CP Violation Beyond the Standard Model

5th Recontres du VietnamHanoi – August 7, 2004

Yossi Nir (Weizmann Institute of Science)

Thanks to:

• Sandrine Laplace, Zoltan Ligeti

CPV BSM 1/21

Motivation

Why do theorists like CP violation?

1. 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 NP gives new sources of CPV;

In particular, CPV probes the mechanism of supersymmetry

breaking.

4. Baryogenesis implies that there must exist sources of CPV

beyond the KM phase.

∗ θQCD is irrelevant in meson decays

CPV BSM 2/21

Plan of Talk

Plan of Talk

1. CP asymmetries

2. s→ uud: K → ππ (ε and ε′)

3. b→ ccs: B → ψK

4. b→ sss: B → φK, η′K, KKK

5. Supersymmetry

CPV BSM 3/21

CP Asymmetries

P 0 fCP

P 0

A1

A2

M∗12

Γ∗12

A1

A2

CPV BSM 4/21

CP Asymmetries

P 0 fCP

P 0

A1

A2

M∗12

Γ∗12

A1

A2

1

2 1

3

1 Decay |A/A| 6= 1 AA= A1+A2

A1+A2Re ε′ P± → f±

2 Mixing |q/p| 6= 1 qp=

2M∗12−iΓ

∗12

∆M−i∆Γ Re ε P 0, P 0 → `±X

3 Interference Imλ 6= 0 λ =M∗

12

|M12|AA

SψKSP 0, P 0 → fCP

CPV BSM 4/21

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 ≡ Imλf 6= 0

– Superweak 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

CPV BSM 5/21

Results and Implications: s→ uud

K → ππ

K0ππ

K0

Re ε′

Re ε

Im ε

|ε| = (2.284± 0.014)× 10−3(

ε = 1−λ01+λ0

)

Christenson, Cronin, Fitch, Turlay (64)

Re ε′/ε = (1.67± 0.26)× 10−3(

ε′ = 16 (λ00 − λ+−)

)

NA31 (88), KTeV (01), NA48 (02)

CPV BSM 6/21

Results and Implications: s→ uud

Lessons from ε

• CP violation has been observed.

• Old new physics: a third generation is required.

• A useful CKM constraint: the KM phase is large.

• The NP CP/flavor problem.

CPV BSM 7/21

CP/Flavor problems

The NP CP/Flavor Problem

• m2H ∼ (m2

H)tree +1

16π2Λ2NP

To avoid fine-tuning of the Higgs mass,

ΛNP ∼< 4πmW ∼ 1 TeV .

• LNP ∼1

Λ2NPsdsd

To avoid too large contributions to εK and to ∆mK,D,B ,

ΛNP ∼> 103−4 TeV .

New Physics at the TeV scale must have a

very non-generic flavor and CP structure

CPV BSM 8/21

Results and Implications: s→ uud

Lessons from ε′/ε

• Direct CP violation has been observed.

• The result is consistent with the SM predictions.

• Large hadronic uncertainties =⇒ no useful CKM constraint.

• The superweak scenario is excluded.Wolfenstein (64)

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

CPV BSM 9/21

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

CPV BSM 10/21

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))

CPV BSM 11/21

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

-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))

CPV BSM 11/21

Results and Implications: b→ ccs

Lessons from SψK

• CPV in B decays has been observed.

• The Kobayashi-Maskawa mechanism of CPV has successfully

passed its first precision test.

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

ImλψKS= sin 2β = 2η(1−ρ)

η2+(1−ρ)2 = 0.74± 0.05

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

is excluded.

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

is disfavored.

CPV BSM 12/21

Results and Implications: b→ ccs

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

CPV BSM 13/21

Results and Implications: b→ ccs

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.

CPV BSM 13/21

Results and Implications

B0 fCP

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 +0.02± 0.67 +0.09± 0.23

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

K+K−KS b→ sss sin 2β +0.54± 0.18 +0.07± 0.13

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

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

ψπ0 b→ ccd sin 2βeff +0.43± 0.38 +0.13± 0.24

π+π− b→ uud sin 2αeff +0.70± 0.31 −0.42± 0.20

ρ+ρ− b→ uud sin 2αeff +0.42± 0.44 −0.17± 0.30

CPV BSM 14/21

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 − +0.02± 0.29(0.67)† +0.09± 0.23

η′KS − +0.27± 0.21 +0.04± 0.13

K+K−KS +∗ +0.54± 0.18 +0.07± 0.13

†Babar: +0.47 ± 0.34 ± 0.07; Belle: −0.96 ± 0.50 ± 0.10

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

CPV BSM 15/21

CP/Flavor problems

A SM CP/Flavor Problem?

