Antonio Pich. IFIC, CSIC Univ. Valencia

Antonio Pich

IFIC, CSIC – Univ. Valencia

Antonio.Pich@ific.uv.es

http://arxiv.org/pdf/0705.4264

ƒ Fermion Masses

ƒ Fermion Generations

ƒ Quark Mixing

ƒ Lepton Mixing

ƒ Standard Model Parameters

ƒ CP Violation

Quarks Leptons Bosons

photon

gluon

Higgs

up down electron neutrino e

charm strange muon neutrino μ

top beauty tau neutrino τ

e

μ

τ

Z

⁰

W ^±

Fermion Masses are New Free Parameters

f

Couplings Fixed: _{H f f} m ^f g = v

m

f

v

f H

( ) ( ) ( )

v

, , , ,

u

2

d

d u l

q q l

m m m c c c

⎡ ⎤ = ⎣ ⎡ ⎤ ⎦

⎣ ⎦

FERMION MASSESS

{ }

1 v

^{d u}

Y H m q q d d q u u l

q m q q m l l

⎛ + ⎞

⎜ ⎟ ⎠

= − + +

L ⎝

SSB

Scalar – Fermion Couplings allowed by Gauge Symmetry

0

0 0

( )

( ) ( )† ( )

( ) ( )† ( )

( ) ( )

(

_u

,

_d

)

_L ^d

(

_d

)

_R ^u

(

_{u R}

) ( , )

_{l L} ^l _R

h.c.

Y

q q c φ q c φ q v l c φ l

φ φ φ

+ +

+

⎛ ⎞ ⎛ ⎞ ⎛ ⎞

⎜ ⎟ ⎜ − ⎟ ⎜ ⎟

⎡ ⎤

⎝ ⎠ ⎝ ⎠ ⎝ ⎠

= − ⎢ + ⎥ − +

⎢ ⎥

⎣ ⎦

L

( )

^{( )}(0) ^(0)†( )†

( )

^{( )}(0)

( ) ( ) ( )

, , h.c.

Y

d u l

j k j k

j j L k R k R j j L k R

j

j k

u d c φ d c φ u v l c

k

φ l

φ φ φ

+ +

+

⎧ ⎡ ⎤ ⎫

⎪ ′ ′ ⎛ ⎞ ′ ⎛ ⎞ ′ ⎛ ⎞ ⎪

⎜ ⎟ ⎜ − ⎟ ′ ′ ⎜ ⎟ ′

= − ⎨ ⎢ + ⎥ − ⎬ +

⎪ ⎣ ⎝ ⎠ ⎝ ⎠ ⎦ ⎝ ⎠ ⎪

⎩ ⎭

∑

L

{ }

1 v h.c.

Y

= − ⎛ ⎜ + H ⎞ ⎟ d

L

′ ⋅ ′ d ⋅ d

R

′ + u ′

L

⋅ ′ ′ u ⋅ u

R

+ ⋅ l

L

′ ′ ′ l ⋅ l

R

+

⎝ ⎠ M M M

L

SSB

Arbitrary Non-Diagonal Complex Mass Matrices

( ) ( ) ( ) v

, _u , ^d , ^u , ^l

d l jk ^⎡ c jk c jk c jk ^⎤

′ ′ ′ =

⎡ ⎤

⎣ M M M ⎦ ⎣ ⎦

WHY ?

FERMION GENERATIONS

Masses are the only difference

N

G

= 3 Identical Copies

0 1 Q

Q

=

= −

2 3 1 3 Q

Q

= +

= −

j j

j j

v u

l d

′ ′

⎛ ⎞

⎜ ′ ′ ⎟

⎝ ⎠ ( j = " 1, , N

G

)

DIAGONALIZATION OF MASS MATRICES

†

†

†

S

d 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

M M M

†

† †

† †

f f

f f f f

f f f f

1 1

=

⋅ = ⋅ =

⋅ = ⋅ =

H H

U U U U S S S S

( ) ¹ v ^{{ d d + u u + }}

Y

= − + H ⋅ d ⋅ ⋅ u ⋅ l ⋅ l ⋅ l

L M M M

diag ( , , ) ; diag ( , , ) ; diag ( , , )

u

= m

u

m

c

m

t d

= m

d

m

s

m

b l

= m

e

m

_μ

m

_τ

M M M

d d ; u u ;

d d ; u u ;

