The B K Puzzle: A Status Report Robert Fleischer CERN, Department - PowerPoint PPT Presentation

The B → πK Puzzle: A Status Report Robert Fleischer CERN, Department of Physics, Theory Division CKM2006, Nagoya, Japan, 12–16 December 2006 • New data @ ICHEP ’06: → implications for B → ππ, πK analysis? • New results: – Prediction of direct CP violation in B 0 d → π + π − , which is still not settled between BaBar and Belle (in contrast to mixing-induced CPV). – Extraction of γ/φ 3 and hadronic parameters, which allow us to address the “ B → πK puzzle” for CP-averaged B → πK branching ratios. – Interesting implications for CP asymmetries of B → πK modes ... [Collaboration with A.J. Buras, S. Recksiegel & F. Schwab → to appear soon]

A Brief History of B → πK 1 • Use the SU (3) flavour symmetry to extract γ from B → πK , ππ decays. [Gronau, Rosner & London (1994); ...] • Electroweak (EW) penguins play an important rˆ ole in certain decays. [R.F. (’94); Deshphande & He (’95); Gronau, Hernandez, London & Rosner (’95); ...] • First tantalising data from the CLEO collaboration about B d → π ∓ K ± , B ± → π ± K , and bounds on the angle γ of the unitarity triangle. [R.F. & Mannel (1997); Neubert & Rosner (1998); ...] • Derivation of sum rules. [Lipkin (’98); Gronau (’98) ... Gronau & Rosner (’06)] • Detailed analyses of charged and neutral B → πK decays. [R.F. & Buras (1998); Neubert (1998); ...] • Analyses of B → ππ, πK within QCDF, PQCD, SCET, sum rules ... [Beneke et al. (’99); Keum, Li & Sanda (2000); Bauer et al. (’01); Khodjamirian (’01)] d → π 0 K 0 by CLEO with a “puzzling” branching ratio • Observation of B 0 and speculation about a modified EW penguin sector. [R.F. & Buras (’00)] • Strategy to analyze the “ B → πK ” puzzle in a systematic way: → our focus: picture after the experimental updates @ ICHEP ’06 1 I shall use the γ notation throughout my talk.

Our Original Strategy [A.J. Buras, R.F., S. Recksiegel & F. Schwab (2003–2005)] • New Physics in the EW penguin sector addressed by many other authors: Yoshikawa (’03); Gronau & Rosner (’03); Barger et al. (’04); Wu & Zhou (’05); ...

Summary of our Working Assumptions • Treatment of hadronic matrix elements: i) SU (3) flavour symmetry of strong interactions: ∗ However, we include SU (3) -breaking corrections through ratios of decay constants and form factors whenever they arise. ∗ We explore the sensitivity of the numerics to non-factorizable effects. ii) Neglect penguin annihilation and exchange topologies: ∗ These contributions can be probed and controlled through data for the B d → K + K − , B s → π + π − system [ → LHCb]. Consistency checks ( γ determination, R , ...) look fine! • Treatment of New Physics (NP) [although basically a SM analysis]: – Assume that it manifests itself only in the EW penguin sector. – Specific NP scenarios: SUSY, Z ′ , models with extra dimensions...

Notation/Formulae for CP Asymmetries • Time-dependent rate asymmetries: 2 Γ( B 0 d ( t ) → f ) − Γ( B 0 d ( t ) → f ) = A dir CP cos(∆ M d t ) + A mix CP sin(∆ M d t ) Γ( B 0 d ( t ) → f ) + Γ( B 0 d ( t ) → f ) • CP-violating observables: 1 − | ξ ( d ) d → f ) | 2 − | A ( B 0 f | 2 f | 2 = | A ( B 0 d → f ) | 2 A dir = CP d → f ) | 2 + | A ( B 0 1 + | ξ ( d ) | A ( B 0 d → f ) | 2 � �� � “direct” CP violation 2 Im ξ ( d ) f A mix = ⇒ “mixing-induced” CP violation CP 1 + | ξ ( d ) f | 2 • Observables are governed by the following quantity: � � A ( B 0 d → f ) ψK S ξ ( d ) ∼ e − iφ d = (42 . 4 ± 2) ◦ . with φ d f A ( B 0 d → f ) 2 We use a similar sign convention for self-tagging B d and charged B decays.

