Amir Rahimi The Ohio State University BABAR Collaboration APS 2007 CLEO-c. Outline

Transcription

1 D 0 -D 0 Mixing Amir Rahimi The Ohio State University BABAR Collaboration APS 2007 CLEO-c Outline Charm Meson Mixing Review of Recent Mixing Analysis Mixing in Semileptonic Decays by Belle and BaBar Quantum Correlation Analysis in CLEO-c Mixing with t-dependent Dalitz Plot by Belle Using D 0 Κ s π π + Evidence for Mixing from BaBar Using D 0 Κπ + Evidence for Mixing from Belle Using D 0 ΚΚ, ππ, and Κπ Summary

2 Brief History Neutral Charm meson is one of the four neutral mesons that can mix with its anti-particle K 0, B 0 and B s0 are the other three K 0 mixing first observed in 1958 B 0 mixing first observed by ARGUS experiment in 1987 B s0 mixing rate first measured by CDF and D0 in 2006 Amir Rahimi APS2007 2

3 Brief History Neutral Charm meson is one of the four neutral mesons that can mix with its anti-particle K 0, B 0 and B s0 are the other three K 0 mixing first observed in 1958 B 0 mixing first observed by ARGUS experiment in 1987 B s0 mixing rate first measured by CDF and D0 in 2006 D 0 mixing was not observed until a few weeks ago Amir Rahimi APS2007 3

4 Formalism Neutral mesons D 0 and D 0 are flavor eigenstates produced via strong interactions Due to weak force, evolve into a mixture of D 0 and D 0 Time evolution described by the weak Hamiltonian 0 0 D () t D () t i Γ = M i t D () t Weak D () t Mass eigenstates: D t pd t qd t 0 0 1,2 () = () ± () Mixing is parameterized by x and y m 1,2, and Γ 1,2 are D 1,2 mass and lifetimes Express time evolution of D 0 as: m m x = Γ Γ Γ y = 2Γ ( ) () im Γ + t D t e D cosh ( y ix) t q = + Γ + D sinh ( y+ ix) Γt p m = m m Γ =Γ Γ m + m m = 2 Γ+Γ 1 2 Γ= Amir Rahimi APS2007 4

5 Mixing Process Box diagram Standard Model charm mixing rate naively expected to be very low (mainly contribute to x) Cabibbo-Kobayashi-Maskawa and Glashow-Iliopoulus-Maiani suppressed D 0 0 D 0 D E.Golowitch, A.Petrov, Phys.Lett. B625 (2005) A.Falk, Y.Grossman, Z.Ligeti, A.Pterov, Phys.Lett. B625 (2005) D x O O 6 5 (10 ) (10 ) 3 Mass difference Long distance effects dominate (mainly contribute to y) D 0 W + c d u u u p + u u d d c d p - u W - SM Mixing: a long-range contribution D 0 x O y O Mass difference 2 (10 ) 2 (10 ) Lifetime difference 2 2 x + y RM = O 2 4 (10 ) Amir Rahimi APS2007 5

6 New Physics Contribution to Charm Mixing Possible enhancements to mixing due to new physics Contributions from new physics enhance x c u G.Burdman, I.Shipsey, Ann.Rev.Nucl.Part.Sci. 53 (2003) H 0 FCNC u c c u q ~ g ~ g ~ ~ q u c Supersymmetry c u W t t W Fourth quark generation c u paper reference Indication of NP would be observation of CPviolation or (mass)>> (lifetime) 2006 upper limit Already constraining New Physics models Mass difference hep-ph/ (A. Petrov) Amir Rahimi APS2007 6

