antonio pich , ific , valenciabenasque.org/benasque/2005wintermeeting/2005winter... · cp violation...

CP Violation A. Pich – Benasque 2005

Antonio Pich , IFIC , Valencia


Slight (~ 0.2 %) CP in K0 decays (1964)

Sizeable CP in B0 decays (2001)

CP : Symmetry of nearly all observed phenomena

C , P : Violated maximally in weak interactions

Huge Matter ─ Antimatter Asymmetryin our Universe Baryogenesis

Complex Phases

Interferences

Thus, CP requires:

CPT Theorem: T CP


BosonsQuarks Leptons

muon

top beauty

photon

gluon

up down electron neutrino e

charm strange neutrino µ

Higgstau neutrino τ

e

µ

τ

ZZ00 WW ±±


FERMION GENERATIONSFERMION GENERATIONSMassesMasses are are thethe onlyonly differencedifferenceGN 3= IdenticalIdentical CopiesCopies

0

1

Q

Q

=

= −

2 3

1 3

Q

Q

= +

= −j j

j j

v ul d′ ′⎛ ⎞

⎜ ⎟′ ′⎝ ⎠( )G1, , Nj = WHY ?WHY ?

( ) ( )( ) (0)† ( )

(0) ( )† (0)( ) ( ) ( ), , h.c.Y j j j jk R k R k RL L

jk

d u ljk jk jku d d u v l lc c c

φ φ φφ φ φ

+ +

+

⎧ ⎫⎡ ⎤⎪ ⎪′ ′ ′ ′⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟ ⎜ ⎟−⎝ ⎠ ⎝

′ ′ ′= + + +⎨ ⎬⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭⎠ ⎝ ⎠

∑L

{ }1v

h.c.Y L R L R L Rud ld d u u l lH ′ ′ ′ ′⎛ ⎞ ′ ′ ′ ′ ′= − ⋅ ⋅ + ⋅ ⋅ + ⋅+⎜ ⎟ ⋅ +⎝ ⎠

M M ML

SSBSSB

ArbitraryArbitrary NonNon--Diagonal Diagonal ComplexComplex MassMass MatricesMatrices( ) ( ) ( ) v, ,

2, ,d u l

ud l jk jk jkjk c c c⎡ ⎤′ ′ ′ = −⎡ ⎤⎣ ⎦ ⎣ ⎦M M M


DIAGONALIZATION OF MASS MATRICESDIAGONALIZATION OF MASS MATRICES

µ

†

†

†

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

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

( ) { }d d + u1 u +vY ud l lH l= − ⋅ ⋅ ⋅+ ⋅ ⋅ ⋅L M M M

diag ( , , ;) diag ( , , ) diag ( , , );u du c t s ed b lm m m m m m m m mµ τ= = =M M M

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

MassMass EigenstatesEigenstates

WeakWeak EigenstatesEigenstates≠

N C N C′ =L Lf f f f ; f f f fL L L L R R R R′ ′ ′ ′= =†u d u d ;L L L L u d′ ′ = ⋅ ⋅ ≡ ⋅S SV V CC CC′ ≠L L

QUARK MIXINGQUARK MIXING


[ ]f f 5Nf

C f f2 sin cos

v aW W

Z Zeµ

µγθ θ

γ−= ∑L

FlavourFlavour ConservingConserving Neutral Neutral CurrentsCurrents

u c t

d s b

FlavourFlavour ChangingChanging ChargedCharged CurrentsCurrents

( ) ( )i5 5CC†

iji j

j1 1 h.c.

2 2 ll

g u d vW lµµ µγ γ γ γ

⎡ ⎤= − + − +⎢ ⎥

⎣ ⎦∑ ∑VL


MeasurementsMeasurements ofof VVijij

W

jdiu

e−

eν

ijV

j i

2

ij( )ed u e ν−Γ → ∝ V

We measure decays of hadrons (no free quarks)

Important QCD Uncertainties


i jV0.9740 0.00050.9729 0.0012

0.2220 0.00250.2208 0.00340.2219 0.0

0.9739

025

Nuclear decay

decays/ , Latti

0.0005

0.2217 0.00250.224 0.012

0.

