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 B0

d → π+π−, which is still not

settled between BaBar and Belle (in contrast to mixing-induced CPV). – Extraction of γ/φ3 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 → πK1

• 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
• le in certain decays.

[R.F. (’94); Deshphande & He (’95); Gronau, Hernandez, London & Rosner (’95); ...]

• First tantalising data from the CLEO collaboration about Bd → 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)]

• Observation of B0

d → π0K0 by CLEO with a “puzzling” branching ratio

and speculation about a modified EW penguin sector. [R.F. & Buras (’00)]

• Strategy to analyze the “B → πK” puzzle in a systematic way:

→

• ur focus: picture after the experimental updates @ ICHEP ’06

1I 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 Bd → K+K−, Bs → 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(B0

d(t) → f) − Γ(B0 d(t) → f)

Γ(B0

d(t) → f) + Γ(B0 d(t) → f)

= Adir

CP cos(∆Mdt) + Amix CP sin(∆Mdt)

• CP-violating observables:

Adir

CP

= 1 − |ξ(d)

f |2

1 + |ξ(d)

f |2 = |A(B0 d → f)|2 − |A(B0 d → f)|2

|A(B0

d → f)|2 + |A(B0 d → f)|2

• “direct” CP violation

Amix

CP

= 2 Im ξ(d)

f

1 + |ξ(d)

f |2

⇒ “mixing-induced” CP violation

• Observables are governed by the following quantity:

ξ(d)

f

∼ e−iφd

• A(B0

d → f)

A(B0

d → f)

• with

φd

ψKS

= (42.4 ± 2)◦.

2We use a similar sign convention for self-tagging Bd and charged B decays.

Step 1: B → ππ

B0

d → π+π−,

¯ B0

d → π+π−

B0

d → π0π0,

¯ B0

d → π0π0

B+ → π+π0, B− → π−π0

CP Violation in B0

d → π+π−: Interesting Progress!

B0

d

b u u d d d π+ π− W

B0

d

W b d d d u u u, c, t G π+ π−

∝ O(λ3) ∝ O(λ3)

A(B0

d → π+π−) = −| ˜

T|eiδ ˜

T

eiγ − deiθ

• There is now – for the first time – a nice agreement between the BaBar

and Belle measurements of the mixing-induced CP asymmetry: [Ferroni] Amix

CP (Bd → π+π−) =

• 0.53 ± 0.14 ± 0.02

(BaBar) 0.61 ± 0.10 ± 0.04 (Belle)

HFAG

⇒ 0.59±0.09.

• On the other hand, the picture of direct CP violation is still not settled:

Adir

CP(Bd → π+π−) =

• −0.16 ± 0.11 ± 0.03

(BaBar) −0.55 ± 0.08 ± 0.05 (Belle) ⇒ ?

The B0

d → π−K+ Mode Clarifies the Picture ...

B0

d

b u d d π− W s u K+

B0

d

W b d d u u u, c, t G π− s K+

∝ Aλ4Rbeiγ ∝ Aλ2

λ2Rb = 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:

Adir

CP(Bd → π∓K±) =

       0.108 ± 0.024 ± 0.008 (BaBar) 0.093 ± 0.018 ± 0.008 (Belle) 0.04 ± 0.16 ± 0.02 (CLEO) 0.058 ± 0.039 ± 0.007 (CDF) HFAG ⇒ 0.093 ± 0.015.

A(B0

d → π−K+) = P ′

1 − reiδeiγ

• SU(3) flavour symmetry and dynamical assumptions specified above:

reiδ = ǫ dei(π−θ) with ǫ ≡ λ2 1 − λ2 = 0.05.

• This relation implies:

[R.F., PLB 459 (’99) 306 & EPJC 16 (’00) 87]

HBR ≡ 1 ǫ fK fπ 2 BR(Bd → π+π−) BR(Bd → π∓K±)

• = −1

ǫ Adir

CP(Bd → π∓K±)

Adir

CP(Bd → π+π−)

• – Since the CP-averaged BRs and Adir

CP(Bd → π∓K±) are well measured,

we may use this relation to predict the value of Adir

CP(Bd → π+π−):

⇒ Adir

CP(Bd → π+π−) = −0.24 ± 0.04

→ favours BaBar ...

• Since we can express HBR, Adir

CP(Bd → π∓K±) and Amix CP (Bd → π+π−)

in terms of γ and d, θ, these parameters can be extracted from the data: γ =

• 70.0+3.8

−4.3

• →

excellent agreement with the SM UT fits →

1 1 0.5 ρ η

Hadronic B → ππ Parameters3

• Ratio of “penguin” to “tree” amplitudes, determined as described above:

d = 0.46 ± 0.02, θ = (156 ± 5)◦.

