cp violation in meson decays - weizmann institute of science

CP Violation in Meson Decays

Workshop on Heavy Quark Physics at the Upgraded Hera Collider21/10/2003

Yossi Nir (Weizmann Institute of Science)

CP Violation 1/28

Motivation

Why do theorists like CP violation?

1. At last, the study of CPV is experiment-driven.

2. CP is a symmetry of the strong interactions∗

=⇒ Various CP asymmetries can be cleanly interpreted.

3. Almost any model of new physics gives new sources of CPV;

In particular, CPV probes the mechanism of DSB.

4. Baryogenesis implies that there must exist sources of CPV

beyond the KM phase.

∗ θQCD is irrelevant in meson decays

CP Violation 2/28

Plan of Talk

Plan of Talk

1. CP violation in meson decays

(a) In decay: |A/A| 6= 1

(b) In mixing: |q/p| 6= 1

(c) In interference of decays with and without mixing: Imλ 6= 0

2. Results and Basic Implications

(a) s→ uud: K → ππ

(b) c→ ssu: D → KK

(c) b→ ccs: B → ψK

(d) b→ sss: B → φK, η′K, KKK

3. Conclusions

CP Violation 3/28

CP Asymmetries

P 0 fCP

P 0

A1

A2

M∗12

Γ∗12

A1

A2

CP Violation 4/28

CP Asymmetries

P 0 fCP

P 0

A1

A2

M∗12

Γ∗12

A1

A2

1

2 1

3

1. In decay: |A/A| 6= 1[

AA= A1+A2

A1+A2

]

2. In mixing: |q/p| 6= 1

[

(

qp

)2

=2M∗

12−iΓ∗12

2M12−iΓ12

]

3. In interference: Imλ 6= 0[

λ = qpAA

]

CP Violation 4/28

CP asymmetries

CP asymmetry in charged B decay

B+ f+A1

A2

Af∓ ≡Γ(B− → f−)− Γ(B+ → f+)

Γ(B− → f−) + Γ(B+ → f+)=|Af/Af |2 − 1

|Af/Af |2 + 1

• CP violation in decay:∣

∣

∣

∣

AfAf

∣

∣

∣

∣

6= 1

[

AfAf

=A1 + A2

A1 +A2

]

• Requires δ2 − δ1, |A2/A1| =⇒ Hadronic uncertainties

CP Violation 5/28

CP asymmetries

CP asymmetry in semileptonic neutral B decay

B0 B0 `−XM∗

12

Γ∗12

ASL ≡Γ(B0

phys(t)→ `+X)− Γ(B0phys(t)→ `−X)

Γ(B0phys(t)→ `+X) + Γ(B0

phys(t)→ `−X)=

1− |q/p|41 + |q/p|4

• CP violation in mixing:∣

∣

∣

∣

q

p

∣

∣

∣

∣

6= 1

[

q

p= − 2M∗

12 − iΓ∗12∆mB − i

2∆ΓB

]

• Requires Γ12 =⇒ Hadronic uncertainties

CP Violation 6/28

CP asymmetries

AfCP B0fCP

B0

A1

A2M∗

12

Γ∗12

A1

A2

1

2 13

• CP asymmetry in neutral B decay into final CP eigenstates:

AfCP(t) ≡Γ(B0

phys(t)→ fCP)− Γ(B0phys(t)→ fCP)

Γ(B0phys(t)→ fCP) + Γ(B0

phys(t)→ fCP)

= −CfCP cos(∆mB t) + SfCP sin(∆mB t)

CfCP = −AfCP =1− |λfCP |21 + |λfCP |2

, SfCP =2ImλfCP1 + |λfCP |2

.

• CP violation in interference of decays with and without mixing:

Imλ 6= 0[

λ = qpAA

]

CP Violation 7/28

CP asymmetries

The case theorists love

B0 fCP

B0

A

M12

A

SfCP

1. Decay dominated by a single CPV phase: |A/A| = 1

2. CPV in mixing negligible: |q/p| = 1

3. The only remaining effect is

SfCP = ImλfCP = ± sin[arg(M∗12) + arg(AfCP)− arg(AfCP)]

CP Violation 8/28

CP asymmetries

Direct vs. Indirect CPV

• Indirect CPV

– Can be accounted for by a phase in M12 only

– |q/p| 6= 1 and/or a single Sf 6= 0

– Superwak models: only indirect CPV

• Direct CPV

– cannot be accounted for by a phase in M12 only

– |A/A| 6= 1 and/or Sf1 6= Sf2

– SM: possibly large direct CPV

CP Violation 9/28

CKM

In case that you never saw a UT before...