ce

974 0.00.97 0.1

h1

ad13

ud

us

cd

cs

e

e

n p e v

K e v

K

v d c X

W c s

V

V

VW

V

β

πτ

π µν

−

−

+

+

±

±

±

±

→

→

→

→

→

±

±

±→

±±

±

0.160.1

*

2

,

0.0414 0.00210.0410 0.0015

0.0033 0.00060.00

0.0411 0.0015

0.0037 0.00050.97

,

47 0.00 9

,

/

0

u j cd c

cb

l

l

l

ub

b

l

V V

B D l vb c l v

B l vb u l v

t bW

V

V

qW

ρ

+−

±±

±±±

→

→→

→

±→

( ) (LEP)∑2 2

uj cjj

V + V = 1.999 ± 0.025

CKM entry Value Source

2

q t qtb VV ∑

2 2 2ud us ubV + V + V = 0.9976 ± 0.0021


i jV0.9740 0.0005

0.2220 0.0

Nuclear decay

decays/

0.2, Lattice

217 0.00250.224 0.012

0.974 0.

0250.2208 0.00340.2219 0.0025

0.9013

0.1ha

7d

1

ud

us

cd

cs

e

e

V

V

V

V

n p e v

K e v

K

v d c X

W c sW

β

πτ

π µν

−

−

+

+

±

±

→

→

→±

→

→±

±±

→

±

±

0.9744 ± 0.00.9769 ± 0. 13

0000

5

0.160.1

*

2

,

0.0414 0.00210.0410 0.0015

0.0033 0.00060.00

0.0411 0.0015

0.0037 0.00050.97

,

47 0.00 9

,

/

0

u j cd c

cb

l

l

l

ub

b

l

V V

B D l vb c l v

B l vb u l v

t bW

V

V

qW

ρ

+−

±±

±±±

→

→→

→

±→

( ) (LEP)∑2 2

uj cjj

V + V = 1.999 ± 0.025

CKM entry Value Source

2

q t qtb VV ∑

Serebrov et al

2 2 2ud us ubV + V + V = 0.9986 ± 0.0021


QUARK MIXING MATRIXQUARK MIXING MATRIX2GNUnitaryUnitary MatrixMatrix::G GN N× parametersparameters

† †⋅ = ⋅ =V V V V 1

arbitraryarbitrary phasesphases::G2 1N −

jii i j j;e eiiu u d dθφ→ → j i )

ij j(

iei θ φ−→V V

ijV

( )G G1 12

N N −

PhysicalPhysical ParametersParameters::

ModuliModuli ;; phasesphasesG G1 ( 1) ( 2)2

N N− −


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

No CPC C

C C

cos sinsin cos

θ θθ θ

⎡ ⎤= ⎢ ⎥−⎣ ⎦

V

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

e

e e

i

i

AA

A A

δ

δ δ

δ δ

λ λ λ ρλ λ λ

λ ρ λ

η

ηλ

−⎡ ⎤⎢

⎡ ⎤− −⎢ ⎥− −⎢ ⎥⎢ ⎥− − −

⎥⎢ ⎥− − −⎢ ⎥

− − −⎢ ⎥⎣ ⎦

⎣ ⎦

≈ +

=V

O

13 0)0 (ηδ ≠≠ CP2 2Csin 0.222 ; 0.84 ; 0.41Aλ θ ρ η≈ ≈ ≈ + ≈


Standard Standard ModelModel : : 33 fermionfermion familiesfamilies neededneededCP

2 2 2 2 2 22( ( ) () ) ( )t c c u t uu m m m m m mM − − −≡H

2 2 2 2 2 22( ( ) )) ( ) (s sb d b dd m m m m m mM − − −≡H

CP 2 2( ) ( ) 0u dM M⋅ ⋅ ≠H H J

212 13 23 12 13 23 13

2 6 410sinc c c s s As λ ηδ −<= =J

•• LowLow--EnergyEnergy PhenomenaPhenomena

•• SmallSmall EffectsEffects ~ ~ JJ

•• BigBig AsymmetriesAsymmetries SuppressedSuppressed DecaysDecays

•• B B DecaysDecays are are anan optimaloptimal place place forfor signalssignalsCP


DIRECT DIRECT CP ( ) ( )P f P f| | | |→ ≠ →T T

( ) 1 1 221 2P f T Ti ii ie ee eδ δφ φ

→ = +T

( ) { }1 21 2*P 1 2fP f T Ti ii iee eeφ δφδη η − −

→ = +T

CP

0dB

( ) ( )( ) ( )

2 12 1

2 11 2

1 22 2

1 2 1 2

si sP f P f 2 T TT T 2 T TP f P f

in( )cos(

n( )cos( ))

δφ φφ φ

δδ δ

Γ → − Γ → −=

+ +Γ → + Γ → −−

−−

OneOne needsneeds::