7 D 0 -D 0 Mixing Parameters Mixing parameters and the quantities measured in the experiments (analyses which are most relevant to this talk): Analysis Wrong-Sign (WS) semileptonic decays WS hadronic decays CP eigenstate lifetime differences Time dependent Dalitz plot analysis Quantum Correlations e + e - y(3770) DD Decay Modes D 0 K l ν, etc. D 0 K π, etc. D 0 KK, (ππ), etc. D 0 K s ππ, etc. -flavored (K - π + ) -CP+ eigenstates (K - K + ) -CP- eignestates (K s π 0 ) -semileptonic (Xeν) Time dependence Time integrated Decay time analysis Decay time analysis Decay time analysis Time integrated parameters x, y, δ, r Amir Rahimi APS R M y CP x, y 2 2 x + y = = 2 N N WS RS x 2, y and r (Doubly Cabibbo Suppressed (DCS) Rate) x' = xcos( δ) + ysin( δ) Strong phase y' = ycos( δ) xsin( δ) = Γ ( CP+ ) Γ( CP ) Γ ( CP + ) +Γ ( CP ) If no CPV: y CP = y

8 Several common event selection in B-Factories Flavor-tag using the charge π s Proper lifetime measurement CM P*(D 0 ) > 2.5 GeV/c Common background categories Correct D 0, wrong π s Misreconstructed D 0 Partially reconstructed or double misid D 0 Combinatorial Each tend to have distinct (M(Kπ), M) distributions * D D π s 0 K - π + beam spot Amir Rahimi APS y D π s + x K π + l decay D 0 t interaction point proper ldecay = cβγ PD 0 βγ = M General Parameters of interest to measure mixing parameters D 0 mass = m(d o candidate ) m = m(d * candidate ) m (Do candidate ) D 0 proper decay time t D 0

9 Mixing with Semileptonic Modes From Belle and BaBar Belle: PRD (RC) 72, (2005) BaBar: Moriond 2007 Previous analysis: E.M. Aitala et al. (E791), PRL 77, 2384 (1996) C. Cawlfield et al. (CLEO II), PRD 71, (2005) B. Aubert et al. (BABAR), PRD 70, (2004) Amir Rahimi APS2007 9

10 D 0 Keν Results from Belle No DCS decays in semi-leptonic modes Simpler time dependence 2 + Γ ( ) exp t t x y WS t τ 0 D 0 τ 4 D * D D π RS: WS: In the limit of no CP violation measure time integrated mixing rate x + y x + y RM = = 2 2 Observable: M = M(πKeν) - M(Keν) Fit of WS is performed in bins of lifetimes to increase sensitivity R M < 1.2 x CL 2 2 D D 0 0 K K l + l + ν ν 253 fb -1 PRD (RC) 72, (2005) Amir Rahimi APS

11 D 0 Keν Results from BaBar Observable: M = M(πKe) - M(Ke), 344 fb -1 Double tag D *+ D 0 π s+ in semileptonic Presented at Moriond 2007 DM RS distribution Five fully reconstructed hadronic tagging modes Unbinned maximum likelihood fit to RS M Predict 2.85 background events, observe 3 (dark gray) DM WS distribution Likelihood profile -1.3 x 10-3 <R M < 1.2 x 90% C. L. Amir Rahimi APS

12 CLEO-c D 0 D 0 Quantum Correlations: Measuring x, y, r (DCS rate) and δ Simultaneously at CLEO-c Asner & Sun, PRD (2006), [hep-ph/ ] Amir Rahimi APS

13 CLEO-c Quantum-coherent D 0 D 0 at CLEO-c e + e - ψ(3770) DD Quantum-coherent D 0 D 0 state provides time-integrated sensitivity for simultaneously measuring x, y, r, and δ. Four types of final states considered: flavored (K - π + ) CP+ eigenstates CP- eignestates semileptonic (Xeν) Reconstruct one (ST) or both (DT) D mesons Event yields can be expressed as a function of: D 0 D 0 pairs produced Branching fractions Mixing parameters y and R M = (x 2+ y 2 )/2 DCS rate r and the strong phase δ Fit to the yields to extract these parameters Pure J PC = initial state + * 0 0 γ DD = ee C 1 Amir Rahimi APS