Step 1: B → ππ ¯ B 0 d → π + π − , B 0 d → π + π − ¯ B 0 d → π 0 π 0 , B 0 d → π 0 π 0 B + → π + π 0 , B − → π − π 0

d → π + π − : Interesting Progress! CP Violation in B 0 d W d π + π + b u, c, t u u W B 0 G b d u u d B 0 π − d π − d d d ∝ O ( λ 3 ) ∝ O ( λ 3 ) T � e iγ − de iθ � d → π + π − ) = −| ˜ T | e iδ ˜ A ( B 0 • There is now – for the first time – a nice agreement between the BaBar and Belle measurements of the mixing-induced CP asymmetry: [Ferroni] � 0 . 53 ± 0 . 14 ± 0 . 02 (BaBar) HFAG A mix CP ( B d → π + π − ) = ⇒ 0 . 59 ± 0 . 09 . 0 . 61 ± 0 . 10 ± 0 . 04 (Belle) • On the other hand, the picture of direct CP violation is still not settled: � − 0 . 16 ± 0 . 11 ± 0 . 03 (BaBar) A dir CP ( B d → π + π − ) = ⇒ ? − 0 . 55 ± 0 . 08 ± 0 . 05 (Belle)

d → π − K + Mode Clarifies the Picture ... The B 0 s W s K + K + u b u, c, t W u b u B 0 G d u B 0 d π − d π − d d d ∝ Aλ 4 R b e iγ ∝ Aλ 2 λ 2 R b = O (0 . 02) ⇒ QCD penguins dominate ... this feature holds, in fact, for all B → πK decays! • Direct CP violation in this decay is now experimentally well established:  0 . 108 ± 0 . 024 ± 0 . 008 (BaBar)    0 . 093 ± 0 . 018 ± 0 . 008 (Belle) A dir CP ( B d → π ∓ K ± ) = 0 . 04 ± 0 . 16 ± 0 . 02 (CLEO)    0 . 058 ± 0 . 039 ± 0 . 007 (CDF) HFAG ⇒ 0 . 093 ± 0 . 015 .

d → π − K + ) = P ′ � 1 − re iδ e iγ � A ( B 0 • SU (3) flavour symmetry and dynamical assumptions specified above: λ 2 re iδ = ǫ de i ( π − θ ) with ǫ ≡ 1 − λ 2 = 0 . 05 . • This relation implies: [R.F., PLB 459 (’99) 306 & EPJC 16 (’00) 87] � 2 � BR ( B d → π + π − ) � f K � � A dir � CP ( B d → π ∓ K ± ) H BR ≡ 1 = − 1 A dir BR ( B d → π ∓ K ± ) CP ( B d → π + π − ) ǫ f π ǫ – Since the CP-averaged BRs and A dir CP ( B d → π ∓ K ± ) are well measured, we may use this relation to predict the value of A dir CP ( B d → π + π − ) : A dir CP ( B d → π + π − ) = − 0 . 24 ± 0 . 04 ⇒ → favours BaBar ... • Since we can express H BR , A dir CP ( B d → π ∓ K ± ) and A mix CP ( B d → π + π − ) in terms of γ and d , θ , these parameters can be extracted from the data: � � ◦ 70 . 0 +3 . 8 γ = → excellent agreement with the SM UT fits → − 4 . 3

