0705.4264 The Standard Model - spiro.fisica.unipd.itroda/Materiale Masiero... · Antonio Pich IFIC,...

Antonio Pich

IFIC, CSIC – Univ. Valencia

2010 International School on Astroparticle Physics (ISAPP 2010)

Zaragoza, Spain, 13-22 July 2010

http://arxiv.org/pdf/0705.4264

The Standard Model

Gauge Invariance: QED, QCD Electroweak Unification: Symmetry Breaking: Higgs Mechanism Electroweak Phenomenology Flavour Dynamics

L YSU(2) U(1)⊗

Standard Model Parameters

QCD: ( )S ZMα 1

EW Gauge / Scalar Sector: 4

2, , ,g g µ λ′ F, , ,Z HG M Mα, , ,W W HM Mα θ

The Standard Model A. Pich - ISAPP 2010

INPUTS( )

( )

5 2

1

1.166 371 0.000 006 10 GeV

137. 035 999 710 0.000 000 09691. 1875 0.0021 GeV

F

Z

G

Mα

− −

−

= ± ×

= ±

= ±

[ ]Exp: 8080. .3994 Ge 9V 0.023WM = ±

2 2

22

2

sin2

sin 1

W WF

WW

Z

MG

MM

π αθ

θ

=

= −

2sin 0.212Wθ =

( )1 2 128.93 0.05ZMα − = ±

( )79.96

( )0.231

µν

W

µ−

e−

eν

g

g

2

F 2W

gG

M


The Photon Couples to Virtual Pairsf f

1 2 1 2 1( ) 137.035999710 ; ( ) 128.93 0( 09 ) . 56 Zem Mα α α− − −= = = ±

( and contributions included )l l− + q q

Vacuum Polarized Dielectric Medium


, , , ,eW e v v v d u s cµ τµ τ− − − − ′ ′→

Ccos sinsin cos

C

C C

d ds s

θ θθ θ

′ ≈ ′ −

Universal CouplingsW llν

Experiment: ( ) ( )( ) ( )( ) ( )

Br 10.65 0.17 %

Br 10.59 0.15 %

Br 11.44 0.22 %

eW e

W

W

µ

τ

ν

µ ν

τ ν

− −

− −

− −

→ = ±

→ = ±

→ = ±

( )Br 10.8%lW l ν− −→ ≈QCD:( )

1 3.115Cs ZMN

απ

+ ≈

( ) ( )( )1Br 11.1%

3 2all Cl

lW l

W lNW

νν

− −− −

−

Γ →→ ≡ = =

+Γ →

W− i, dl−

j, ulνj , ;u u c=


LEPTON UNIVERSALITY

e

ggµ

ggµτ


K K

W W

eB

B B

τ µ τ

τ π π µ

τ µ

τ µ

τ τ→

→ →

→ →

→ →

Γ Γ

Γ Γ

1.0006 0.0022

0.996 0.005

0.979 0.017

1.039 0.013

±

±

±

±

/g gτ µ1.0018 0.0015

1.0021 0.0016

1.004 0.007

1.002 0.002

0.997 0.010

±

±

±

±

±

K K

K K

W W

e

e

e

e

e

B B

B B

B B

B B

B B

τ µ τ

π µ π

µ

πµ π

µ

→ →

→ →

→ →

→ →

→ →

/ eg gµ

W W e

B

B Bτ µ µ τ

τ

τ τ→

→ →

1.0005 0.0023

1.036 0.014

±

±

/ eg gτ


Z

f

f

( ) ( )( ) ( )22

inv invisible 2 1.9551 4sin 1W

l l

llN N N

ZZZ l l Z l lν ν ν

ν ν

θ+ − + −

Γ →Γ Γ →≡ = = =

Γ → Γ → − +

, l lZ l l v v− +→

( ) ( )2 2vl lZ l l aΓ → ∝ +

Experiment:

inv 5.942 0.016l l

Γ= ±

Γ3.04Nν =

( )1.989

(2.99)

2.9840 0.0082vN = ±

µ


{ }2

2 2f f(1 cos ) cos - (1 cos ) cos8

Add s

N B Ch Dσ α θ θ θ θ = + + + + Ω

, Z f fe e γ+ − → →

e+, Zγe− f

f

2

f( )

