.982 0.013

Quantum Numbers of MatterQuantum Numbers of Matter QuarksQuarks

LeptonsLeptons

LL

R R

R R

upQ

down

U upD down

SU(3)c SU(2)L UY(1)

333

211

1/ 34 / 32 / 3

?

LL

R R

R R

Le

NE e

111

211

102

tripletsdoublets

singlets

3 / 2Q T Y Electric charge

3T

3T

1212-

0

0

V-A currents in

weak interactions

The group structure of the SMThe group structure of the SM

Casimir Operators

For SU(N)

QCD analysis definitely singles out the SU(3) group as the symmetry group of strong interactions

Electro-weak sector of the SMElectro-weak sector of the SMSU(2) x U(1) versus O(3)

The heavy photon gives the The heavy photon gives the neutral current without flavour neutral current without flavour violationviolation

Discovery of neutral currents was a crucial test of the gaugegauge model of weak interactions at CERN in 1973

3 gauge bosons 1 gauge boson 3 gauge bosonsAfter spontaneous symmetry breaking one has

3 massive gauge bosons(W+ , W- , Z0) and 1 massless (γ)

2 massive gauge bosons(W+ , W- ) and 1 massless (γ)

Gauge InvarianceGauge Invariance( ) ( ) exp[ ( ) ]a a

iji j ij jx U x i x T 1,2,...,a N

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

i x x i x U x U x x

i x x x U x U x x

Gauge transformation

parameter matrix

Fermion Kinetic term

Covariant derivative a aD I gA T I g A Gauge field

( ) ( ) ( )D x U x D x 1( ) ( ) ( ) ( ) ( ) ( )gA x U x A x U x U x U x

matrix 1U U

Gauge invariant kinetic term ( ) ( )i x D x

[ , ] [ , ]D D G A A g A A ( ) ( ) ( ) ( )G x U x G x U x

Gauge field kinetic term 14 Tr G G

Field strength tensor

( ) ( )jii jx U x

Lagrangian of the SMLagrangian of the SM

gauge Yukawa HiggsL L L L 1 1 14 4 4

†( ) ( )

a a i igaugeL G G W W B B

iL D L iQ D Q iE D E

iU D U iD D D D H D H

L D UYukawaL y L E H y Q D H y Q U H

2 † † 22 ( )HiggsL V m H H H H †

2H i H

(3) (2) (1)c L YSU SU U

α,β=1,2,3 - generation index

Fermion Masses in the SMFermion Masses in the SM

0L RL R L RR L

c cL LL L

Direct mass terms are forbidden due to SU(2)L invariance !

SU(2) doublet SU(2) singlet

Dirac Spinors

5 50 0 2 *1 1, , , ,

2 2c

L R C i

left right Dirac conjugated Charge conjugated

Lorenz invariant Mass termsSUL(2)

c cR RR R

SUL(2) & UY(1) UY(1)

Unless Q=0, Y=0

cR R

Majorana mass term

( )

0exp( )

v22

H H i H H S

Spontaneous Symmetry BreakingSpontaneous Symmetry Breaking(3) (2) (1) (3) (1)c L Y c EMSU SU U SU U

0

HH

H

2 † † 22 ( )V m H H H H

Introduce a scalar field with quantum numbers: (1,2,1)

With potential

Unstable maximum

Stable minimumAt the minimum

0

0exp( )

v2v22

HH

H i SS iPH

scalar

pseudoscalar

v.e.v.

Gauge transformation Higgs boson

h

0v

H

3 - 3 -14 + 3 + 3

gW ' 2gW gW ' 2gW 0(0 v)

v2gW -gW ' 2gW -gW '

g B g B

g B g B

The Higgs MechanismThe Higgs Mechanism

1e e e ea a a a a a a ai i i i

gW W

a a

Q: What happens with missing d.o.f. (massless goldstone bosons P,H+ or ξ ) ?

A: They become longitudinal d.o.f. of the gauge bosons Wμi, i=1,2,3

Gauge transformation

Longitudinal components

Higgs field kinetic term 22 '

2 2 g gD H H W H B H

22 2 3 21v v ( ' )

2 4g W W gW g B

1 2

3

3

2

Z sin cos

cos sinW W

W W

W WW

B W

B W

2 2 212

2 2 2 212

v

( +g' )v W

Z

M g

M g

tan /0

W g gM

The Higgs Boson and Fermion The Higgs Boson and Fermion MassesMasses

2 † † 22 ( )V m H H H H

0

v2

H h

42 2 3 4v vv

2 82V h h h

( )v, ( )v, ( )vu u d d l li i iM Diag y M Diag y M Diag y

2 2 vhm m

2 2v /m

E D UYukawaL y L E H y Q D H y Q U H

α, β =1,2,3 - generation indexDirac fermion mass

( )vN Niy L N H M Diag y

Dirac neutrino mass

The Running CouplingsThe Running Couplings

( ) ( / ) ( )Bare RZ

2 2( / ) 1 ( / ) ...Z b Log

2 2 2 2 2 2( / ) ( / ) ( / )Log p Log Log p

Radiative Corrections ~α (log Λ2/p2 +fin.part) UV divergence

Renormalization operation

UV cutoff Renormalization scale

Renormalization constant

Subtraction of UV div

Finite( )R 2 22 2( ), ( ) ( / )d d Log Z

d d

Running coupling

Renormalization GroupRenormalization Group2 2 2 2 2( , ( )) (1 ( ) ( ))PTR Q b Log Q O

2 2 22 2 2( ) 0d dR R

d d

2 2 2 2

22

( , ( )) (1, ( , ))

( )

RG PTR Q R Q

dQdQ

Observable

RG Eq.

Solution to RG eq.

Effective coupling

( )

Solution to RG eq. sums up an infinite series of the leading Logs coming from Feynman diagrams

2 22 2(1, ) , (1 ( ) ...)

1 ( )PTR b Log Qb Log Q

Asymptotic Freedom and Asymptotic Freedom and Infrared SlaveryInfrared Slavery

2( ) b

One-loop order 4/3 nf QED

-11+2/3 nf QCD

2 2 1 ( )b Log Q

QED QCD

α_

α_

UV Pole IR Pole

Comparison with ExperimentComparison with ExperimentGlobal Fit to Data Higgs Mass Constraint

Remarkable agreement of ALL the data with the SM predictions - precision tests of radiative corrections and the SM

Though the values of sin w extracted from different experiments are in good agreement, two most precise measurements from hadron and lepton asymmetries disagree by 3

• Inconsistency at high energies due to Landau polesInconsistency at high energies due to Landau poles• Large number of free parametersLarge number of free parameters• Still unclear mechanism of EW symmetry breakingStill unclear mechanism of EW symmetry breaking• CP-violation is not understoodCP-violation is not understood• The origin of the mass spectrum in unclearThe origin of the mass spectrum in unclear• Flavour mixing and the number of generations is arbitraryFlavour mixing and the number of generations is arbitrary• Formal unification of strong and electroweak interactionsFormal unification of strong and electroweak interactions

Where is the Dark matter?

The SM and BeyondThe SM and BeyondThe problems of the SM:The problems of the SM:

The way beyond the SM:The way beyond the SM:

• The SAME fields with NEW The SAME fields with NEW interactions and NEW fieldsinteractions and NEW fields

GUT, SUSY, String, EDGUT, SUSY, String, ED

• NEW fields with NEW NEW fields with NEW interactionsinteractions

Compositeness, Technicolour,Compositeness, Technicolour, preonspreons

We like elegant solutionsWe like elegant solutions