• Ratio of “colour-suppressed” to “colour-allowed tree” amplitudes xei∆:

Isospin ⇒ √ 2A(B+ → π+π0) = −| ˜ T|eiδ ˜

Teiγ

1 + xei∆ √ 2A(B0

d → π0π0)

= |P|eiδP 1 + (x/d)eiγei(∆−θ) .

• We have additional B → ππ observables at our disposal:

Rππ

+−

≡ 2 BR(B± → π±π0) BR(Bd → π+π−) τB0

d

τB+ = 2.02 ± 0.16 Rππ

00

≡ 2 BR(Bd → π0π0) BR(Bd → π+π−)

• =

0.50 ± 0.08 ⇒ x = 0.92+0.08

−0.09,

∆ = −(49+11

−14)◦.

3EW penguins have a tiny impact on the B → ππ system, but are included in our numerical analysis.

CP Violation in Bd → π0π0

• The hadronic parameters and γ imply the following predictions:

Adir

CP(Bd → π0π0)

• SM

= −(0.40+0.14

−0.21)

Amix

CP (Bd → π0π0)

• SM

= −(0.71+0.16

−0.17)

⇒ exciting perspective of large CP violation!

• Experimental status:

Adir

CP(Bd → π0π0) =

−(0.33 ± 0.36 ± 0.08) [BaBar] −(0.44+0.73+0.04

−0.62−0.06)

[Belle] HFAG ⇒ −

• 0.36+0.33

−0.31

• ⇒

excellent agreement (note signs)!

• Conversely, the measurement of one of the CP-violating Bd → π0π0
• bservables would allow a theoretically clean determination of γ.

Step 2: B → πK

B0

d → π−K+,

¯ B0

d → π+K−

B+ → π+K0, B− → π− ¯ K0 B0

d → π0K0,

¯ B0

d → π0 ¯

K0 B+ → π0K+, B− → π0K−

QCD penguins @ work, but also EW penguins important →

Electroweak Penguins ⇒ B → πK Classification:

• EW penguins can be colour-suppressed: → tiny contributions ...

B0

d

W b d d u u π− s K+ t Z, γ W b s t Z, γ B+ u u d d K0 π+

• EW penguins can be colour-allowed: → sizeable, competing with trees!

b t d d s W Z B0

d

K0 π0 u, d u, d b t s W Z π0 u, d u, d B+ K+ u 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 B0

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+K0) = −P ′ 1 + ρceiθceiγ – The doubly Cabibbo-suppressed parameter ρceiθc is usually neglected: ⇒ Adir

CP(B± → π±K) = 0 exp

= −0.009 ± 0.025 → nice agreement!

• Finally, we can predict the following ratio through our strategy:

R ≡ BR(Bd → π∓K±) BR(B± → π±K) τB+ τB0

d

SM

= 0.942 ± 0.012

exp

= 0.93 ± 0.05 ⇒ excellent consistency with the SM, no anomalous ρc indicated!

This picture of ρc follows also from B± → K±K decays [R.F. & Recksiegel (’04)].

Moreover Bs → K+K− Results ...

Impact of EW penguins is tiny as well (colour-suppressed)

• SM predictions of the Bs → K+K− observables in our strategy:

– CP asymmetries: Adir

CP(Bs → K+K−)

= 0.093 ± 0.015 Amix

CP (Bs → K+K−)

= −0.234+0.017

−0.014.

– CP-averaged branching ratio: ∗ In contrast to the CP asymmetries, an SU(3)-breaking form-factor (FF) ratio enters [QCDSR result by Khodjamirian et al. (’03→’04)]: BR(Bs → K+K−) =

• (27.9+7.1

−5.1) × 10−6

[B → ππ data] (28.1+7.0

−5.1) × 10−6

[B → πK data].

• Observation of Bs → K+K− @ CDF: [CDF Collaboration, hep-ex/0607021]

BR(Bs → K+K−) = (33 ± 5.7 ± 6.7) × 10−6; update @ BEAUTY ’06: (24.4 ± 1.4 ± 4.6) × 10−6 ⇒ nice agreement!

