A window for New Physics in Bs→KK decays

Joaquim Matias

Universitat Autònoma de Barcelona

David London & JM, PRD (2004)

David London &JM & Javier Virto, PRD (2005)

February 2005

Search for New Physics

Precision Flavour Physics Era

B Physics

[Experiment+Theory]

How do we prove for NP in CP violation ?

Overdetermining the Unitarity Triangle:

• Determination of sides:

CKM fit:

Compare with the determination of angles from CP-asymmetries and <BR>.

Two strategies a) consistency check b) measure NP

CP violation in non-leptonic B decays

Several channels:

Fundamental role in determining and but also New Physics

-Main problem: How to deal with Hadronic Matrix Elements

Construct clean observable with small QCD Polution.

Evaluation of hadronic parameters from QCD. Flavour Symmetries to extract maximal information from data.

-Main hypothesis based on experimental data:

*There are NO sizeable New Physics effects in b→d penguin amplitudes.

*If there is Physics beyond the SM will affect b→s penguin amplitudes.

Anatomy of Bs→K+K- decay

STANDARD MODEL DESCRIPTION

• It is governed by the quark-level process

T’: Tree colour allowed, P’ gluonic penguins, P’CEW colour suppressed EW penguins, E’ exchange and PA’ Penguin Annihilation topologies.

• Two types of contributions: charged-current: Vub*Vus A’uCC

penguin Vub*Vus(P’u-P’t)+Vcb*Vcs(P’c-P’t)

The SM amplitude can be written:

Hadronic parameters:

Remarks: - θC’ is irrelevant in the Standard Model but not in presence of New Physics. - All factorizable corrections to d’ drop out. Weak parameters: CKM angle

BEYOND STANDARD MODEL DESCRIPTION

In presence of New Physics in the b→s penguin:

• NP operators assumed same size as SM b→s penguin.

• There are many (q=u,d,s,c)

• All New Physics strong phases are negligible

- Aq and Φq are process dependent.

The amplitude is now:

There are 3 measurements in Bs→K+K- decay:

* From the time-dependent CP asymmetry (Adir and Amix):

• In the SM these CP asymmetries are:

AdirSM(Bs→K+K-)=f(d’,θ’,) and Amix

SM(Bs→K+K-)=g(d’, θ’, Φs)

* CP Averaged Branching Ratio in the SM:

• In presence of New Physics the SM CP asymmetries and CP-averaged branching ratio are modified:

Total number of parameters:

BNP, DNP and MNP are complicated functions of ALL these parameters.

Parameter determination:

• Weak parameters measured independently:

CKM angle : B→DK unaffected by New Physics α from B→, B→ρ, B→ρρ β from Amix(Bd(t)→J/ψKs)

CKM fit. Weak mixing phase Φs from CP violating Bs→J/ψΦ:

NP contributions to the mixing Φs= ΦsSM+δΦs

contribution controlled by Bd(t)→J/ψKs <20%

• Hadronic Parameters:

Keypoint: U-spin (interchange d↔s) related process Bd→+-

quark level transition available to B Factories.

no New Physics contribution.

Amplitude in SM

Wolfenstein parametrization in SM:

Same functional dependence

U-spin

Can we determine d, and C? Present Experimental Situation:

• Babar and Belle are inconsistent • If we average naïvely the asymmetries:

• A large direct CP asymmetry from Belle (large strong phases) would be troublesome for QCD-NLO factorization.

• Three measurements: Adir(Bd→ ), Amix(Bd→ ) and BR(Bd→)

Total parameters in SM: - 3 hadronic parameters - 2 weak parameters:

But d from Amix(Bd→J/Ks) and from QCD sum rules

From Adir(Bd→ ), Amix(Bd→ ), BR(Bd→), Amix(Bd→J/Ks) and CKM fit

BABAR BELLE

Table of results

From + U-spin breaking effects Our predictions for Amix, Adir of Bs→KK and Rd

s in SM:

Also from the Bd→and BR(Bs→KK) we can give a prediction for in SM:

350 ≤ ≤ 740

In the NEAR FUTURE we will MEASURE NEW PHYSICS:

Adir(Bs→ ), Amix(Bs→ ), BR(Bs→), Amix(Bs→J/)

Observable (SM) Babar BelleAdir(Bs→ ) (-1 , 1) (-.02 , .18)

Amix(Bs→ ) (-1 , 1) (-.19 , .05)

Rds (0.1 , 13.9) (3.6 , 85.5)

In the meanwhile…

Consistency check for the PRESENCE of NEW PHYSICS :

In the SU(3) limit depend on four theoretical parameters:

- Penguin parameters: - Weak mixing angle:

- CKM angle CKM fit (Rb and Rt)

Including all theoretical uncertainties:

And experimental errors at 1σ:

Alternative in the future: DETERMINE GAMMA/PRESENCE OF NP

Once the CP asymmetries of Bs→K+K- are measured

SM range strongly restricted Sensitivity to U-spin breaking is very reducedAllowed region to the SM:

Conclusions

Non-leptonic B decays are playing a fundamental role in the exploration of CP violation.

Recent measurement of BR(Bs→K+K-) together with the future data on the CP asymmetries Adir(Bs→K+K-) and Amix(Bs→K+K-) will open exciting new perspectives and strategies:

To search for New Physics signals in B decays

To determine CKM angle gamma

Present experimental situation is quite uncertain:

• Babar and Belle are inconsistent• If we average naïvely

• A large direct CP asymmetry from Belle (large strong phases) would be troublesome for QCD-NLO factorization.

Deviation from U-spin1. Only non-factorizable

effects in 2. Explored dependence of

the predictions on U-spin deviations

for 3. Prediction: 350 ≤ γ≤

740