2 Interfering Amplitudes

2 Different Weak Phases

2 Different FSI Phases 2 1sin( ) 0δ δ⎡ ⎤− ≠⎣ ⎦

2 1sin( ) 0φ φ⎡ ⎤− ≠⎣ ⎦


INDIRECT INDIRECT : : KK00 ── KK00 MIXINGMIXING¯̄CP0 0

2( , )i

i j ijij

j SS r rK K Oηλ λ ∆ =

⎧ ⎫⎨ ⎬⎩ ⎭∑H ∼

2 2* ( , ); ,i i si i Wd ir m i uV V cM tλ =≡≡

( )( )2/9 0 0 2 22

4( ) ˆ3L L L L K KS Ks BK s d s d K MO fα

αα µ γ γ−∆ =

⎛ ⎞= ≡ ⎜ ⎟⎝ ⎠

0 0 0LK Kp Kq+∼ ( ) ( )1 1K Kq p ε ε≡ − +

0 0( ) ( );l ls u s uK l K lπ ν π ν− + + −→ →→ →

( ) ( )( ) ( )

( )0 0

0 0

2

2 2 2

2 2 Re1 |

| | | || |

(0.327 0| |

. )%|

012K

K

L Ll l

L Ll l

p qK l K l

K l K ql pπ ν π ν

π ν π ενε− + + −

− + + −

Γ → − Γ →=

−= = ±

Γ → + Γ → ++

ReRe ((εεKK) = (1.64 ) = (1.64 ±± 0.06) 0.06) ·· 1010--33¯


( )( ) K

L

S

T KT K

ππ

επηπ

+ −

+− + −→

≡ ≈→

0 0

00 0 0( )( )

L

SK

T KT K

π πηπ π

ε→≡ ≈

→

3(2.271 0.017) 10 iK e εφε −= ± ⋅

(43.5 0.5)εφ = ±( ) 2 20.22 .1 0 43ˆ 1KBA Aη ρ⎡ ⎤+ =⎣ ⎦−

Buras et al

DIRECT in K DIRECT in K →→ ππ ππCP

Kε ′+ 2 Kε ′−

( ) 00 42

1Re / 1 (17.2 1.8) 106K K

ηε εη+−

−⎧ ⎫⎪ ⎪′ ≈ − = ± ⋅⎨ ⎬⎪ ⎪⎩ ⎭

NA48, NA31

KTeV, E731

Short-distance OPECiuchini et al, Buras et al

Long-distance χPTPallante-Pich-ScimemiCirigliano-Ecker-Neufeld-Pich

( ) ( )11 49ThRe / 19 10K Kε ε + −

−′ = ⋅


BB00 ── BB00 MIXINGMIXING¯̄3

ud ub cd cb td tbV V V V V V Aλ∗ ∗ ∗∼ ∼ ∼

20 220 4( , )H ˆ3 Bt B BttdB B V S fr r M B⎛ ⎞

⎜ ⎟⎝ ⎠

∼

01(0.502 0.006) ps

dBM −∆ = ± tdV

0114.5 ps (95% C.L.)

sBM −∆ >22

ts tdV V

0 02 2/ / 1tbB BM m m∆Γ ∆ ∼

2 2/1 c tmq p m− ∼

0 0/ 0.770 0.011d dB BM∆ Γ = ±

( )0Re 0.0007 0.0017dBε = − ±

CP very small

010.19(0.47 0.01) ps0 C4 F.2 D

sB−+∆Γ = ±−


BB00 ── BB00 MIXING AND DIRECT MIXING AND DIRECT ¯̄ CP0 0

f f f f f0 0

f f f f f

T T[ f ] ; T T[ f ] ; T / T

T T[ f ] ; T T[ f ] ; T / T

B B

B B

ρ

ρ

→ → → − → ≡

→ → → − → ≡

0B

0B

f

0 0 ; f fB B= − =CP CP

( ) ( )

( ) ( )

0 2 2 2f f f f

0 2 2 2f f f f

cos( ) sin( )

cos( ) sin( )

