時間依存性と Dalitz plot を用いた B ρπ 崩壊過程における CP 非対称度の測定

Transcription

1 時間依存性と Dalitz plot を用いた B 崩壊過程における CP 非対称度の測定 pril 13 th, 27 HEP seminar at Kyoto University kito KUSK University of Tokyo

2 Outline Introduction KM model (CPV in B) and CKM angle φ 2 B Time-dependent Dalitz plot analysis nalysis procedure Event selection and signal extraction Unbinned Maximum Likelihood Fit Constraint on φ 2 Penguin contribution and isospin relation Constraint from B hep-ex/7115 ccepted by PRL

3 Introduction

4 Kobayashi-Maskawa (KM) Model K M CKM matrix V V V ud cd td V V V us cs ts V V V ub cb tb K and M proposed For CP, quarks have to have three generations. n irreducible complex phase in quark mixing matrix violates CP. Unitarity triangle V ud V * ub * * VcdVcb VtdVtb =

5 CKM triangle and φ 2 Why φ 2 is important? UT triangle closure = an important SM test. Current constraints φ = φ φ σ >> φ = = (21± 1) (93 (6 σ φ 1 ) ) * V ub V ud * V tb V td * V cb V cd φ 1 β φ 2 α φ 3 γ Provided by CKM fitter

6 CKM triangle and φ 2 (α) V ud V * ubφ3 φ 2 V td V * tb φ 1 V cd V * cb b d V tb d B B V td t t V * td V * tb b Mixing diagram b B d V ub V * ud u d u d / / Decay diagram (tree)

7 CKM triangle and φ 2 (α) b B d V ub V * ud u d u d / / B B B ()

8 壊数時間崩n example: B ( ) CP eigenstate B f CP = B f CP = CP B B 弱め合う 強め合う 強め合う ~ sin 2φ 2 弱め合う

9 Determination of Δt and qtag B s are boosted Δt is measured from vertex positions B s are entangled flavor of B 1 at time t 2 is determined by B 2 decay

10 Time-dependent CPV analysis The case of B = ( B = ( B ) ) Direct CP Violation Δt from vertex Δt / τ e 4τ B B [( ) ( ) q tag q tag 2Im cos ΔmΔt ( e ) m t] 2iφ1 * sin Δ Δ Tag side B flavor ~ sin 2φ 2

11 Why B? B, has discrete ambiguity Only sin2φ 2 is measured B has a potential to solve the ambiguity. In addition to sin2φ 2, cos2φ 2 is measured. mbiguity from QCD is dependent on mode It is valuable to measure with various mode.

12 B B B Snyder & Quinn (1993) ~ sin(2φ 2 δ ) sin(2φ δ ) ~ sinδ ~ cosδ ~ sin 2φ 2 ~ cos 2φ 2

13 How to identify ± : Dalitz plot s ( p p p : the same final state 2 2 ), s ( p ) s (GeV 2 ) s f f 2 f 2 s (GeV 2 ) s (GeV 2 ) s s (GeV 2 ) s (GeV 2 ) s (GeV 2 ) B B B Kinematical overlap Interference

14 Dalitz plot dependent amplitudes Dalitz plot dependent amplitudes ), ( ), ( 1 f f f s s e f f f s s i = = φ ) ( ) ( ) ( = = = B B B Kinematics (Dalitz plot) Complex amplitudes to be determined M ) ( 2 1 = φ B e i

15 Time- and Dalitz- dependence Time-dependence in terms of 3 Direct CP violation effect Δt / τ e 4τ B B [( ) ( ) q 3 3 q tag tag 3 2 Im 3 cos ΔmΔt ( e ) m t] 2iφ1 * sin Δ Δ 3 3 Dependences of sin(2φ 2 δ) sin(2φ 2 ) cos(2φ 2 ) etc

16 Experimental apparatus

17 KEKB accelerator Main ring 1km Belle Lineac ~7/fb until now This analysis: 414/fb, 449MBB (until last summer)

18 Belle Detector SC solenoid 1.5T CsI(Tl) 16X TOF conter erogel Cherenkov cnt. n=1.15~ GeV e 8 GeV e Central Drift Chamber small cell He/C 2 H 6 Si vtx. det. 3/4 lyr. DSSD μ / K L detection 14/15 lyr. RPCFe