1 ; 1 ; 1CZ

qls MN N N h

απ

= = + + = ±

2

2

2 2 2 2

2 2

2 2

2

2

f f f

f f f

f f f

f f f

1 2 Re( ) +

4 Re( ) +

vν (v ) (v )

v v

v (v ) v

v v

8

2 Re( ) + 2

4 Re( ) + (v )4

e e e

e e e

e e e

e e e

A a a

B a a a a

C a a a

D a a a

χ χ

χ χ

χ χ

χ χ

+ +

+

+

= +

=

=

=

2

2 /2 2F Z

Z Z Z

G M ss M i s M

χπα

=− + Γ

f

f

e− +eθ


, Z f fe e γ+ − → →

e+, Zγe− f

f

f

f

e− +eθ

f f

f f

( ) ( ) 2

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

F B

F B1 1

( 1) ( 1)

1 1 1 1F F B B

1 1 1 1F F B B

f

( )

( )

38

4;3

3(8

)

h h

h h

BA

C A

s

s

N NN N

s

N N N NN N

A

DA

N

sN N

σσ σ π ασ σ

=+ =−

=+ =−

+ − + −

+ − + −

≡

≡ =

≡

−+

−

+

−

=

= −

− +−

+ + +=

FB

Pol

PolFB

{ }2

2 2f f(1 cos ) cos - (1 cos ) cos8

Add s

N B Ch Dσ α θ θ θ θ = + + + + Ω


2Z(s = M )Z Peak

f22 f; ( f f

12 )ZZ

e ZM

σ πΓ Γ

= Γ ≡ Γ →Γ

f f3 34

( ) ; ( ) ; ( )4e e

s s s= = = Pol

FB Pol FB

L R

L Rf;( ) ( )

34e

s sσ σσ σ

−≡ = − =

+−

LRLR FB

f ff f 2 2

f f

2 vv

aAa

−≡ − =

+Final Polarization Only Available for f = τ

l21v 1 4sin 1

2lθ= − + Sensitive to Higher Order Corrections


Sensitive to Heavier Particles: TOP , HIGGSThe Standard Model A. Pich - ISAPP 2010

Evidence of Electroweak Corrections

12( ) 128.93 0.05ZMα− = ±

Low Values of MH Preferred

August 2009 LEPEWWG September 2005


LEPEWWG September 2005( ) ( hadrons)bR Z bb Z≡ Γ → Γ →

Bernabéu-Pich-Santamaría 1988


Heavy Quarks (Leptons) Favour High (Low) MH

(172.7 2.9) GeVtm = ±

700186(300 ) GeVHM

+−=

LEPEWWG September 2005

12( ) 128.93 0.05ZMα− = ±


LEPEWWG August 2009

mt = (173.1 ± 1.3) GeV (CDF + D0)


114.4 GeV 157 GeV(186)HM< < (95% CL)The Standard Model A. Pich - ISAPP 2010

LEPEWWG (August 2009)

CDF / D0 (January 2010)

H → W+W−

MH ∈ [162,166] excluded (95% CL)

e e W W+ − + −→

Evidence of Gauge Self-Interactions

W −

W +

, Zγ

e−

e+

W −

W +

e−

e+eν


e e Z Z+ − →

, Zγ

e−

e+

Ze−

e+

e−

Z

Z

Z

?

No Evidence of or couplingsZ Z ZZ ZγThe Standard Model A. Pich - ISAPP 2010

Searching forthe HIGGS

Branching Ratios Total Decay WidthD. Denegri

Interaction proportionalto mass 2 2( , , )W Z fM M m

The Higgs decays into theheaviest possible particles


ATLASCMS

The Large Hadron Collider


Quarks Leptons Bosons

photon

gluon

Higgs

up down electron neutrino e

charm strange muon neutrino µ

top beauty tau neutrino τ

e

µ

τ

Z0 W ±


Fermion Masses areNew Free Parameters

f

Couplings Fixed: fHf fmg v=

fmv

f

H

( ) ( ) ( ) v, , , ,2ud

d u lq q lm m m c c c =

FERMION MASSESS

{ }1 v udq q u uY d d lH m q q m q q m l l = − + + +

SSB

Scalar – Fermion Couplings allowed by Gauge Symmetry

0

0 0( )

( ) ( )† ( )

( ) ( )† ( )( ) ( )( , ) ( ) ( ) ( , ) h.c.du L R u R L Rdu

ll

dY c cq q q q v l lcφ φ φφ φ φ

+ +

+

−

= − + − +


( ) ( )( ) (0)† ( )