• CP asymmetries in b→ sss: Sη′KS, SφKS

• Polarization in B → φK∗: fσ ≡|Aσ|

2

|A0|2+|A‖|2+|A⊥|2

– Theoretically (HQE),

(f‖ + f⊥)/f0 = O(1/m2B), f⊥/f‖ = 1 +O(1/mB).

– Experimentally, f0(ρ0K∗+) = 0.96± 0.16,

f0(ρ0ρ+) = 0.96± 0.07, f0(ρ

+ρ−) = 0.99± 0.08

but f0(φK∗0) = 0.58± 0.10, f⊥(φK

∗0) = 0.41± 0.11,

f0(φK∗+) = 0.46± 0.12.

• The lipkin sum rule: RL ≡ 2 Γ(B+→K+π0)+Γ(B0→K0π0)Γ(B+→K0π+)+Γ(B0→K+π−)

– Theoretically (isospin),

RL = 1 +O(

PEW+TP

)2= 1 +O(10−2)

– Experimentally, RL = 1.24± 0.10.

CPV BSM 16/21

CP/Flavor problems

A SM CP/Flavor Problem – Not Yet...

• Sη′KS= 0.27± 0.21:

∼ 2σ.

• SφKS= +0.02± 0.67:

Experimental situation needs to be resolved.

• f0(φK∗0) = 0.58± 0.10, f⊥(φK

∗0) = 0.41± 0.11:

Charming penguins (SCET) / Annihilation diagrams (QCDF)

can account for the data.

• RL = 1.24± 0.10:

∼ 2.4σ

More theoretical effort is needed to determine T/P

CPV BSM 17/21

Supersymmetry

Supersymmetry for Phenomenologists

FV CPV

Y + +

µ − +

A + +

mg − +

m2f

+ +

B − +

80 real + 44 imaginary parameters

CPV BSM 18/21

Supersymmetry

CP Violation in Supersymmetry

• K physics: ImMSUSY12

ImMexp12

∼ 106(

1 TeVm

)2(

∆m212

m2

)2

Im[

(Kd12)

2]

– Heavy squarks: m > 1 TeV ;

– Universality: ∆m221 ¿ m2;

– Alignment: |Kd12| ¿ 1;

– (Approximate CP: sinφ¿ 1)

• B physics: SexpψK ' SSMψK

– 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).

CPV BSM 19/21

Supersymmetry

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?

CPV BSM 20/21

Supersymmetry

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?

• Yes: δd23 ↔ δd13

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

CPV BSM 20/21

Supersymmetry

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?

• Yes: δd23 ↔ δd13

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

• Yes: δdRR ↔ δdLR

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

CPV BSM 20/21

Supersymmetry

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?

• Yes: δd23 ↔ δd13

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

• 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

CPV BSM 20/21

Conclusions

Conclusions

• The KM mechanism is, very likely, the dominant source of the

CP violation observed in meson decays

• CPV observed (≥ 3σ from Babar+Belle) in three modes:

SψKS= 0.74± 0.05, SK+K−KS

= −0.54± 0.18,

AK∓π± = −0.114± 0.024 (direct CPV!)

• No evidence for new flavor/CP physics

• ∼ 2σ effect in Sη′KS

• “∼ 2.5σ” effect in SD∗+D∗−

• We left the era of hoping for NP altenratives to KM;

We are in the era of seeking for NP corrections to KM

• The field is experiment-driven

Waiting for new results from Belle/Babar/TeVatron

CPV BSM 21/21

Conclusions

Unitarity Triangles 2004

-1.5

-1

-0.5

0

0.5

1

1.5

-1 -0.5 0 0.5 1 1.5 2

K+ → π+νν

|Vub/Vcb|

εK

εK

α

βγ

ρ

η

excluded area has CL < 0.05

C K Mf i t t e r

-1.5

-1

-0.5

0

0.5

1

1.5

-1 -0.5 0 0.5 1 1.5 2

sin 2β

B → ρρ

B → ρρ

∆md

|Vub/Vcb|

sin 2β

α

βγ

ρ

η

excluded area has CL < 0.05

C K Mf i t t e r

-1.5

-1

-0.5

0

0.5

1

1.5

-1 -0.5 0 0.5 1 1.5 2

sin 2β

∆ms & ∆md

|Vub/Vcb|

sin 2β

α

βγ

ρ

η

excluded area has CL < 0.05

C K Mf i t t e r

s→ d

ε, B(K+ → π+νν)

b→ d

∆mBd , SψK , Sρρ

b→ s

∆mBs , SφK,η′K,KKK

There is still a lot to be learnt from future measurements

Laplace (04)

CPV BSM 22/21

Conclusions

Unitarity Triangles 2002

-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

Laplace (02)

CPV BSM 23/21

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

AfCP(t)=SfCP sin(∆mB t)

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

CPV BSM 24/21