• A geometrical presentation of V ∗ubVud + V ∗

tbVtd + V ∗cdVcb = 0

γ

α

βu

t

c

V =

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

CP Violation 10/28

CKM

In case that you never saw a UT before...

• A geometrical presentation of V ∗ubVud + V ∗

tbVtd + V ∗cdVcb = 0

γ

α

βu

t

c

V =

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

• Rescale and rotate: Aλ3 [(ρ+ iη) + (1− ρ− iη) + (−1)] = 0

(0, 0) (1, 0)

(ρ, η)

γ

α

β

V =

1− λ2

2λ Aλ3(ρ− iη)

−λ 1− λ2

2Aλ2

Aλ3(1− ρ− iη) −Aλ2 1

Wolfenstein (83); Buras et al. (94)

α ≡ φ2; β ≡ φ1; γ ≡ φ3

CP Violation 10/28

Results and Implications: s→ uud

K → ππ

K0ππ

K0

Re ε′

Re ε

Im ε

|ε| = (2.27± 0.01)× 10−3(

ε = 1−λ01+λ0

)

Christenson, Cronin, Fitch, Turlay (64)

Re ε′/ε = (1.66± 0.16)× 10−3(

ε′ = 16 (λ00 − λ+−)

)

NA31 (88), KTeV (01), NA48 (02): (1.47 ± 0.22) × 10−3

CP Violation 11/28

Results and Implications: s→ uud

Lessons from ε′/ε

• Direct CP violation has been observed.

• The superweak scenario is excluded.Wolfenstein (64)

• The result is consistent with the SM predictions.

• Large hadronic uncertainties =⇒ no useful CKM constraint.

• New physics (e.g. Supersymmetry) may contribute significantly.e.g. Masiero and Murayama (99)

CP Violation 12/28

Results and Implications: c→ ssu

D0 K+K−

D0

• Define (yCP → y in the CP limit)

yCP ≡ Γ(D→K+K−)

Γ(D0→π+K−)− 1

• Assume no direct CP violation:

yCP = y cosφ− x(|q/p| − 1) sinφ (φ− π ≡ arg λ)Bergmann et al. (00)

• Experiments (FOCUS, E791, CLEO, BELLE, BABAR):

yCP = (1.0± 0.7)× 10−2

CP Violation 13/28

Results and Implications: c→ dsu

D0 K+π−

D0

• K+π− 6= CP e.s. =⇒ analysis complicated by strong phases:

x′ ≡ x cos δ + y sin δ, y′ ≡ y cos δ − x sin δ• Assume no direct CP violation:

Γ(D0(t)→ K+π−) ∝ R+√R|q/p|(y′cφ − x′sφ)Γt+ |q/p|2(y2 + x2)(Γt)2/4

Γ(D0(t)→ K−π+) ∝ R+√R|p/q|(y′cφ + x′sφ)Γt+ |p/q|2(y2 + x2)(Γt)2/4

• Experiment (CLEO):

R = (4.8± 1.3)× 10−3, y′ = −0.025+0.014−0.016, x′ = 0.000± 0.015

|q/p|2 − 1 = 0.23+0.63−0.80, sinφ = 0.0± 0.6

CP Violation 14/28

D0 −D0 mixing

Lessons from D → KK,Kπ

• No signal of mixing yet:

CPV (NP) CPC (SM)

y = ∆Γ2Γ < 0.046 < 0.022

x = ∆mΓ < 0.063 < 0.050

• y = O(0.01) is possible within the SM (phase space effects).Falk, Grossman, Ligeti, Petrov (02)

• CP violation is important in two ways:

1. CPV would be the only unambiguous signal of NP.

2. CPV has to be taken into account when constraining NP:

φ 6= 0, δ 6= 0 (NP) φ = 0, δ = 0 (PDG)|M12|

10−11 MeV< 5.4 < 2.3

Raz (02)

CP Violation 15/28

Results and Implications: b→ ccs

B0 ψKS

B0

Carter and Sanda (80)

Bigi and Sanda (81)

• Within SM, dominated by a single phase =⇒ CψKS = 0

(Subleading phase CKM- and loop-suppressed)

• Within SM, M∗12 ∝ (V ∗

tbVtd)2, A ∝ V ∗

cbVcd =⇒ SψKS = sin 2β

• With NP, still SψKS ' sin[arg(M∗12)− 2 arg(V ∗

cbVcd)] and

CψKS ' 0, but SψKS 6= sin 2β is possible.

