CKM Matrix and CP Violation in Standard Model

FisicadellePar,celleElementari,AnnoAccademico2014-15http://www.roma1.infn.it/people/rahatlou/particelle/

ShahramRahatlou

Measurementofsin2β.ConstraintsonCKMLecture17

2

+e-e

B0 → J/ψ Ks

CP Violation in Interference between Mixing and Decay

z

Δ zΔ t βγ c≈< >

Brec

Btag( )4sΥ

βγΥ(4S) = 0.55

zΔ-π

0sK +π

+µ-µ

Coherent BB pair

B0

B0

µ�

Κ�

Separate B0 and B0

Any CP Eigenstate

3

Time-Evolution of B Decays to CP Eigenstates

n  Probability of |B0>|B0> → |fCP>|ftag> depends on n  Difference Δt between decay time of the two B mesons

n  Decay amplitudes

n  Oscillation parameter

n  Flavor of tagging neutral B meson: B0 or B0

n  Convenient parameter to describe time evolution n  Takes into account combined effect

of oscillation and decay

CP

CP

0f CP

0f CP

A f | H | B , t

A f | H | B , t

= 〈 〉

= 〈 〉

12 i2

12

Mq ep M

− β= − =

CP CP

CP

CP CP

f ff

f f

AAq q=p A p A

λ = η

4

Time-Dependent Decay Rates to CP Eigenstates

n  Expression and complexity of λ depends on specific final states n  Decay amplitudes A and A can be more or less complicated depending on

number of amplitudes contributing to total amplitude

CP CP

CP

CP CP

f ff

f f

AAq q=p A p A

λ = η

5

Time-Dependent CP Asymmetry in Interference

n  CP Violation occurs if

n  But even with |λ|=1 it is sufficient to have Imλ ≠ 0

| | 1q Ap A

λ = ≠

1qp= 1A

A=No CP Violation

in Mixing No Direct CP Violation

In Standard Model we expect |λ|≅1 in most of B decays

6

Simple Case with |λCP|=1

n  Very simple expression for CP violating asymmetry

n  Amplitude of asymmetry defined by phase difference between mixing parameter q/p and ratio of decay amplitudes

n  Complex phase ΦM depends on specific final state n  Can probe different angles of Unitarity triangle through different B decays

M βΦ =

7

At ϒ(4S): integrated asymmetry is zero à  must do a time-dependent analysis !

This is impossible to do in a conventional symmetric

energy collider producing ϒ(4S)→BB !!

+∞

−∞

Δ =∫ CPfa d t 0

Why do We Need Time Dependence?

sin (�mB�t)

8

CPV In Interference Between Mixing and Decay

0 0Neutral B Decays into CP final state accesible by both & decays

This is CPV when 1 and 1 and the CP parameter of interest is

CPV Asymmetry is defined as :

=

Γ=

≡= CP

CP

CP

CP CP

CP

ff f

f

CP

f

f

CPf

f B B

q Ap

q ApA A

a

λ η

( ) ( )( ) ( ) ( )

( )( )

( )

20 0

20 0 2

1( ) ( ) - cos

( ) (

When B decay is dominated by a single

2sin

diagram, 1 sin

11)

= ⇒

−→ −Γ →= Δ

Γ → +Δ

+

=

Γ → +

Δ

CPCP

C

CP CP CP

PP C

fphys CP phys CPB

phy

f

s CP ph

f f f

ys f

BC

B

fP

mB t

tf B t f

m t

a m

B t f B t f

tλ λ

λ λ

λλ

Im

Im

+ 2

+ 2

≠ B0

B0

B0 fcp

B0 fcp

B0

B0 fcp fcp

CP asymm. can be very large and can be cleanly related to CKM angles

0Bϕfi

CPA eCPf

0Bϕ−

=12

2 Mi

Mie

ϕ− fiCPA e

9

Golden Decay Mode B0 àJ/ψK0

10 55

Golden Decay Mode J/ψ K0

37

*c

*ub u

b cs

-2

s*

cb cs

(V V )

Aexpect -1

V V 1Since

V V 50

=10 A

⇒; T is the dominant amplitude

Hence "Platinum" mode !

Penguin:: u,c,t loops

* * *P tb ts cb cs ubt usc u A =V V +V V VP V + PP

Tree

*T cb cs ccsA V V T =

* * *tb ts cb cs ub us

T P c*

cb cs

*cb

*ub u

cs

cs c t u ts

*ub us

V V

Use Unitarity relation V V V V V V to rearrange terms

A A (T P P ) (P P )

= (V V )

V V

+(V

A

V

+ +

+ = + − + −=

T ) P×

Golden Decay Mode B0 "J/ψK0

11

CPV In Interference Between Mixing and Decay: B0 àJ/ψK0

1λ

β)sin(2)Im(λ

S

S

ψK

ψK

=⇒

=⇒

L SψK ψKλ λ= −

ηCP = -1 (+1) for J/ψ K0

S(L)