Powerful Extraction of γ from Bs → K+K−, Bd → π+π− @ LHCb:

• Illustration for the observables listed above [φs = −2◦ and φd = 42.4◦]:

– Adir

CP(Bs → K+K−) = +0.09, Amix CP (Bs → K+K−) = −0.23;

– Adir

CP(Bd → π+π−) = −0.24, Amix CP (Bd → π+π−) = +0.59:

30 60 90 120 150 180 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

γ [deg] d() Bd → π+π− Bs → K+K− ⇒ γ = 70◦, d = 0.46

[R.F. (1999)]

Observables with a Sizeable Impact of EW Penguins

• The key quantities:

[Buras & R.F. (’98)]

Rc ≡ 2 BR(B+ → π0K+)+BR(B− → π0K−) BR(B+ → π+K0) + BR(B− → π− ¯ K0)

• Exp

= 1.11 ± 0.07 Rn ≡ 1 2 BR(B0

d → π−K+) + BR( ¯

B0

d → π+K−)

BR(B0

d → π0K0)+BR( ¯

B0

d → π0 ¯

K0)

• Exp

= 0.99 ± 0.07

• Features of the EW penguins:

– Enter in colour-allowed form through the modes involving π0’s. – Description through the following parameters: q

SM

= 0.60 (→ “strength”)

• SU(3) [Neubert & Rosner(’98)]

, φ

SM

= 0◦ (→ CP-violating phase) – Provide an interesting avenue for NP to manifest itself...

[R.F. & Mannel (’97); Grossman, Neubert & Kagan (’99); ...]

Time Evolution of the Experimental Values of the Rc,n

2000 2001 2002 2003 2004 2005 2006 0.5 1 1.5 2 Rc Rn

• We observe that the central values have significantly moved up (mainly

due to radiative corrections affecting final states with charged particles

[Baracchini & Isidori (’06)]), while the errors were only marginally reduced.

• In particular the central value of Rn has now approached 1 ...

Situation in the Rn–Rc Plane

0.6 0.7 0.8 0.9 1 1.1 0.6 0.8 1 1.2 1.4 1.6 =260° =270° =280° =290° =300° =80° =90°

2005 2003 2003

Rn Rc

φ φ φ φ φ φ φ

• exp. region

SM q = 0.58 q = 0.69 q = 1.22 q = 1.75

• The SM prediction is very stable, with further reduced errors!
• The B-factory data have moved quite a bit towards the SM, implying:

q = 0.65+0.39

−0.35,

φ = −(52+21

−50)◦.

Reminder: CPV in b → s Penguin-Dominated Modes

• We observe here the same trend, i.e. the data move towards the SM:

→ see in particular the history of (sin 2β)φKS ... NP could be present, but still cannot be resolved!?

Closer Look at CPV in B0

d → π0KS, B± → π0K±

→ received a lot of attention, and can be analyzed in our strategy:

• Mixing-induced and direct CP violation in Bd → π0KS:

→ we obtain a SM prediction much sharper than the current data:

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2004

Amix

CP (Bd → π0KS)

Adir

CP(Bd → π0KS)

φ φ φ φ φ φ φ φ φ φ φ φ φ φ

• exp. region

SM q = 0.58 q = 0.69 q = 1.22 q = 1.75

⇒ can reach the experimental central values for large positive φ ...

• Direct CP violation in B± → π0K±:

Adir

CP(B± → π0K±) SM

= −0.001+0.050

−0.042 exp

= −0.047 ± 0.026 – Good agreement between the prediction and the data within the errors. – Turns out to be almost independent of NP for our new input data: ⇒

• ∆A ≡ Adir

CP(B± → π0K±) − Adir CP(Bd → π∓K±) = 0 is likely

to be generated through hadronic effects, i.e. not through NP!

• A fit to Rn, Rc and the CP asymmetries of B0

d → π0KS yields:

q = 1.7+0.5

−1.3

φ = +

• 73+6

−18

• – These parameters – in particular the large positive phase – would also

allow us to accommodate (sin 2β)φKS and the CP asymmetries of other b → s penguin modes with central values smaller than (sin 2β)ψKS. – The large value of q would be excluded by constraints from rare decays in simple scenarios where NP enters only through Z penguins, but could still be accommodated in other scenarios (e.g. leptophobic Z′). Errors too large to draw conclusions: → stay tuned ...

Conclusions

• The BFRS strategy continues to provide a powerful tool:

– Thanks to progress at the B factories, we could now only use data where BaBar and Belle are in full agreement. – Still our SM predictions are very stable (since 2003)!

• Using the braching ratio and direct CP asymmetry of B0

d → π−K+, we

could clarify the picture of direct CP violation in B0

d → π+π−:

– We predict Adir

CP(Bd → π+π−) = −0.24 ± 0.04, which favours BaBar.

– We find γ =

• 70.0+3.8

−4.3

• , in excellent agreement with the SM UT fits!
• The status of the B → πK system can be summarized as follows:

– All colour-suppressed modes are in excellent agreement with the SM. – The data for Rn,c have moved quite a bit towards our SM predictions, which are almost unchanged, thereby reducing the “B → πK” puzzle. – ∆A = 0 seems to be caused by hadronic and not by new physics! – Amix

CP (Bd → π0KS) still looks puzzling, and could be accommodated

through a modified EW penguin sector with a large, positive φ (?) ...

The new data put NP in B → πK under a shadow: can NP get out into the sun once the data improve?