Phi3/gamma. Hitoshi Yamamoto Tohoku University. H. Yamamoto, HQL06 Munich

Transcription

1 Phi3/gamma Hitoshi Yamamoto Tohoku University

2 Contents B D (*) K (*) : 3 / D CP (*) K (*) (GLW method ) D DCS (*) K (*) (ADS method ) D Ks (*) K (*) (Dalitz Analysis) B D (*) (*) : ( )/ (2 + ) Flavor-tagged time-dependent analyses Full and partial reconstructions ( * = )

3 B DK Diagrams Includes FSI rescatterings #cc is odd no penguins r A(D 0 K ) A(D 0 K ) ~ 0.1 A(D 0 K ) λ c V cb V us * A(D 0 K ) λ u V ub V cs * (T: tree, C: color-suppressed, A: annihilation) arg λ u λ c ~ ϕ 3

4 Oft-used observables B D cp K (cp = ±) Direct CPV between B and B + : A ± = Γ(D ±K ) Γ(D ± K + ) Γ(D ± K )+ Γ(D ± K + ) = ±2r sinϕ 3 sinδ R ± δ : strong phase between A(D 0 K ) and A(D 0 K ) CP=+ or decay rate averaged over B ±, in unit of favored rate. R ± = 2 Γ(D ± K )+ Γ(D ± K + ) Γ(D 0 K )+ Γ(D 0 K + ) =1+ r2 ± 2r cosϕ 3 cosδ (R + + R )/2 = 1 + r 2 ~ 1 (r 2 ~0.01) Not sensitive to r. Correction due to DCS same order.

5 BaBar 253M B ± (PRD 73, (R) 2006) CP+ 131 evts DK modes D decays used Favored: K + CP 148 evts CP+ : K + K, + CP : K S 0 / / Fit E and PID Α + = 0.35±0.13±0.04 Α = 0.06±0.13±0.04 R + = 0.90±0.12±0.04 R = 0.86±0.10±0.05 DK D

6 Belle 232M B ± (PRD 73, (R) 2006) DK DK modes Α + = 0.06±0.14±0.05 Α = 0.12±0.14±0.05 R + = 1.13±0.16±0.05 R = 1.17±0.14±0.05 D*K modes Α + = 0.20±0.22±0.04 Α = 0.13±0.30±0.08 R + = 1.41±0.25±0.06 R = 1.15±0.31±0.12 DK D

7 CP- CP- CP+ CP- CP+ CP- CP+ D 0 K* D* 0 K D 0 K CP+ CP- CP+ CP- CP+ R cp deviation from 1 opposite for CP+/ A cp opposite sign for CP+/ More statistics needed for the CPV to be seen

8 GLW method (original) Measure 4 quantities for given CP A(D CP K ), A(D CP K + ) A(D 0 K ) = A(D 0 K + ) A, A(D 0 K ) = A(D 0 K + ) B Construct two triangles 3 / Problem : Difficult to measure the suppressed modes due to D 0 DCSD ADS noticed that there is a large CPV effect in DCSD modes ADS method Measure at least 4 modes including DCSD modes (two types) E.g. (K + )K, (K + K )K and conjugates Solve for r, 3, 1, 2.

9 ADS Modes ('DCSD' modes) D decays that are flavor-specific and suppressed ( DCSD ) B re i(δ ϕ 3 ) B + re i(δ+ϕ 3 ) D 0 K D 0 K D 0 K + D 0 K + r D e iδ D K + π r D e iδ D K π + Statistics not enough yet to perform the ADS analysis. For now, measure the suppressed mode Br. R ADS = (K + π )K + (K π + )K + (K π + )K + (K + π )K ~ + r2 + r 2 D + 2rr D cos(δ δ D )cosϕ 3 Get DCSD factor r D from D analysis sensitivity to r

10 ADS Mode : Belle Results 386M B ± (K + )K Varying 0< 3 <, ±2 for r D, R ADS = ( ±1.0) 10 3 r < 0.18

11 232M B ± ADS Mode : Babar Results DK* (K S ) R ADS r DK <0.029 <0.23 DK D*K <0.023 (D 0 0 ) <0.045 (D 0 ) <0.16 DK* < ±0.14 D K + Still not enough to claim signal

12 B ± DK ±, D K S + Dalitz Dalitz distribution (assume CP in D decay) B + D 0 K + + re iθ D 0 K + 2 Amp = f (m K S π + 2,m K S π )+ re iθ 2 f (m K S π 2, m K S π + ) = θ = δ ±ϕ 3 (B ± ) Asymmetry of f(x,y) under x y Sensitivity to r,, 3. Atwood, Dunietz, Soni, PRD 2001 (K + 0 ) Bonder, BINP Mini-workshop on Dalitz analysis, Sep Giri, Grossman, Soffer, Zupan, PRD 2003