( ) [ ]0 /,/ 1 sin2 sin( )tS L CPB J K e mtτψ η β−→ ∝ Δ−Γ

( ) [ ]0 /,/ 1 sin2 sin( )tS L CPB J K e mtτψ η β−→ ∝ Δ+Γ

0Bϕfi

CPA eCPf

0Bϕ−

=12

2 Mi

Mie

ϕ− fiCPA e

Same is true for a variety of B →(cc) s final states

S

S

S

*cb cs*cb cs

*cs cd*cs

*t

* *ψKB tb cbb td td

* *cd

ψK *B ψK tb cb cdtb td tdcd

Vq A V V Vλ = V VV VV V

V VV

=- = -p A V VV V VV V

2ie β−

12

Time-Dependent CP Asymmetry with a Perfect Detector

•  Perfect measurement of time interval t=Δt •  Perfect tagging of B0 and B0 meson flavors • For a B decay mode such as B0→ψKs with | λf|=1

sin 2β

B0 B0

Asy

mm

etry

AC

P

CPV

ACP (�t) = sin 2� sin (�m�t)

13

Charmonium+K0 CP Sample for BABAR (�02)

1 modesfη = −

( )

0 0

0 0 0 0

0

0

0 01

0 0

2

η π

+ −

+ −

+ −

→ →→ →→ →

→ →→ →

l lCP S

CP S

CP

S

CP c S

CP c S

B J/ψK { π π }B J/ψK { π π }B ψ S { or

J/ψπ π }KB χ { J/ψγ}KB { KK }K

(after tagging & vertexing)

988 signal candidates, purity 55%

1506 signal candidates, purity 94%

modes 1f −=η

1 modefη = +0 0CP LB J/ψK→

BABAR 81.3 fb�1

14

Calibration with Flavor eigenstates

sin2β = 0.017 ± 0.022

Control Sample with no expected CP asymmetry

01

( )B D π /ρ /a +∗ − + +→

B0 B0

10 times larger than signal

15

Observation of CP Violation (BaBar 2001)

B0 à J/ψ KS

B0 à ψ(2S) KS B0 à χc KS B0 à ηc KS

sin2β = 0.755 ± 0.074 B0 B0

16

BABAR Result for sin2β (July 2002)

sin2β = 0.755 ± 0.074

ηCP = -1 ηCP = +1

sin2 0 741 0 067 0 033(stat) (syst). . .β = ± ±

17

Updated (ICHEP04) sin2β results from Charmonium Modes

0( ) ( odd) modesScc K CP

−1205 on peak or 227 pairs7730 CP events (tagged signal)

fb M BB

0( ) ( even) modesLcc K CP

= + ± ±−

= = ± ±+

βλλ

2

2

sin2 0 722 0.040 0.0231 | | 0.051 0.033 0.0141 | |

.

CLimit on direct CPV

S

L

cc K cc K+

18

Belle Results on sin2β from Charmonium Modes

386M pairsBB

2

2

sin 2 0 652 0.039 0.0201 | | 0.010 0.026 0.0361 | |

= ± ±−

= = − ± ±+

.

C

βλλ

Belle 2005

BàψKS Sample

New Belle value lower than in �03 but still consistent with BaBar�04 sin2 0 728 0.056 0.023= + ± ±.β

19

CP Violation in B Decays Firmly Established

20

Lessons From sin2β Measurement With B0→J/ψK0

n  In 2001, large CP Violation in B system was observed in this mode by BaBar and Belle. n  First instance of CPV outside the Kaon system.

n  First instance of a CPV effect which was O(1) in contrast with the Kaon system n  Confirms the 1972 conjecture of Kobayashi & Maskawa. n  Excludes models with approximate CP symmetry (small CPV).

n  In 2007 sin2β became a precision measurement (5%) and agrees well with the constraints in the ρ-η plane from measurements of the CKM magnitudes (will be discussed in tomorrow�s lecture)

n  Appears unlikely to find another O(1) source of CPV n  enterprise now moves towards looking for corrections rather than

alternatives to SM/CKM picture

n  Focus now shifts to measurements of time-dependent asymmetries in rare B decays n  dominated by Penguin diagrams in the SM and where New Physics could

contribute to the asymmetries

21

Constraints on Unitarity Triangle from Measurements of CKM Elements and CKM Angles

22

4

3( )

( )3

21 / 22 2

(1 )

1 / 22 1

A i

O

A i

A

ACKM

λ ρ η

λ

λ ρ η

λ λ

λ λ λ

λ

+

⎛ ⎞−⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟− −⎜ ⎟⎝ ⎠

−

− −

−

=Vβ

-i

-i

γ1 11 1 1

1 1

e

e

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

ud us ub

CKM cd cs cb

td ts tb

V V VV V VV V V

⎛ ⎞⎜ ⎟= ⎜ ⎟⎜ ⎟⎝ ⎠

V

23

Determination of CKM Elements from Measurements

UTfit http://www.utfit.org

CKM Fitter http://ckmfitter.in2p3.fr

24

Bd mixing + CPV in K mixing (εK)

~ (1 )Kε η ρ−

25

Add |Vub/ Vcb|

26

+ BS Mixing constraint

27

+ Sin2β

28

+ α constraint

29

+ γ measurement

All measurements consistent, apex of (ρ,η) well defined

30

Unitarity Triangle after All Constraints

Includes constraints from all CKM-related measurements

31

Impact of Angle Measurements on CKM Fit

Measurements of angles dominate the constraint on the UT apex!

32

Status of UT in 2007

All constraints Only angles from B and εK from Kaons