14 CLEO-c Preliminary Fit Results and Future Work at CLEO-c D.M. Asner et al, Int.J.Mod.Phys; ,2006 Fit inputs: 6 ST, 14 hadronic DT, 10 semileptonic DT, efficiencies, crossfeeds, background branching fractions and efficiencies Preliminary fitted results when r 2 constrained (281 pb -1 dataset) cosd = 1.08 ± 0.66 ±? y = ± ±? Final results on 281 pb -1 dataset awaiting collaboration approval Includes systematic errors and new modes K s η, K s ω, and K L π 0 First measurement of δ Expect σ(y) ~ and σ(cosδ Kπ ) ~ 0.3 Project 750 pb -1 by 2008 Expect σ(y) ~ 0.01 and σ(cosδ Kπ ) ~ hep-ex/ χ2 = 17.0 for 19 d.o.f. (C.L. = 59%). Uncertainties are statistical only Parameter N D 0 D 0 y r 2 r(2cosδ Kπ ) R M preliminary Value (1.09 ± 0.04 ±?)x ± ±? ± ±? ± ±? (1.74 ± 1.47 ±?)x10-3 Q.C. technique very promising for future high-statistics experiments (BES III, Super Flavor Factory ) Amir Rahimi APS

15 Time dependent Dalitz Plot Analysis of D 0 Κ s π π + at Belle arxiv: v1 [hep-ex], Moriond EW/QCD 2007 Previous analysis: D. M. Asner et al. (CLEO), PRD 72, (2005) H. Muramatsu et al. (CLEO), PRL 89, (2002) Amir Rahimi APS

16 Time-dependent Dalitz Plot Analysis of D 0 K s π π + Decay matrix element to a final state f ( m, m,) t ( m, m,) t + M K π sπ Ks λ1t λ2t 1 p 2 2 λ1t λ2t M( m, m,) t f D () t ( m, m ) e e ( m, m ) e e + = = A A 2 q i λ = im ( Γ ) 2 Where: 1,2 1,2 1,2 (function of x and y) Analogous for M and D 0 (t) In the limit of CP conservation: m Amir Rahimi APS M mk (, π ) D D π ± * s ± = * 0 mk ( s, π ) D D π Measurement directly sensitive to x and y p q Using the notation: = 1, A = A = M M

17 Mass plots and Dalitz Fit for D 0 K s π π + Belle preliminary, 540 fb -1 ~700Million Charm Pairs M= M(K p) Q = M(K s p + p - p slow ) - M(K s p + p - ) -M(p slow ) 534x10 3 signal events purity 95% Dalitz model: 13 (BW) resonances, non-resonant, bkg. For scalar ππ, K-matrix formalism also used Results with refined model consistent with Belle φ 3 /g meas. PRD73, (2006) m 2 + [GeV/c 2 ] 2 m 2 - [GeV/c 2 ] 2 m 2 pp [GeV/c 2 ] 2 Amir Rahimi APS

18 Results of Time-dependent Dalitz Plot Analysis of D 0 K s π π + at Belle arxiv: v1 [hep-ex], Moriond EW/QCD 2007 Results: x = 0.80±0.29±0.17 % y = 0.33±0.24±0.15 % τ = 409.9±0.9 fs Most sensitive measurement of x; (2.4 σ 1-d significance) Cleo, PRD72, (2005) x = 1.8 ± 3.4 ± 0.6% y = -1.4 ± 2.5 ± 0.9 % 95% C.L. contour; (0,0) point has -2 log(l)=7.3 C.L. 2.6% (1.9 σ) fit projection Amir Rahimi APS

19 Evidence For Mixing Using 0 D + K π at BaBar hep-ex/ Submitted To PRL Previous analysis: R. Godang et al. (CLEO), PRL 84, 5038 (2000) J.M. Link et al. (FOCUS), PRL 86, 2955 (2001) B. Aubert et al. (BABAR), PRL 91, (2003) J.M. Link et al. (FOCUS), PLB 618, 23 (2005) J. Li et al. (Belle), PRL 94, (2005) L.M. Zhang et al. (Belle), PRL 96, (2006) Amir Rahimi APS