1[ ( ) f ] | T | 1 | | 1 | | 2 Im2

1[ ( ) f ] | T | 1 | | 1 | | 2 Im2

t

t

M t MqB t ep

pB t eq

t

M t M t

ρ ρ ρ

ρ ρ ρ

−Γ

−Γ

⎧ ⎫⎛ ⎞Γ → + + − −⎨ ⎬⎜ ⎟

⎝ ⎠⎩ ⎭

⎧ ⎫⎛ ⎞Γ

∆ ∆

∆ ∆→ + + − −⎨ ⎬⎜ ⎟⎝ ⎠⎩ ⎭

∼

∼

2f2 ff f

2 2 2 2f

f f ff f f

f

2 Im 2 Im1 | |1 | | ; ; ;

1 | | 1 | | 1 | | 1 | |C S C

q pp S q

ρ ρρρ

ρ ρ ρ ρ

⎛ ⎞ ⎛ ⎞−⎜ ⎟ ⎜ ⎟−− ⎝ ⎠ ⎝ ⎠≡ ≡ ≡ − ≡

+ + + +

( )( )

0

0

*2

* 0; M

d

s

Mtqtb

tqtb

i B

B

qp

e φ βφ− ≈≈ =

⎧⎨⎩

V VV V

M∆Γ ∆


BB00 ── BB00 MIXING AND DIRECT MIXING AND DIRECT ¯̄ CPCP self-conjugate: ff fη=0B

0B

f

( )( )

0

0

*2

* 0; M

d

s

Mtqtb

tqtb

i B

B

qp

e φ βφ− ≈≈ =

⎧⎨⎩

V VV V

Assumption: Only 1 decay amplitude

*

*2A

ADqqb qqq qb

qqqb

i

b qqq

e φ′→ ′

′→ ′

−= =V VV V

( ) ( )( ) ( )

0 0

f0 0 sin(f f

sin(f

2 ) ;f

) M D

B BM t

B Bφ φ φ φη

Γ → − Γ →= ∆

→=

+ Γ+

Γ →

DirectDirect informationinformation onon thethe CKM CKM matrixmatrix


0dB π π+ −→0 0/ SdB J K→ Ψ 0 0 0

SsB Kρ→

2cscbV V Aλ∗ ∼

2tstbV V Aλ∗ −∼

( )3ub udV V A iλ ρ η∗ −∼

( )3 1tb tdV V A iλ ρ η∗ − +∼

( )3ub udV V A iλ ρ η∗ −∼

( )3 1tb tdV V A iλ ρ η∗ − +∼

φ β φ β γ π α+ = − φ γ≠

*** ***** ** BADBAD


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 →

BABAR

SignalCP

sin(2β) = 0.726 ± 0.037,/ , (2 ) , ,c cS L S S SJ K S K K Kψ ψ χ η

[BABAR, BELLE, ALEPH, CDF, OPAL]


UNITARITYUNITARITYTRIANGLES TRIANGLES

* * * ( )0ui uj ci cj ti tj i jV V V V V V ≠+ + =

( )2 3

2 2

3 2

41 /2 ( )

1 /2(1 ) 1

AA

A

i

i A

η

η

λ λ λ ρλ λ λ

λ ρ λλ

⎡ ⎤− −⎢ ⎥− −⎢ ⎥⎢ ⎥− − −⎣ ⎦

≈ +V O


* * * 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

0.347 0.025

0

112112

.196 0.045

η

ρ

η λ

ρ λ

= ±

=

⎛ ⎞≡ −⎜

±

⎟⎝ ⎠⎛ ⎞≡ −⎜ ⎟⎝ ⎠

96.1 7.0 ; 23.4 1.5 ; 60.3 6.8α β γ= ± ° = ± ° = ± °

UTUTfitfit


{ }f f0 cos( ) sin) 1 ([ ( f ] )MC t M tSB t ∆→ + ∆Γ −∼

Cππ Sππ

BABAR - 0.09 ± 0.15 ± 0.04 - 0.30 ± 0.17 ± 0.03

BELLE - 0.56 ± 0.12 ± 0.06 - 0.67 ± 0.16 ± 0.06

0dB π π+ −→

0dB

φ β γ π α+ = − ??

Direct , Penguins2

f2f

f

1 | |1 | |

0C ρρ

−≡ ≠

+ CP

IsospinIsospin RelationsRelations (Gronau – London)

01

2( )T B π π+ −→

0 0 0( )T B π π→

0 0( ) ( )TT B Bπ ππ π+ −+ −= →→

01

2( )T B π π+ −→

0 0 0( )T B π π→

• Significant penguin pollution

P / T = 0.3 ± 0.1 (Buras et al)

• FSI phases (ambiguities)

• EW penguins

• B → π ρ , ρρ , a1 π


MEASURING HADRONIC CONTAMINATIONSMEASURING HADRONIC CONTAMINATIONS

Time Evolution

Transversity Analysis: B → V V

Isospin Relations (Gronau-London)

Mixing (Gronau-Wyler, Atwood-Dunietz-Soni)

Dalitz Analysis

SU(3) Relations: B → πK , π π , ...