L L L L L L

R R R R R R

d u l

u u

d d l l

l l

l l

′ ′ ′

≡ ⋅ ≡ ⋅ ≡ ⋅

′ ′ ′

≡ ⋅ ⋅ ≡ ⋅ ⋅ ≡ ⋅ ⋅

S S S

S U S U S U

Mass Eigenstates Weak Eigenstates ≠

N C N C

′ =

L L

f f _L ′ ′ _L = f f _{L L} ; f f _R ′ ′ _R = f f _{R R}

QUARK MIXING

u d ′ ′ = _{L L} u _L ⋅ V ⋅ d _L ; V ≡ S _u ⋅ S

†

_d L ′ ≠

_{C C}

L

_{C C}

μ

[

f f 5

]

N C

f

f f

2 sin c a

os v

W W

Z

e Z

μ γ μ

θ θ − γ

= − ∑

L

Flavour Conserving Neutral Currents

u c t

d s b

Flavour Changing Charged Currents

( ) ( )

†

C C 5 i 5

i

i j

j

1 j 1 h.c.

2 2 l ^l

g W _μ ^⎡ u γ ^μ γ d v γ ^μ γ l ^⎤

= − ⎢ − + − ⎥ +

⎣ ∑ ^V ∑ ⎦

L

i

( ) i ( )

C 5 j

ij

j

†

C

(1 ) h.c.

2 2

l

l

W l

L g _μ

μ ν γ γ

= − ∑ − ^V +

Separate Lepton Number Conservation

( Minimal SM without ν

R

)

i

( ) j ij

l

ν

l

≡ ν V

( ) †

CC

(1

5

) h.c.

2 2

l

l l

L = − g W

_μ

∑ ν γ

^μ

− γ l +

z IF ^{m ν}

_i

^{= 0}

( Co

, , _e n served )

L e L _μ L _τ L + L _μ + L _τ z IF ν _R ⁱ exist and m _ν

_i

≠ 0

BUT ^{Br ( μ → e γ ) < 1.2 × 10}

⁻¹¹

^{; Br ( τ → μ γ ) < 4.5 10 ×}

⁻⁸

(90 % CL)

Measurements of V _ij

j i

2

( d u e ⁻ ν _e ) ij

Γ → ∝ V

We measure decays of hadrons (no free quarks)

Important QCD Uncertainties

W

d j ⁱ

u

e

⁻

ν e

V ij

0.97377 0.00027 0.9746 0.0019

0.2233 0.0024 0.2165 0.0031 0.2232 0.0020

Nuclear decay

decays

/ , L

0.97378 0.00027

0.222

0

0 0.0015 0.230 0.

attice

.95

011

0.97

7 0.09 .

5 4 0 01

ud

us

c

l d

cs

e

e

n p e v

K e v

K

v d c X D

V K l v

V

V

V

β

π π τ μν

−

−

±

±

±

± ±

±

±

±

±

±

→

→

→

→

→

*

,

0.0386 0.0013 0.0416 0.0006 0.0

3

0.0412 0.0011

0.0039 0.0004 0.89

0.68 ;

035 0.0006 0.0041 0.000

1

had ,

/ 4

,

cb

u

l l

l l b

tb

u j cd cb

W V V

B D l v b c l v

B l v

V

V

V

b u l v

t bW qW

p p tb X π

+

±

±

>

> <

±

→

→

→

→

→

→

→

±

±

+

±

76 2

2 2 2

us

ud ub

V + V + V = 0.99 ± 0.001 ^∑

_j

( ^V

^{uj 2}

^{+ V}

^{cj 2}

) = 1.999 ± 0.025

^(LEP)

CKM entry Value Source

V i j

2 q t q

tb V

V ∑

QUARK MIXING MATRIX

z Unitary Matrix: N _G × N _G N _G ² parameters

z 2 N _G − 1 arbitrary phases:

i j

i e ⁱ i ; j e ⁱ j

u → ^φ u d → ^θ d V _ij → e ^{i ( θ}

^j

^{− φ}

ⁱ

⁾ V _{i j}

V ij

( )

G G

1 1

2 N N −

Physical Parameters:

Moduli ; ¹ (

_G

1) (

_G

2) phases

2 N − N −

† †

⋅ = ⋅ =

V V V V 1

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

No CP

C C

C C

cos sin

sin cos

θ θ

θ θ

⎡ ⎤

= ⎢ ⎣ − ⎥ ⎦

V

2 2

sin

C

0.223 ; A 0.83 ; 0.48

λ ≈ θ ≈ ≈ ρ + η ≈ δ

₁₃

≠ 0 ( η ≠ 0) CP

ij

cos

ij

;