η 1 0 . 5 0 1 0 ρ

Hadronic B → ππ Parameters 3 • Ratio of “penguin” to “tree” amplitudes, determined as described above: θ = (156 ± 5) ◦ . d = 0 . 46 ± 0 . 02 , • Ratio of “colour-suppressed” to “colour-allowed tree” amplitudes xe i ∆ : � √ T e iγ � 1 + xe i ∆ � 2 A ( B + → π + π 0 ) −| ˜ T | e iδ ˜ = √ Isospin ⇒ | P | e iδ P � 1 + ( x/d ) e iγ e i (∆ − θ ) � 2 A ( B 0 d → π 0 π 0 ) = . • We have additional B → ππ observables at our disposal: � τ B 0 � BR ( B ± → π ± π 0 ) R ππ d ≡ 2 = 2 . 02 ± 0 . 16 + − BR ( B d → π + π − ) τ B + � BR ( B d → π 0 π 0 ) � R ππ ≡ 2 = 0 . 50 ± 0 . 08 00 BR ( B d → π + π − ) x = 0 . 92 +0 . 08 ∆ = − (49 +11 − 14 ) ◦ . ⇒ − 0 . 09 , 3 EW penguins have a tiny impact on the B → ππ system, but are included in our numerical analysis.

CP Violation in B d → π 0 π 0 • The hadronic parameters and γ imply the following predictions: � A dir CP ( B d → π 0 π 0 ) − (0 . 40 +0 . 14 = − 0 . 21 ) � SM � A mix CP ( B d → π 0 π 0 ) − (0 . 71 +0 . 16 = − 0 . 17 ) � SM ⇒ exciting perspective of large CP violation! • Experimental status: � − (0 . 33 ± 0 . 36 ± 0 . 08) [BaBar] A dir CP ( B d → π 0 π 0 ) = − (0 . 44 +0 . 73+0 . 04 − 0 . 62 − 0 . 06 ) [Belle] � � 0 . 36 +0 . 33 HFAG ⇒ − ⇒ excellent agreement (note signs)! − 0 . 31 • Conversely, the measurement of one of the CP-violating B d → π 0 π 0 observables would allow a theoretically clean determination of γ .

Step 2: B → πK ¯ B 0 d → π − K + , B 0 d → π + K − B + → π + K 0 , B − → π − ¯ K 0 d → π 0 ¯ ¯ B 0 d → π 0 K 0 , B 0 K 0 B + → π 0 K + , B − → π 0 K − QCD penguins @ work, but also EW penguins important →

Electroweak Penguins ⇒ B → πK Classification: • EW penguins can be colour-suppressed : → tiny contributions ... W s K 0 W s K + b b t t d u B + Z, γ B 0 Z, γ d u d d u π + π − d u • EW penguins can be colour-allowed : → sizeable , competing with trees! u, d u, d π 0 π 0 Z Z b b u, d u, d t t B 0 B + d W W s s d u K 0 K + d u

Observables with a Tiny Impact of EW Penguins • For the determination of γ discussed above, we have already used the CP- averaged branching ratio and the direct CP asymmetry of B 0 d → π − K + : ⇒ γ = (70 . 0 +3 . 8 − 4 . 3 ) ◦ , in excellent agreement with the SM UT fits! • Another decay with colour-suppressed EW penguins is at our disposal: A ( B + → π + K 0 ) = − P ′ � 1 + ρ c e iθ c e iγ � – The doubly Cabibbo-suppressed parameter ρ c e iθ c is usually neglected: CP ( B ± → π ± K ) = 0 exp ⇒ A dir = − 0 . 009 ± 0 . 025 → nice agreement! • Finally, we can predict the following ratio through our strategy: � τ B + � BR ( B d → π ∓ K ± ) exp SM R ≡ = 0 . 942 ± 0 . 012 = 0 . 93 ± 0 . 05 BR ( B ± → π ± K ) τ B 0 d ⇒ excellent consistency with the SM, no anomalous ρ c indicated! This picture of ρ c follows also from B ± → K ± K decays [R.F. & Recksiegel (’04)].