CKM Matrix and CP Violation in Standard · PDF fileCKM Matrix and CP Violation in Standard...

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CKM Matrix and CP Violation in Standard Model Fisica delle Par,celleElementari, Anno Accademico 2014-15 http://www.roma1.infn.it/people/rahatlou/particelle/ Shahram Rahatlou Measurement of sin2β. Constraints on CKM Lecture 17

Transcript of CKM Matrix and CP Violation in Standard · PDF fileCKM Matrix and CP Violation in Standard...

Page 1: CKM Matrix and CP Violation in Standard  · PDF fileCKM Matrix and CP Violation in Standard Model Fisica delle Par,celleElementari, Anno Accademico 2014-15

CKM Matrix and CP Violation in Standard Model

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

ShahramRahatlou

Measurementofsin2β.ConstraintsonCKMLecture17

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+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

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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

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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

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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

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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 =

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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)

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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

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Golden Decay Mode B0 àJ/ψK0

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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

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

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−

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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)

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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

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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

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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

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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 = ± ±

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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+

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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

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CP Violation in B Decays Firmly Established

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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

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

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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

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Determination of CKM Elements from Measurements

UTfit http://www.utfit.org

CKM Fitter http://ckmfitter.in2p3.fr

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Bd mixing + CPV in K mixing (εK)

~ (1 )Kε η ρ−

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Add |Vub/ Vcb|

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+ BS Mixing constraint

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+ Sin2β

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+ α constraint

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+ γ measurement

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

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Unitarity Triangle after All Constraints

Includes constraints from all CKM-related measurements

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Impact of Angle Measurements on CKM Fit

Measurements of angles dominate the constraint on the UT apex!

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Status of UT in 2007

All constraints Only angles from B and εK from Kaons