20 Time-dependent Mixing Analysis Using D 0 Kπ at BaBar D 0 Hadronic wrong-sign (WS) decay mix Separate DCS decays from the mixed decays using their different time evolution There is also interference effect Time evolution, assuming x << 1 and y << t x + y Γ WS( t) = e RD + y RD( Γ t) + ( Γt) 4 DCS Interference Mixing x' = xcos( δ) + ysin( δ) Γ y' = ycos( δ) xsin( δ) DCS D 0 DCS + mix. CF 2 K + π - Amir Rahimi APS CF d is the phase difference between DCS and CF decays note: 2 x + y = x + y

21 RS and WS Data Sets After Event Selection x10 3 RS events/1 MeV/c 2 M(Kp) WS M(Kp) M(Kp) [GeV/c 2 ] 1,229,000 RS candidates 64,000 WS candidates DM [GeV/c 2 ] RS DM WS DM events/0.1 MeV/c 2 M(Kp) [GeV/c 2 ] DM [GeV/c 2 ] Fit M, M and lifetime using unbinned maximum likelihood method Amir Rahimi APS

22 RS Decay Time Fit D 0 lifetime and resolution function fitted in the RS sample RS decay time, signal region τ = (410.3 ± 0.6 (stat)) fs Consistent with PDG ± 1.5 fs plot selection: 1.843<m<1.883 GeV/c < m< GeV/c 2 Amir Rahimi APS

23 WS Fit With no Mixing Fit results assuming no mixing WS decay time, signal region Poor residuals in the signal region χ 2 /bin = 49.7/28 data - no mix PDF plot signal region: 1.843<m<1.883 GeV/c < m< GeV/c 2 Amir Rahimi APS

24 WS Fit with Mixing WS decay time, signal region Fit results allowing mixing: R D = (3.03±0.16±0.10)x10-3 x 2 = (-0.22±0.30±0.21)x10-3 y = (9.7±4.4±3.1)x10-3 x 2 and y correlation = Mixing fit describes data better χ 2 /bin = 31/28 data - no mix PDF mix - no mix PDF What is the significance of the signal? plot signal region: 1.843<m<1.883 GeV/c < m< GeV/c 2 Amir Rahimi APS

25 Signal Significance for Kπ Mixing Results at BaBar y, x 2 contours computed by change in log lilkelihood Best-fit point in nonphysical region x 2 < 0, but 1-sigma contour extends into physical region Contours include systematic errors 1s 2s 3s4s 5s 1 CL = 3.17 x 10-1 (1s) 4.55 x 10-2 (2s) 2.70 x 10-3 (3s) 6.33 x 10-5 (4s) 5.73 x 10-7 (5s) best fit X (0,0) Physical solution (y'=6.4x10-3 ) Accounting for systematic errors, the no-mixing point is at 3.9-sigma contour clear evidence for D 0 D 0 mixing R D : ( ) x 10-3 x 2 : ( ) x 10-3 y : ( ) x 10-3 No evidence for CP violation found hep-ex/ Submitted To PRL Amir Rahimi APS

26 Validation: Alternative Fit Strategy Fit M and M(Kπ) in bins of lifetime If no mixing the ratio of WS to RS signal should be constant No assumptions made in resolution model and the time evolution of background Each time bin is fit independently (stat. only) Consistent with prediction based on resolution model and mixing parameters from full likelihood fit χ 2 =1.5 Inconsistent with no-mixing hypothesis χ 2 =24 Amir Rahimi APS

27 Evidence For Mixing From Belle Using CP modes KK and ππ and flavor mode Kπ hep-ex/ v1 Submitted to PRL Previous analysis: E791, PRL 83, 32 (1999) FOCUS, PLB 485, 62 (2000) CLEO, PRD 65, (2002) Belle, PRL 88, (2002) BABAR, PRL 91, (2003) Belle, Lepton Photon 2004 Amir Rahimi APS

28 Mixing with CP Lifetimes at Belle Mixing alters the decay time distribution of D 0 D 0 decaying into CP states. The CP lifetime difference can be expressed as: 0 τ + y CP = 1 ( τ + τ ) where τ τ = 2 τ 0 is Kπ lifetime τ + (τ ) is lifetime for CP+ final states of D 0 (D 0 ) KK and ππ Mixing (and CPV) studied with K - π +, K + K - and π π + at Belle: y CP CPV τ ( K τ ( K : A Γ π K + + Γ( D = Γ( D ) 1 ) 0 0 = no CPV K K Γ y = 2Γ K K + + ) Γ( D ) + Γ( D 0 0 K K Same for ππ K K + + ) ) Amir Rahimi APS