• BABAR and BELLE measure

mode CP SψKS CψKS

ψKS − +0.74± 0.05 0.02± 0.04

CP Violation 16/28

Results and Implications

Unitarity Triangles

-1

0

1

-1 0 1 2

∆md

∆ms & ∆md

|Vub/Vcb|

ρ

η

CK Mf i t t e r

p a c k a g e

Tree level + CPC observables

∆mB , ∆mBs

Using CKMFitter package (Hocker et al., Eur. Phys. J. C21, 225 (01))

CP Violation 17/28


Unitarity Triangles

-1

0

1

-1 0 1 2

∆md

∆ms & ∆md

|Vub/Vcb|

ρ

η

CK Mf i t t e r

p a c k a g e

Tree level + CPC observables

∆mB , ∆mBs

-1

0

1

-1 0 1 2

sin 2βWA

εK

εK

|Vub/Vcb|

ρη

CK Mf i t t e r

p a c k a g e

Tree level + CPV observables

ε, SψKS

Using CKMFitter package (Hocker et al., Eur. Phys. J. C21, 225 (01))

CP Violation 17/28


Unitarity Triangles

-1

0

1

-1 0 1 2

∆md

∆ms & ∆md

εK

εK

|Vub/Vcb|

ρ

η

CK Mf i t t e r

p a c k a g e

Without SψK

∆mB , ∆mBs , ε

CP Violation 18/28


Unitarity Triangles

-1

0

1

-1 0 1 2

sin 2βWA

∆md

∆ms & ∆md

εK

εK

|Vub/Vcb|

ρ

η

CK Mf i t t e r

p a c k a g e

Without SψK

∆mB , ∆mBs , ε

CP Violation 18/28


Unitarity Triangles

-1

0

1

-1 0 1 2

sin 2βWA

∆md

∆ms & ∆md

εK

εK

|Vub/Vcb|

ρ

η

CK Mf i t t e r

p a c k a g e

Without SψK

∆mB , ∆mBs , ε

-1

0

1

-1 0 1 2

sin 2βWA

∆md

∆ms & ∆md

εK

εK

|Vub/Vcb|

ρη

CK Mf i t t e r

p a c k a g e

With SψK

∆mB , ∆mBs , ε, SψKS

CP Violation 18/28


Lessons from ACP(B → ψKS)

• CPV in B decays has been observed.

• The Kobayashi-Maskawa mechanism of CPV has successfully

passed its first precision test.

• Approximate CP (in the sense that all CPV phases are small)

is excluded.

• A significant constraint on the CKM parameters (ρ, η):

ImλψKS = sin 2β = 2η(1−ρ)η2+(1−ρ)2 = 0.736± 0.048

• New, CPV physics that contributes > 20% to B0 −B0 mixing

is disfavored.

CP Violation 19/28


The KM mechanism

• The KM mechanism successfully passed its first precision test

Very likely, the KM mechanism is the dominant

source of CP violation in flavor changing processes

CP Violation 20/28


The KM mechanism

• The KM mechanism successfully passed its first precision test

Very likely, the KM mechanism is the dominant

source of CP violation in flavor changing processes

• ‘Very likely’: The consistency could be accidental

=⇒ More measurements of CPV are crucial.

• ‘Dominant’: There is still room for NP at the O(20%) level

=⇒ A challenge for theorists.

• ‘FC processes’: FD CPV can still be dominated by NP

=⇒ Search for EDMs.

CP Violation 20/28

Results and Implications: b→ sss

B0 φKS , η′KS ,KKK

B0

C

S

• Within SM, dominated by a single phase =⇒ C ≈ 0

(Subleading phase CKM-suppressed)

• Within SM, A ∝ V ∗cbVcd =⇒ S ≈ SψKS (≈ +0.74)

• With NP, S 6= SψKS , Sf1 6= Sf2 and C 6= 0 are possible.

mode CP −ηCPS C

φKS − −0.14± 0.33(0.69)† −0.04± 0.26

η′KS − +0.27± 0.21 +0.04± 0.13

K+K−KS +∗ +0.51± 0.26+0.18−0.00 +0.17± 0.16

†Babar: +0.45 ± 0.43 ± 0.07; Belle: −0.96 ± 0.50 ± 0.10

∗Isospin analysis is used to argue CP = + dominance.