19 Belle Collaboration omori U. BINP Chiba U. Chonnam Nat l U. U. of Cincinnati Ewha Womans U. Frankfurt U. Gyeongsang Nat l U. U. of Hawaii Hiroshima Tech. IHEP, Beijing IHEP, Moscow IHEP, Vienna ITEP Kanagawa U. KEK Korea U. Krakow Inst. of Nucl. Phys. Kyoto U. Kyungpook Nat l U. EPF Lausanne Jozef Stefan Inst. / U. of Ljubljana / U. of Maribor U. of Melbourne Nagoya U. Nara Women s U. National Central U. National Taiwan U. National United U. Nihon Dental College Niigata U. Osaka U. Osaka City U. Panjab U. Peking U. U. of Pittsburgh Princeton U. Riken Saga U. USTC Seoul National U. Shinshu U. Sungkyunkwan U. U. of Sydney Tata Institute Toho U. Tohoku U. Tohuku Gakuin U. U. of Tokyo Tokyo Inst. of Tech. Tokyo Metropolitan U. Tokyo U. of gri. and Tech. Toyama Nat l College U. of Tsukuba VPI Yonsei U. 13 countries, 55 institutes, ~4 collaborators

20 nalysis

21 nalysis procedure Event selection Vertexing & Flavor Tagging Unbinned Maximum Likelihood Fit φ 2 extraction

22 nalysis procedure Event selection Vertexing & Flavor Tagging Unbinned Maximum Likelihood Fit φ 2 extraction

23 Event selection Event (B ) reconstruction M = reconstruction PID (K/ separation) 2 beam Continuum suppression (event shape) bc ΔE = E p * E B E beam * 2 B e B e e q e B q

24 s (Ge 25 Dalitz Veto 2 Consider the radial excitations as contamination s (GeV 2 ) Still the and enters into the mass window Systematic error

25 Event Reconstruction 971 ± 42 B candidates Efficiency ~1% Purity ~3% Events /.2GeV/c M bc Other components SCF (Incorrectly reconstructed signal) ~5% Continuum (qq) ~57% Other B decay ~8% Events /.1GeV M bc (GeV/c 2 ) qq background ΔE signal ΔE (GeV)

26 nalysis procedure Event selection Vertexing & Flavor Tagging Unbinned Maximum Likelihood Fit φ 2 extraction

27 Vertexing and Flavor Tagging B s are boosted Δt is measured from vertex positions B s are entangled flavor of B 1 at time t 2 is determined by B 2 decay

28 Vertexing: : Detector Silicon Vertex Detector (SVD) 3(SVD1)/4(SVD2) layers Double-sided Silicon Strip Detector beam pipe r=1.5cm (SVD2) 1 st layer r=2.cm (SVD2) ~12k channels (SVD2)

29 Vertexing: : Resolution Measured Δt is smeared by resolution σ z ~ 6μm (CP side) σ Δz ~12μm Smeared by detector resolution P( Δt) P( Δt) R( Δt)

30 Flavor Tagging: lgorithm Likelihood composed of Tag side B information Leptons l primary lepton l secondary lepton B b Kaons B b W W Slow pions b W c B d ν c c W W D* D u d s s ν s K M D* M D =145MeV High r Low ε Middle r High ε Low r Low ε r: Quality ε: Efficiency

31 Flavor Tagging: Calibration Wrong tag fraction is measured using B - B mixing. Real amplitude of mixing is known to be unity. Observed amplitude corresponds to dilution due to wrong tagging. Effective tagging efficiency ~3%. Control sample Worst Best B -B mixing in each tagging quality (r) region

32 nalysis procedure Event selection Vertexing & Flavor Tagging Unbinned Maximum Likelihood Fit φ 2 extraction

33 Unbinned Maximum Likelihood fit Likelihood function L L = i Event-by-Event PDF P P( ΔE, M ; s, s ; Δt, q bc tag Index over events, r) P( ΔE, M bc ; s, s ; Δt, q tag, r) = (1 f qq f BB ) P sig f qq P qq f BB P BB Signal Continuum Other B decays

34 Signal PDF Signal PDF [( ) ( ) ( ) ] t m e q t m q e r q t s s i B t B Δ Δ Δ Δ = Δ Δ sin 2 Im cos 4 ),, ;, ( 3 * 2 tag tag / tag 3 1 φ τ τ P Dalitz plot dependent Dilution due to miss-tagging is taken account ) ( ),, ;, ( ), ( tag bc sig t R r q t s s M E P P Δ Δ Δ = P Resolution function