29 Decay Time Fit Simultaneous binned likelihood fit to KK/Kπ/ππ final states Parameters to vary include τ D0, y cp, some of the resolution func. parameters and the normalizations Quality of fit: c 2 =1.084 (289) Amir Rahimi APS

30 Mixing Results with K - π +, K + K - and π π + at Belle Results Belle preliminary, 540 fb -1 y CP = 1.31 ± 0.32 ± 0.25 % 3.2 σ (stat.+syst.) 4.1 σ (stat.) Clear evidence for D 0 -D 0 mixing To measure CPV, fit for τ D of D0 and D0 separately: A G = 0.01 ± 0.30 ± 0.15 % Consistent with no CPV hep-ex/ Submitted to PRL Amir Rahimi APS

31 Summary I: R M and Y cp E.M. Aitala et al. (E791), PRL 77, 2384 (1996) C. Cawlfield et al. (CLEO II), PRD 71, (2005) B. Aubert et al. (BABAR), PRD 70, (2004) K. Able et al. (Belle), PRD 72, , 2005 Statistical and systematic errors assumed uncorrelated preliminary E791, PRL 83, 32 (1999) FOCUS, PLB 485, 62 (2000) CLEO, PRD 65, (2002) Belle, PRL 88, (2002) BABAR, PRL 91, (2003) Belle, hepx-ex/ Symmetrized statistical, systematic errros stat. errors for two Belle analysis have correlation= all systematic errors assumed uncorrelated preliminary Many Thanks to Heavy Flavor Averaging Group (HFAG) 2007 Amir Rahimi APS

32 Summary II Mixing contours from 2006 PDG Kπ decay the dominant mode in the search for mixing CP lifetimes sensitive to measuring y Semileptonic sensitive to R M = (x 2+ y 2 )/2 PDG % CL allowed CPV allowed y CP =( )% d Kp =0 o assumed d Kp ~ 0 o : measured Amir Rahimi APS2007 by CLEO 32

33 Summary II Assuming CP conservation BaBar has found evidence for mixing at 3.9σ CL using D 0 Kπ decay mode (384 fb -1 ) y cp by Belle also evidence for mixing at 3.2σ CL (540 fb -1 ) Mixing is observed Most sensitive measurement of x by Belle (D 0 K s ππ) A precision measurement of cosδ needed to express mixing in x and y CLEO-c quantum correlation BaBar and Belle B-factories Are also charm factories Searches for CP violation Improved techniques More data hep-ex/ Submitted To PRL(Belle) hep-ex/ Submitted To PRL (BaBar) v1 [hep-ex], Moriond EW/QCD 2007(Belle) Updated with new results for this talk (HFAG plots will be available soon) 95% CL allowed CPV allowed Belle y cp (1s) Belle y cp BaBar Kp Belle K s pp d Kp =0 o assumed d Kp ~ 0 o : measured Amir Rahimi APS2007 by CLEO 33

34 Recent Theoretical Work D-Dbar Mixing And New Physics: General Considerations and Constraints on the MSSN (M. Ciuchiniet al) hep-ph/ v1 Lessons from BaBar and Belle measurements of D0- D0bar mixing parameters, (Y. Nir) hep-ph/ v1 Littlest Higgs Model with T-Parity Confronting the New Data on D0-D0bar Mixing,(M. Blanke et al) hep-ph/ v1 Basics of D0-D0bar Mixing, (P. Ball) hep-ph/ v1 Amir Rahimi APS

35 Extra Slides Amir Rahimi APS

36 Comparison of Results Amir Rahimi APS

37 Previous BaBar Kπ Analysis Fully consistent with previous BaBar analysis Best fit 1σ 384 fb -1 2σ 3σ 4σ 5σ y' / PRL 91, fb -1 CPV allowed CP conserved x' 2 /10-3 Amir Rahimi APS