CP Violation 21/28


Supersymmetry for Phenomenologists

FV CPV

Y + +

µ − +

A + +

mg − +

m2f

+ +

B − +

80 real + 44 imaginary parameters

CP Violation 22/28


CP Violation in Supersymmetry

• K physics: ImMSUSY12

ImMexp12

∼ 108(

100 GeVm

)2(

∆m212

m2

)4

Im[

(Kd12)

2]

– Heavy squarks: mÀ 100 GeV ;

– Universality: ∆m221 ¿ m2;

– Alignment: |Kd12| ¿ 1;

– (Approximate CP: sinφ¿ 1)

• B physics: SexpψKS' SSMψKS

– consistent with exact universality,

– constrains U(2) and U(1) models, disfavors heavy squarks.

• D physics: x, y ∼< 0.05

– probes alignment.

• EDMs:dSUSYN

6.3×10−26 e cm∼ 300

(

100 GeVm

)2sinφA,B

– can distinguish MFV (∼< 10−31) from SUSY CPV (∼

> 10−28).

CP Violation 23/28


SUSY contributions to B → φKS

b sbR sR

s

s

sR(δd23)RR

• Could there be large effects in B → φKS and not in B → ψKS?

CP Violation 24/28



b sbR sR

s

s

sR(δd23)RR


• Yes: δd23 ↔ δd13

• Could there be large effects in B → φKS and not in B → Xsγ?

CP Violation 24/28



b sbR sR

s

s

sR(δd23)RR


• Yes: δd23 ↔ δd13


• Yes: δdRR ↔ δdLR

• Are there well-motivated models with (δd23)RR = O(1)?

CP Violation 24/28



b sbR sR

s

s

sR(δd23)RR


• Yes: δd23 ↔ δd13


• Yes: δdRR ↔ δdLR

• Are there well-motivated models with (δd23)RR = O(1)?

• U(1) flavor symmetry: (δd23)RR ∼ (ms/mb)/|Vcb|• SO(10) GUTs: (δd23)RR ∼ θ`23

CP Violation 24/28


B0 φKS , η′KS ,KKK, πK,DD,ψπ, ππ

B0

C

S

fCP b→ qqq′ SM −ηCPS = ± 2Imλ1+|λ|2

C = 1−|λ|2

1+|λ|2

ψKS b→ ccs sin 2β +0.74± 0.05 +0.02± 0.04

φKS b→ sss sin 2β −0.14± 0.69 −0.04± 0.26

η′KS b→ sss sin 2β +0.27± 0.21 +0.04± 0.13

K+K−KS b→ sss sin 2β +0.51± 0.26 +0.17± 0.16

π0KS b→ uus sin 2β +0.48± 0.40 +0.40± 0.30

D∗+D∗− b→ ccd sin 2βeff −0.05± 0.31 +0.25± 0.19

ψπ b→ ccd sin 2βeff +0.43± 0.38 +0.13± 0.24

ππ b→ uud sin 2αeff +0.58± 0.50 −0.38± 0.16

CP Violation 25/28


Lessons from ACP(B → fCP)

• CPV has not yet been observed in B decays other than

B → ψK.

(A 2.4σ effect in Cππ .)

• Direct CPV has not yet been observed in B decays.

(2.5σ effect in SDD ↔ SψK .)

• No evidence of new physics.

(A 2.2σ effect in Sη′K ↔ SψK .) Grossman, Isidori, Worah (98)

• The measurements of BR and CP asymmetries in B → ππ

decays are at a stage where restrictions on the CKM

parameters and on hadronic parameters begin to emerge.