ij

sin

ij

c ≡ θ s ≡ θ

● N _f = 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

4

1 /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 e

e e

i

i

A A

A A

δ

δ δ

δ δ

λ λ λ ρ

λ λ λ

λ ρ λ

η η

λ

⎡

−

⎤

⎢

⎡ − − ⎤

⎢ − − ⎥

⎢ ⎥

⎢ − − − ⎥

⎢ − − − ⎥ ⎥

⎢ ⎥

− − −

⎢ ⎥

⎣ ⎦

⎣ ⎦

≈ +

V =

O

Standard Model Parameters

QCD: α

S

⁽ M

Z

⁾ 1

EW Gauge / Scalar Sector: 4

2

, , ,

, , , ,

_W

,

_W

,

_{H F Z H}

g g ′ μ h ⇔ α θ M M ⇔ α G M M

13 Yukawa Sector:

1 2 3

, ,

, ,

, ,

, , ,

e

d s b

u c t

m m m

m m m

m m m

μ τ

θ θ θ δ

18 Free Parameters (+ Neutrino Masses / Mixings ?)

TOO MANY !

ƒ Complex Phases

ƒ Interferences

Thus, CP requires:

CPT Theorem: T CP

z C , P : Violated maximally in weak interactions z CP : Symmetry of nearly all observed phenomena z Slight (~ 0.2 %) CP in decays (1964)

z Sizeable CP in decays (2001)

z Huge Matter Antimatter Asymmetry

in our Universe Baryogenesis K 0

B 0

Meson – Antimeson Mixing

B

0

B

⁰

B

0

B

0

f

2 Interfering Amplitudes

CP

0 0

0 0

( / ) ( / )

( / ) ( / ) 0

S S

S S

B J K B J K

B J K B J K

ψ ψ

ψ ψ

Γ → − Γ →

Γ → + Γ → ≠

Signal

BABAR

* * * ud ub cd cb td tb 0

V V + V V + V V =

* *

ud ub cd cb

V V V V

^{* *}

td tb cd cb

V V V V

2

2

0.342 0.012

0 1 1

2 1 1

2 .147 0.029 η

ρ

η λ

ρ λ

= ±

=

⎛ ⎞

≡ ⎜ −

±

⎝ ⎟ ⎠

⎛ ⎞

≡ ⎜ ⎝ − ⎟ ⎠

91.2 6.1 ; 21.9 1.0 ; 66.7 6.4

α = ± ° β = ± ° γ = ± °

UT _fit

Complex phases in Yukawa couplings only:

The CKM matrix V is the only source of CP

( ) ( )

jk j

( ) (0) †

j j L (0) k R k ( )† k R

j k

( , )

^{d u}

h. c .

Y

u d c d u

L φ c φ

φ φ

+

+

⎡ ⎛ ⎞ ⎛ ⎞ ⎤

′ ′ ′ ′

= − ∑ ⎢ ⎣ ⎜ ⎝ ⎟ ⎠ + ⎜ ⎝ − ⎟ ⎠ ⎥ ⎦ +

(0)

v / 2

⎡ φ = ⎤

⎣ ⎦

SSB

{

^{jL ( )jk k R jL (jk) k R}

}

1 v h.c

v .

2

u Y

c

d

L = − ⎛ ⎜ + H ⎞ ⎟ d ′ d ′ + u ′ c u ′ +

⎝ ⎠

( ) jk

c q diagonalization

{

^{jL j jR j L j jR}

}

†

CC i 5 j

i j

ij

1 h.c.

(1 ) h.c.

2 2

Y

v

d u

L d d u u

L g

m

W H

u d

m

μ

γ

μ

γ

⎛ ⎞

= − ⎜ ⎝ + ⎟ ⎠ + +

= − ∑ − ^V +

http://hitoshi.berkeley.edu/neutrino

Neutrino Oscillations

CP

ν R ^, ?

NEW PHYSICS

Lepton Mixing

Neutrino Oscillations

2 5 2

21

2 3 2

32 2

12 2

23 2

(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

−

−

Δ = ± ⋅

Δ = ± ⋅

= ±

>

<

THE STANDARD THEORY OF

FUNDAMENTAL INTERACTIONS ^{SU 3} ( ) _C ^{⊗ SU 2} ( ) _L ^{⊗ U 1} ( ) _Y

Electroweak + Strong Forces

z Gauge Symmetry Dynamics z 3 Gauge Parameters:

z All Known Experimental Facts Explained z Problem with Mass Scales / Mixings:

( )

^Z2

^{, ,}

^W

s M

α α θ

- 15 Additional Parameters - Why 3 Families ?

- Why Left ≠ Right ? - Why ? - Does the Higgs Exist ? - Flavour Mixing

- CP Violation

- Neutrino Masses / Oscillations t Z

m > M

e

μ

τ