(0) ( )† (0)( ) ( ) ( ), , h.c.Yd u l

j k j kj j j jk R k R k RL Ljj

kku d c c cd u v l l

φ φ φφ φ φ

+ +

+

′ ′ ′ ′ −

′ ′ ′= − + − +

∑

{ }1 h.c.vY L R L R L Rud lH d d u u l l ′ ′ ′ ′ ′ ′ ′ ′ ′= − + ⋅ ⋅ + ⋅ ⋅ + ⋅ ⋅ +

M M M

SSB

Arbitrary Non-Diagonal Complex Mass Matrices( ) ( ) ( ) v, ,

2, ,d u lud l jk jk jkjk c c c ′ ′ ′ = M M M

WHY ?

FERMION GENERATIONSMasses are the only differenceGN 3= Identical Copies

0

1

Q

Q

=

= −

2 3

1 3

Q

Q

= +

= −j j

j j

v ul d′ ′

′ ′ ( )G1, , Nj =


DIAGONALIZATION OF MASS MATRICES†

†

†

Sd d d d d d d

u u u u u u u

l l l l l l l

′ = ⋅ = ⋅ ⋅ ⋅

′ = ⋅ = ⋅ ⋅ ⋅

′ = ⋅ = ⋅ ⋅ ⋅

M H U S S U

M H U S U

M H U S S U

†

† †

† †

f f

f f f f

f f f f

1

1

=

⋅ = ⋅ =

⋅ = ⋅ =

H H

U U U U

S S S S

( ) { }d d + u1 u +vY ud l lH l= − ⋅ ⋅ ⋅+ ⋅ ⋅ ⋅ diag ( , , ;) diag ( , , ) diag ( , , );u du c t s ed b lm m m m m m m m mµ τ= = =

d d ; u u ;d d ; u u ;

L L L L L L

R R R R R R

ud l

u ud d l l

l ll l

′ ′ ′≡ ⋅ ≡ ⋅ ≡ ⋅

′ ′ ′≡ ⋅ ⋅ ≡ ⋅ ⋅ ≡ ⋅ ⋅

S S SS U S U S U

Mass Eigenstates

Weak Eigenstates≠

N C N C′ = f f f f ; f f f fL L L L R R R R′ ′ ′ ′= =

QUARK MIXING

†u d u d ;L L L L u d′ ′ = ⋅ ⋅ ≡ ⋅V V S S C C C C′ ≠

µ


[ ]f f 5N Cf

f f2 sin c

aos

vZW W

Ze µµγ

θ θγ−= − ∑

Flavour Conserving Neutral Currents

u c t

d s b

Flavour Changing Charged Currents

( ) ( )†C C i5 5i

i jj

j1 1 h.c.2 2 llg u d v lWµ

µ µγ γ γ γ

= − − + − + ∑ ∑V


( )CC i 5 j

ij

† ( )ij(1 ) h.c.2 2

l lgL lWµµν γ γ= − − +∑ V

Separate Lepton Number Conservation R( )νMinimal SM without

i( )ijj

llν ν≡ V

( ) †CC 5(1 ) h.c.2 2l

ll

gL W lµµ ν γ γ= − − +∑ IF im 0ν =

( Co, n, served )eeL L L LL L µµ ττ + +

IFi

iR exist and m 0νν ≠

BUT 11 8Br ( ) 1.2 10 Br ( ) 4.4 10eµ γ τ µ γ− −→ < × → < ×;(90 % CL)


Measurements of Vij

j i

2

ij( )ed u e ν−Γ → ∝ V

We measure decays of hadrons (no free quarks)

Important QCD Uncertainties

W

jdiu

e−

eν

ijV


00.9746 0.00190.9741 0.0026

0.2246 0.00120.2165 0.00310.2259 0.0015

Nuclear decay

decays/ , Lattice

0.97425 0.00022

0.2244 0.0012

0.2 , Latti0.230 0.011

0 02 c29 . 6

ud

us

cd

e

e

e

V

V

V

n p e ve

K e v

K

v d c XD l

β

π π ν

πτπ µν

π ν

−

+ +

−

→±±

±±±

→

→

→±± →

±→

±

*

0.0407 0.0007

0.985 0.104

0.0386 0.00110.0415 0.0007

0.0034 0.00040.0041 0.00030.0038 0.0003

0.890

e, Lattice

/

/.74 ; 1

cs

cb

ub

t

l

l

l

b

l

D K l

B D Dl vb c l v

B l vb u l v

t bW qW

V

V

p p tb X

V

V

ν

π±

±>

>

±

±±

±±

→

→→

→→

→

→ +<

95 02 22usud ubV + V + V = 0.99 ± 0.001 ( ) (LEP)2 002 7∑ 2 2uj cjj V + V = . ± 0.02