35 Quinn & Silva (2) 26(27) parameters to be fitted Signal PDF is a product of Δt and Dalitz PDF 2 Dalitz: 9 functions Δt: 3 functions e Δt / τ Re[ ] 2 Im[ ] e e Δt Δt / τ / τ cos( ΔmΔt) sin( ΔmΔt) Re[ Im[ ] ] Re[ Im[ ] ] 2 Signal PDF: linear combination of 3x9 = 27 functions Coefficients of them are fit parameters

36 Quasi-Two Two-Body Parameters Using the information of non-interfering parameters alone. Dominant systematic error is from potential B () BG. 2 Dalitz: 9 functions Δt: 3 functions e e e Δt / τ Δt / τ Δt / τ cos( ΔmΔt) sin( ΔmΔt) Re[ ] 2 Im[ ] Re[ ] Im[ ] Re[ ] Im[ ] 2

37 Fit result: Mass and Helicity Projections of Dalitz plot Events /.25GeV/c 2 Events / m (GeV/c 2 ) Helicity cosθ Mass Events /.25GeV/c 2 Events / m - (GeV/c 2 ) cosθ - Events /.25GeV/c 2 Events / m (GeV/c 2 ) cosθ Data distribution is well described by fitted PDF.

38 Fit result: Δt distribution Events/ps Events/ps BG subtracted asym sym. = q ( C ΔC)cos( ΔmΔt) tag Δt (ps) q tag B tag B tag Δt(ps) ( S ΔS)sin( ΔmΔt) Events/ps Events/ps BG subtracted asym sym. = -.5 q q ( C ΔC)cos( ΔmΔt) tag Δt (ps) tag Δt(ps) ( S ΔS)sin( ΔmΔt) C ΔC S ΔS =.13 ±.9 ±.5 =.36 ±.1 ±.5 =.6 ±.13±.5 =.8 ±.13 ±.5 CP Violating

39 Direct CP violation: Direct CP violation: and and ) ( ) ( ) ( ) ( Γ Γ Γ Γ = B B B B ) ( ) ( ) ( ) ( Γ Γ Γ Γ = B B B B Calculated from Q2B parameters

40 Quasi-Two Two-Body: Direct CPV 1 =.21±.8 ±.4 =.8 ±.17 ± Confidence Level (σ) Correlation: vs. DCPV Confidence Level ~2.3σ

41 Quasi-Two Two-Body: B sym. = q tag q tag ( C S S cos( ΔmΔt) sin( ΔmΔt) ) =.49 ±.36 ±.28 =.17 ±.57 ±.35 First measurement Events/ps Events/ps BG subtracted asym. Δt distribution of B Δt(ps) Δt (ps)

42 φ 2 (α) extraction

43 Penguin pollution b d V tb t t V * td d b B B b B d V ub V * ud u d u d Tree diagram / / φ 2 V td V * tb Mixing diagram b B d V tb t V * td d u u / d/ Penguin diagram

44 Dalitz Isospin nalysis Uses both interfering and non-interfering parameters. In particular, interfering parameters play important roles. Primary systematic error radial excitations ( and ) 2 Dalitz: 9 functions Δt: 3 functions e e e Δt / τ Δt / τ Δt / τ cos( ΔmΔt) sin( ΔmΔt) Re[ ] 2 Im[ ] Re[ ] Im[ ] Re[ ] Im[ ] 2

45 Dalitz Isospin nalysis: Result Combined analysis of Our result Charged mode info. s allowed region, we obtain: <φ 2 <5 23 <φ 2 <34 68 <φ 2 <95 19 <φ 2 <18

46 Combined analysis Gluon penguin contribution is mode dependent ddition of B,, Decrease the uncertainty from penguin

47 W (B (, ) ) our result We obtain 83<φ 2 <95 (deg.) at 68.3%C.L. Our measurement of B improves the constraint on φ 2. To solve the ambiguity, we need more data.

48 Comparison with Global fit Global fit w/o direct measurement φ 2 = (deg.) veraged direct measurement 83 < φ 2 < 95 (deg.)

49 Conclusion B time-dependent Dalitz plot analysis Potential capability of killing discrete ambiguity solution. Very interesting, but a complex analysis. We perform the analysis with 449M BB data collected at Belle/KEKB Indication of direct CP violation First measurement of S Constraint on φ 2 Our analysis: 68<φ 2 <95 (deg.) Combined,, and our : 83<φ 2 <95 (deg.) Consistent with the expectation from other measurements. hep-ex/7115 ccepted by PRL