…

0 0D -D0 0 0

0 0 0 0

2 T( ) T( ) T( )

2 T( ) T( ) T( )S S Sd

B D K B D K B D K

B D K B D K B D K

+ + + + + ++

+ ++

→ = → + →

→ = → + →


DIRECT DIRECT CP 5.9 5.9 σ σ signalsignal

0 00

0 0

Br( ) Br( )( )

Br( ) Br(0.113 0.

)019d d

dd d

B K B KA B K

B K B K

π ππ

π π

− + + −±

− + + −

→ − →→

→±≡ =

+ →∓

0BABAR0.133 0.030 0.009

0.1 BE01 0.025 0.00 L E5( )

LdA B Kπ ±→

± ±

± ±=

⎧⎪⎨⎪⎩

∓

•• B B →→ ππππ datadata

•• SU(3) SU(3) symmetrysymmetry

•• NeglectNeglect ““penguinpenguin”” andand““exchangeexchange”” topologiestopologies

0th

0.1410.143 0.08( ) 3dA B Kπ ±

−→ +=∓

Buras et al


K K →→ ππ νν νν̄̄( ) ( )* 2 2, /i s i W L L L LidF V V m s KM dµ µν γ ν π γT ∼

Buchalla – BurasIsidori , Misiak – UrbanFalk et alMarciano - Parsa

( )

( )

11

0 1

4

21

2 2

4

Br (7.7 1.1) 10

Br (2.6 0.

(1.4 )

5) 10L

K

K

A

A

η ρπ ν ν

π ν ν η

+ + −

−

⎡ ⎤+ −⎣→ = ± ⎦×

→ = ± ×

∼

∼

Long-distance contributions are negligible

CP( )0 0LK π ν ν→ ≠T

BNL: BNL: few events!

KTEV:KTEV:

( ) 10Br 10K π ν ν+ + −→ ∼

( )0 7Br 5.9 10 (90% C.L.)LK π ν ν −→ < ×

NewNew ExperimentsExperiments NeededNeeded


SUMMARY SUMMARY remains a major pending question

Related to Flavour Structure

Related to SSB Scalar Sector (Higgs)

Important cosmological implications (Baryogenesis)

Sensitive to New Physics

Highly constrained in the SM: 1 phase only

Many interesting signals within experimental reach

Better control of QCD effects urgently needed

CP

CP


ComplexComplex phasesphases in in YukawaYukawa couplingscouplings onlyonly::

( ) ( )jk j

( ) (0)†

j j L k R k R(0) ( )†j k

k( , ) h.c.Yd uL d d uc cu

φ φφ φ

+

+

⎡ ⎤⎛ ⎞ ⎛ ⎞′ ′ ′ ′= + +⎢ ⎥⎜ ⎟ ⎜ ⎟−⎝ ⎠ ⎝ ⎠⎣ ⎦

∑

(0) v / 2φ⎡ ⎤=⎣ ⎦SSBSSB

{ }( )jL k R j

( )jk jL Rk k h.c.

2v1

vYd uc dL d cu uH ′ ′⎛ ⎞+⎜ ′ ′= − + +⎟

⎝ ⎠

( )jkqc diagonalization

{ }jj

C

jL jR jL jR

†iC ij5 j

i j

h.c.

(1 ) h.c.

1v

2 2

Y udL

L

d d u u

g W d

m

u

mH

µµ γ γ

= − ⎛ ⎞+⎜ + +

= − +

⎟⎝ ⎠

∑ V

TheThe CKM CKM matrixmatrix VVijij isis thethe onlyonly sourcesource ofof CPCP

CP Violation A. Pich – Benasque 2005The Standard Model A. Pich - CERN Summer Lectures 2004


( )i 5 j

i

( )CC

jij

† (1 ) h.c.2 2

ll Wg lL µµ ν γ γ= − +∑ V

SeparateSeparate LeptonLepton NumberNumber ConservationConservation R( )νMinimal SM without

i( )ijj

llν ν≡ V

( ) †5CC (1 ) h.c.

2 2l

ll

lgL W µµ ν γ γ− += ∑IFIF i

m 0ν =

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

IFIF i

iR exist and m 0νν ≠

BUTBUT 11 7Br ( ) 1.2 10 Br ( ) 3.1 10eµ γ τ µ γ− −→ < × → < ×;(90 % CL)

antonio pich , ific , valenciabenasque.org/benasque/2005wintermeeting/2005winter... · cp violation...

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