13 Dalitz Amplitude Need to know the Dalitz amplitude f(m 122,m 132 ) Fit known resonances to the D 0 sample (D* + tag) model dependence Use Breit-Wigner form (BW) BaBar : 390K samples, 16 BWs + NR, 3 are DCS. Belle : 260K samples, 18 BWs + NR, 5 are DCS. Different formalisms for resonances used for systematics study Belle

14 Dalitz Distribution (D* tag) Belle fit data

15 BaBar Dalitz : D (*) K (*) Signals 347M B ± s DK DK, D*K D* 0 D 0 0, D 0 Belle Belle 386M B ± s DK, D*K, DK* D*K D* 0 D 0 0 K* K S DK*

16 DK B B + Fit parameters (r,, 3 ) do not behave well Fit the amplitude of the suppressed B ± decay x ± = Re(re i(δ±ϕ 3 ) ), y ± = Im(re i(δ±ϕ 3 ) ) 4 parameters with D*K (D 0 0 ) x y 2 + = x y also (x + x ) 2 + (y + y ) 2 = 2r sinϕ 3 D*K (D 0 )

17 x-y fit results DK D*K B B + B + B Different r, for different B decays x,y: relative for D 0 and D 0 0 due to parity property. (Bonder, Gershon 2004) DK D*K DK* Belle

18 Extraction of : BaBar DK D*K = 91±41(stat)±11(sys)±12 (model) r DK = [0, 014] r D*K = [0.02, 0.20]

19 ϕ 3 = (stat)±3(sys)±9 o (model) Extraction of 3 : Belle DK r r DK = ± ± r D*K = ± 0.013± r DK* = ± 0.041± r Ambiguities: 3 3 +(n+m), +(n-m) (n,m: any integers) Require 0< 3 < to Resolve ambiguity. D*K DK* r 3 3

20 D (*) (*) : mixing flavor specific r = DCS/CF~0.02 CF + annihilations DCS

21 B 0 tag D (*) (*) Γ B 0 (D m π ± ;t) 1± cosδmt + s m sinδmt Γ B 0 (D m π ± ;t) 1 m cosδmt s ± sinδmt s ± ~ 2r sin(2ϕ 1 +ϕ 3 ±δ) r = 0.1 D*+pi- D*- pi+ Tag-side interference s ± a = 2r sin(2β +γ)cosδ b = 2r'sin(2β +γ)cosδ' c = 2 cos(2β +γ)(r sinδ r'sinδ') Primed parameters : tag-side effects. Absent for lepton tag. use a and c lep to extract dt

22 D (*) (*) Full-recon. BaBar D 232M Bpairs D* D a D = ± ± a D* = ± ± a D = ± ± c D = ± ± c D* = ± ± c D = ± ± 0.018

23 D (*) (*) partial-recon. BaBar D 0 not reconstructed. Fast and slow s only. Plot missing D 0 mass. High statistics More background a= 0.034±0.014±0.019 c lep = 0.025±0.020±0.013

24 D (*) full-recon. Belle 392M Bpairs Full reconstruction of D + and D* + S + (D* )=0.049±0.020±0.011 S (D* )=0.031±0.019±0.011 S + (D )=0.031±0.030±0.012 S (D )=0.068±0.029±0.012 s s D* + : lepton tag s + s +

25 D (*) (*) World Averages Deviation of a from 0 is seen

26 Measurement of r(d (*) (*) ) Br(D S ) = (1.3±0.3±0.2) 10 5 Br(D S * ) = (2.8±0.6±0.5) 10 5 BaBar Assume SU3 with correction for decay constants f D, f Ds : r = tanθ c f D f DS Br(B 0 D + S π ) Br(B 0 D π + ) r(d ) = (1.3±0.2±0.1) 10 2 r(d* ) = (1.9±0.2±0.2) 10 2 Annihilation diagram in D is ignored. (No annihilation for D S, since #ss is odd)

27 Extraction of sin(2β+γ) and γ Combine, Belle and BaBar Full and partial reconstructions All D(*)π(*) modes Use r s from SU3

28 D CP K modes : Clear CPV not seen yet. DK ADS modes : Summary Suppressed modes are not seen (some hints?). Constraints on r is obtained. DK Dalitz analysis : 3 / error is ~20. Improvement expected with more stat. D (*) (*) time-dependent analysis : Beginning to produce meaningfull result for sin( ). Determination of r(d ) is an issue.