38 Kπ Analysis from Belle Last year Belle published analysis of Kp decays: PRL 96, fb -1 no-mixing excluded at 2σ Amir Rahimi APS

39 Kπ Analysis from Belle Last year Belle published analysis of Kπ decays: PRL 96, fb -1 Results consistent within 2σ: BaBar 1σ stat. only BaBar 2σ BaBar 3σ no-mixing excluded at 2σ (0,0) Belle 2σ statistical Amir Rahimi APS

40 Belle Results from Moriond Belle presented two new mixing results at Moriond EW: Dalitz analysis of D 0 K s ππ 540 fb -1 no-mixing excluded at 2.4σ Amir Rahimi APS

41 Belle Results from Moriond Belle presented two new mixing results yesterday at Moriond EW: Dalitz analysis of D 0 K s ππ 540 fb -1 Compare assuming δ=0: (x'=x, y'=y) 384 fb -1 Best fit no-mixing excluded at 2.4σ Within 1σ Amir Rahimi APS

42 Belle Results from Moriond Lifetime ratio in D 0 KK/ππ to Kπ 540 fb -1 K + K /π + π are CP-even eigenstates If no CP violation, directly measures lifetime of mass eigenstate Also evidence of D 0 mixing! Amir Rahimi APS

43 Belle Results from Moriond Lifetime ratio in D 0 KK/ππ to Kπ Compare assuming δ=0: 540 fb -1 (x'=x, y'=y) 384 fb -1 Best fit Belle (1σ) Within 2σ, less if δ 0 Also evidence of D 0 mixing! Amir Rahimi APS

44 Single-tag and Double-tag rates Hadronic rates (flavored and CP eigenstates) depend on mixing/dcsd. Semileptonic modes (r = δ = 0) resolve mixing and DCSD. Also measure BF s simulatenously Data clearly favors QC interpretation showing constructive and destructive interference and no effect as predicted CLEO-c Rate enhancement factors, to leading order in x, y and r 2 : f f l- CP+ f R M /r 2 1+r 2 (2-(2cosδ) 2 ) 1 1+r (2cosδ) l+ 1 1 CP+ 0 CP- - CP- 1-r (2cosδ) X 1+ ry (2cosδ) 1 1-y 1+y Ratio! Amir Rahimi APS

45 Several Other Validation Studies Fit to MC with no mixing No signal found Fit not biased Fit to MC with mixing Fit reproduces the signal Fit not biased Fit RS data for mixing No signal found D 0 decay time distribution is described properly Tested the coverage of -2 LogL Generated >10000 toys without mixing to test coverage Toys expected consistent with number observed LL is χ 2 distributed for 2-DOF -2 lnl gives correct frequentist coverage Amir Rahimi APS

46 Validation: Coverage of -2 LogL Generated >10000 toys without mixing to test coverage -2 lnl gives correct frequentist coverage 1σ 2σ 3σ 4σ #toys to the greater than line #toys expected greater than line, if LL is distributed as a χ 2 for 2 DOF observed in data Amir Rahimi APS

47 CPV Allowed Contours Fit D 0 and D 0 separately: x +2 : (-0.24±0.43±0.30)x10-3 x -2 : (-0.20±0.41±0.29)x10-3 y + : (9.8±6.4±4.5)x10-3 y - : (9.6±6.1±4.3)x D 0 D A D =(-2.1±5.2±1.5)% A significant difference in (+), (-) fits would suggest CP violation No evidence for CP violation found Amir Rahimi APS

48 Decay Time Fit Belle preliminary, 540 fb -1 Lifetime distribution Resolution function: Resolution fucn. Background term from normalized distribution of event proper time uncertainty σ t ideally, each σ i represents Gaussian p.d.f. distribution of pulls? p.d.f. = sum of 3 Gaussians for each σ i Common offset Scale factor R(t) studied in details with D 0? K - π + and dedicated MC samples, including slight changes in running conditions (two SVD detectors, small misalignments) Amir Rahimi APS