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Discovery History u d tc sb six quarks e e six leptons 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
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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