CKM entry Value Sourcei jV

2

q t qtb VV ∑


QUARK MIXING MATRIX Unitary Matrix: parametersG GN N×

2GN

arbitrary phases:G2 1N −

jii i j je ; e

iiu u d dθφ→ → j i( )ij ijei θ φ−→V V

ijV

( )G G1 12

N N −

Physical Parameters:

Moduli ; phasesG G1 ( 1) ( 2)2

N N− −

† †⋅ = ⋅ =V V V V 1


● Nf = 2 : 1 angle, 0 phases (Cabibbo)

No C CC C

cos sinsin cos

θ θθ θ

= −

V

2 2Csin 0.225 ; 0.81 ; 0.37Aλ θ ρ η≈ ≈ ≈ + ≈ 13 0)0 (ηδ ≠≠

ij ij ij ijcos ; sinc sθ θ≡ ≡● Nf = 3 : 3 angles, 1 phase (CKM)

( )

13

13 13

13 13

12 13 12 13 13

12 23 12 23 13 12 23 12 23 13 23 13

12 23 12 23 13 1

2 3

2 2

3 2

2 23 12 23 13 23 13

41 /2 ( )

1 /2(1 ) 1

i

i i

i i

c c s c s

s c c s s c c s s s s c

s s c c s c s s c s

e

e

c c

i

i

e

e e

AA

A A

δ

δ δ

δ δ

λ λ λ ρλ λ λ

λ ρ λ

η

ηλ

−

− − − − − − −

− − −

− − −

≈ +

=V


Standard Model ParametersQCD: ( )S ZMα 1

EW Gauge / Scalar Sector: 42 , , ,, , , , , , F ZW H HWg g h M M MM Gµ α θ α⇔⇔′

13Yukawa Sector:

1 2 3

, ,

, ,, ,

, , ,

e

sd b

u c t

m m m

m m mm m m

µ τ

θ θ θ δ

18 Free Parameters (+ Neutrino Masses / Mixings ?)

TOO MANY !The Standard Model A. Pich - ISAPP 2010

Complex Phases

Interferences

Thus, requires:

Theorem:

, : Violated maximally in weak interactions

: Symmetry of nearly all observed phenomena

Slight (~ 0.2 %) in decays (1964)

Sizeable in decays (2001)

Huge Matter Antimatter Asymmetryin our Universe Baryogenesis

0K0B


Meson – Antimeson Mixing

0B 0B

0B

0B

f2 Interfering Amplitudes

0 0

0 0

( / ) ( / )0

( / ) ( / )S S

S S

B J K B J KB J K B J K

ψ ψψ ψ

Γ → −Γ →≠

Γ → + Γ →

SignalBABAR


* * * 0ud ub cd cb td tbV V V V V V+ + =

* *ud ub cd cbV V V V * *td tb cd cbV V V V


2

2

0.342 0.014

0

112112

.154 0.022

η

ρ

η λ

ρ λ

= ±

=

≡ −

±

≡ −

92.0 3.4 ; 22.0 0.8 ; 65.6 3.3α β γ= ± ° = ± ° = ± °

UTfit

http://hitoshi.berkeley.edu/neutrino

Neutrino Oscillations

Rν ?,NEW PHYSICS

Lepton Mixing


Neutrino Oscillations

2 5 221

2 3 232

212

223

213

(7.59 0.21) 10 eV

(2.43 0.13) 10 eV

sin (2 ) 0.87 0.04

sin (2 ) 0.92

sin (2 ) 0.19

m

m

θ

θ

θ

−

−

∆ = ± ⋅

∆ = ± ⋅

= ±

>

<


González-García, Maltoni, Salvado, 2010

LEPTON FLAVOUR VIOLATION90% CL Upper Limits on Br(l−→ X −) [BABAR / BELLE]

Decay U.L. Decay U.L. Decay U.L. µ−→ e−γ 1.2 ⋅ 10−11 µ−→ e−e+e− 1.0 ⋅ 10−12 µ−→ e−γγ 7.2 ⋅ 10−11

