A window for New Physics in B s →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. 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 B s →K + K - decay STANDARD MODEL DESCRIPTION It is governed by the quark-level process T’: Tree colour allowed, P’ gluonic penguins, P’ C EW colour suppressed EW penguins, E’ exchange and PA’ Penguin Annihilation topologies. Two types of contributions: charged-current: V ub *V us A’ u CC penguin V ub *V us (P’ u -P’ t )+V cb *V cs (P’ c -P’ t )

The SM amplitude can be written: Hadronic parameters: Remarks: - θ C’ 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 - A q and Φ q are process dependent. The amplitude is now:

There are 3 measurements in B s →K + K - decay: * From the time-dependent CP asymmetry (A dir and A mix ): In the SM these CP asymmetries are: A dir SM (B s →K + K - )=f(d’,θ’,  ) and A mix SM (B s →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: B NP, D NP and M NP 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 A mix (B d (t)→J/ψKs) CKM fit.  Weak mixing phase Φ s from CP violating B s →J/ψΦ:  NP contributions to the mixing Φ s = Φ s SM +δΦ s  contribution controlled by B d (t)→J/ψKs <20%

Hadronic Parameters: Keypoint: U-spin (interchange d↔s) related process B d →  +  - 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: A dir (B d →  ), A mix (B d →  ) and BR(B d →  )  Total parameters in SM: - 3 hadronic parameters - 2 weak parameters: But  d from A mix (B d →J/  Ks) and from QCD sum rules

From A dir (B d →  ), A mix (B d →  ), BR(B d →  ), A mix (B d →J/  Ks) and CKM fit BABAR BELLE

Table of results From + U-spin breaking effects Our predictions for A mix, A dir of B s →KK and R d s in SM: Also from the B d →  and BR(B s →KK) we can give a prediction for  in SM: 35 0 ≤  ≤ 74 0 In the NEAR FUTURE we will MEASURE NEW PHYSICS: A dir (B s →  ), A mix (B s →  ), BR(B s →  ), A mix (B s →J/  ) Observable (SM) BabarBelle A dir (B s →     ) (-1, 1) (-.02,.18) A mix (B s →     ) (-1, 1) (-.19,.05) R d s (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 (R b and R t ) Including all theoretical uncertainties: And experimental errors at 1σ:

Alternative in the future: DETERMINE GAMMA/PRESENCE OF NP Once the CP asymmetries of B s →K+K - are measured SM range strongly restricted Sensitivity to U-spin breaking is very reduced Allowed 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-spin 1.Only non-factorizable effects in 2.Explored dependence of the predictions on U-spin deviations for 3. Prediction: 35 0 ≤ γ≤ 74 0