Model independent constraints are still mild.

sin 2αeff ≡Imλππ|λππ|

: sin2(αeff − α) ≤ B00/B+0 ≤ 0.61

Grossman and Quinn (98); Charles (99); Gronau, London, Sinha, Sinha (01)

CP Violation 26/28

Conclusions: CKM

Unitarity Triangles

-1

0

1

-1 0 1 2

K+ → π+νν

εK

εK

|Vub/Vcb|

ρ

η

CK Mf i t t e r

p a c k a g e

-1

0

1

-1 0 1 2

sin 2βJ/ΨKs

∆md

|Vub/Vcb|

ρ

ηCK M

f i t t e rp a c k a g e

-1

0

1

-1 0 1 2

sin 2βΦKs

∆ms & ∆md

|Vub/Vcb|

ρ

η

CK Mf i t t e r

p a c k a g e

s→ d

ε, B(K+ → π+νν)

b→ d

∆mBd , SψKS

b→ s

∆mBs , SφKS

CP Violation 27/28

Conclusions: CKM

Unitarity Triangles

-1

0

1

-1 0 1 2

K+ → π+νν

εK

εK

|Vub/Vcb|

ρ

η

CK Mf i t t e r

p a c k a g e

-1

0

1

-1 0 1 2

sin 2βJ/ΨKs

∆md

|Vub/Vcb|

ρ

ηCK M

f i t t e rp a c k a g e

-1

0

1

-1 0 1 2

sin 2βΦKs

∆ms & ∆md

|Vub/Vcb|

ρ

η

CK Mf i t t e r

p a c k a g e

s→ d

ε, B(K+ → π+νν)

b→ d

∆mBd , SψKS

b→ s

∆mBs , SφKS

There is still a lot to be learnt from future measurements

CP Violation 27/28

Conclusions: New Physics

New Physics

• We are leaving the era of hoping for NP alternatives to CKM.

(Superweak models and approximate CP - excluded.)

• We are entering the era of seeking for NP corrections to CKM.

• It is still possible that the corrections are large in ∆mBs , in CP

asymmetries in Bs decays, and in Imλ(ss)KS .

CP Violation 28/28

Results and Implications: b→ ccd

B0 ψπ,D∗D∗

B0

C

S

• Penguins are not CKM suppressed and carry a different phase:

=⇒ C 6= 0 is possible

• Atree ∝ V ∗cbVcd and Apeng ∝ V ∗

tbVtd

=⇒ S = SψKS +O(Apeng/Atree) .

mode CP −ηCPS C

ψπ + +0.43± 0.38 +0.13± 0.24

D∗+D∗− +∗ −0.05± 0.31 +0.25± 0.19

∗Angular analysis is used to separate CP = + from CP = −.

CP Violation 29/28

Results and Implications: b→ uud

B0 ππ

B0

C

S

• Penguins are not CKM suppressed and carry a different phase

=⇒ Cππ 6= 0 is possible (a test of BBNS ↔ KLS).

• Atree ∝ V ∗ubVud =⇒ Sππ = sin 2α+O(Apeng/Atree) .

• Sππ 6= SψK is expected (Direct CPV).

Expt. S C

BABAR −0.40± 0.22± 0.03 −0.19± 0.19± 0.05

BELLE −1.23± 0.41+0.08−0.07 −0.77± 0.27± 0.08

WA −0.58± 0.20(0.50) −0.38± 0.16

CP Violation 30/28

Results and Implications: b→ uud

α from Cππ and Sππ

-1

0

1

-1 0 1 2

Standard SM fit

ρ

η

CK Mf i t t e r R&D P/T from

BBNS

-1

0

1

-1 0 1 2

Standard SM fit

ρ

η

CK Mf i t t e r R&D P/T from

BBNS

BABAR data BELLE data

Experimental input: Cππ, Sππ

Theoretical input: |P/T | from BBNS

CP Violation 31/28

K physics

K0 π0νν

K0

Littenberg (89)

• CP violation in mixing and in decay are negligible.

• Hadronic uncertainties are negligible.

• A huge experimental challenge.

• The charged (CPC) mode has been measured by E787:

B(K+ → π+νν) = (1.57+1.75−0.82)× 10−10

CP Violation 32/28

K physics

Lessons from B(K+ → π+νν)

• Consistent with the SM:

B(K+ → π+νν)SM = (0.72± 0.21)× 10−10

Buchalla and Buras (99)

• There is still (much!) room for new physics.D’Ambrosio and Isidori (01)

• Provides a model-independent upper bound on the KL-decay:

B(KL → π0νν) < 1.7× 10−9

Grossman and Nir (97)

A more precise measurement would be extremely interesting

both as a CKM constraint and as a probe of new physics

CP Violation 33/28

cp violation in meson decays - weizmann institute of science

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