τ−→ e−γ 3.3 ⋅ 10−8 τ−→ e−e+e− 3.6 ⋅ 10−8 τ−→ e−e+µ− 2.7 ⋅ 10−8

τ−→ µ−γ 4.4 ⋅ 10−8 τ−→ e−µ+µ− 3.7 ⋅ 10−8 τ−→ µ−e+µ− 2.3 ⋅ 10−8

τ−→ e−e−µ+ 2.0 ⋅ 10−8 τ−→ µ−µ+µ− 3.2 ⋅ 10−8 τ−→ e−π0 8.0 ⋅ 10−8

τ−→ µ−π0 1.1 ⋅ 10−7 τ−→ e−η’ 1.6 ⋅ 10−7 τ−→ µ−η’ 1.3 ⋅ 10−7

τ−→ e−η 9.2 ⋅ 10−8 τ−→ µ−η 6.5 ⋅ 10−8 τ−→ e−Κ*0 5.9 ⋅ 10−8

τ−→ e−ΚS 3.3 ⋅ 10−8 τ−→ µ−ΚS 4.0 ⋅ 10

−8 τ−→ µ−ρ0 2.6 ⋅ 10−8

τ−→e−K+K− 1.4 · 10−7 τ−→e−K+π− 1.6 · 10−7 τ−→e−π+K− 3.2 · 10−7

τ−→µ−K+K− 2.5 · 10−7 τ−→µ−K+π− 3.2 · 10−7 τ−→µ−π+K− 2.6 · 10−7

τ−→e−π+π− 1.2 · 10−7 τ−→µ−π+π− 2.9 · 10−7 τ−→Λπ− 7.2 ⋅ 10−8

τ−→e+K−K− 1.5 · 10−7 τ−→e+K−π− 1.8 · 10−7 τ−→e+π−π− 2.0 · 10−7

τ−→ µ−Κ*0 5.9 ⋅ 10−8 τ−→ e−φ 3.1 ⋅ 10−8 τ−→ µ−ω 8.9 ⋅ 10−8

τ−→µ+K−K− 4.4 · 10−7 τ−→µ+K−π− 2.2 · 10−7 τ−→µ+π−π− 0.7 · 10−7


THE STANDARD THEORY OF FUNDAMENTAL INTERACTIONS ( ) ( ) ( )C L YSU 3 SU 2 U 1⊗ ⊗

Electroweak + Strong Forces

Gauge Symmetry Dynamics

3 Gauge Parameters:

All Known Experimental Facts Explained

Problem with Mass Scales / Mixings:

( )2 , ,Z Ws Mα α θ

- 15 Additional Parameters- Why 3 Families ?

- Why Left ≠ Right ?- Why ?- Does the Higgs Exist ?- Flavour Mixing- Violation- Neutrino Masses / Oscillations

Ztm M>


e

µ

τ

Número de diapositiva 1Número de diapositiva 2Número de diapositiva 3Número de diapositiva 4Número de diapositiva 5Número de diapositiva 6Número de diapositiva 7Número de diapositiva 8Número de diapositiva 9Número de diapositiva 10Número de diapositiva 11Número de diapositiva 12Número de diapositiva 13Número de diapositiva 14Número de diapositiva 15Número de diapositiva 16Número de diapositiva 17Número de diapositiva 18Número de diapositiva 19Número de diapositiva 20Número de diapositiva 21Número de diapositiva 22Número de diapositiva 23Número de diapositiva 24Número de diapositiva 25Número de diapositiva 26Número de diapositiva 27Número de diapositiva 28Número de diapositiva 29Número de diapositiva 30Número de diapositiva 31Número de diapositiva 32Número de diapositiva 33Número de diapositiva 34Número de diapositiva 35Número de diapositiva 36Número de diapositiva 37Número de diapositiva 38Número de diapositiva 39Número de diapositiva 40Número de diapositiva 41Número de diapositiva 42Número de diapositiva 43Número de diapositiva 44Número de diapositiva 45Número de diapositiva 46Número de diapositiva 47Número de diapositiva 48Número de diapositiva 49Número de diapositiva 50Número de diapositiva 51Número de diapositiva 52Número de diapositiva 53Número de diapositiva 54Número de diapositiva 55Número de diapositiva 56Número de diapositiva 57

0705.4264 The Standard Model - spiro.fisica.unipd.itroda/Materiale Masiero... · Antonio Pich IFIC,...

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