1. Strong Phase Measurements – Towards g at CLEO-c Andrew Powell (University of Oxford) On behalf of the CLEO-c collaboration D measurements relevant to determining g via B ±  DK ± D  K p, K ppp, K pp 0 (ADS) D  K S pp (Binned Dalitz)

2. 2 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg g is unique: only CP violation parameter than can be measured via both ‘ tree ’ and ‘ loop ’ B decays Tree-level: g SM Loop-level: g SM + g NP Comparison of these measurements sensitive to New Physics (NP) Tree-level measurement currently poorly constrained Why Measure Tree-Level g ? [CKM Fitter, Summer 2009] 1

3. 3 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Rates dependent on the B -specific parameters: r B d B g …and D-specific parameters (analogous to those of B ): r D d D g from B ±  DK ± 2 Methodology and formalism given in previous talk (S. Ricciardi) Strong-phases, d D, directly accessible in Quantum-Correlated D-decays

4. 4 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Introduction to CLEO-c Detector at the Cornell Electron Storage Ring (CESR) Operated at energies equal to and above cc threshold Relevant data sets for precision CKM measurements: E CM = 4170 MeV L int ~ 600 pb -1 Determination of form factor f Ds at CLEO-c, a critical test of LQCD and sensitive to New Physics [ see talks by Rademacker & Spradlin] y (3770) L int = 818 pb -1 Important for analyses discussed in this talk 3 Cornell University, Ithaca, NY, USA

5. 5 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Introduction to CLEO-c Detector at the Cornell Electron Storage Ring (CESR) Operated at energies equal to and above cc threshold Relevant data sets for precision CKM measurements: E CM = 4170 MeV L int ~ 600 pb -1 Determination of form factor f Ds at CLEO-c, a critical test of LQCD and sensitive to New Physics [ see talks by Rademacker & Spradlin] y (3770) L int = 818 pb -1 Important for analyses discussed in this talk ( C = -1) y (3770) e + e -  y(3770)  D 0 D 0 Quantum-Correlated System, conserving C = -1 Enables ‘ CP -tagging ’ Reconstructing one D -meson in a CP -eigenstate, can infer the ‘ opposite-side ’ D -meson to be of opposite CP Perks to threshold running: Very clean – no fragmentation particles Allows for reconstruction of unseen particles ( K L ) y (3770)  D 0 (K ppp )D 0 ( pp ) 3 Cornell University, Ithaca, NY, USA

6. ‘ADS’ Type Measurements

7. 7 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg 2-Body ADS f(D) = non- CP eigenstate (e.g. K ¡ p ± ) Defining strong-phase difference: Generalised matrix element: 4 [Phys Rev Lett 78, 3257 (1997)]

8. 8 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg 2-Body ADS f(D) = non- CP eigenstate (e.g. K ¡ p ± ) Defining strong-phase difference: Generalised matrix element: Generalised rate (trivial phase space): Four charge combinations  2 suppressed (high g sens.) + 2 favoured rates (low g sens.) What about multi-body, non- CP eigenstates of the D -meson? [Phys Rev Lett 78, 3257 (1997)] 4

9. 9 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Multi-Body ADS f(D) = non- CP eigenstate (e.g. K ¡ p ± p 0 ) Defining strong-phase difference: Generalised matrix element: 5 Must now consider the amplitudes at each point in multi-body phase space ( x ) [Phys Rev. D 68, 033003 (2003)]

10. 10 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Multi-Body ADS Must now consider the amplitudes at each point in multi-body phase space ( x ) Defining strong-phase difference: Generalised matrix element: Generalised rate (integrating over ALL multi-body phase space): The “Coherence Factor” 5 [Phys Rev. D 68, 033003 (2003)] f(D) = non- CP eigenstate (e.g. K ¡ p ± p 0 )

11. 11 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Quantum Correlations at y (3770) 6 e+e+ e-e- y ’’ D (f)D (f) D (g)D (g) Generalised double-tagged (DT) rate: Q M = 1 – (x 2 – y 2 )/2 R M = (x 2 + y 2 )/2 To access d K p, consider K p tagged against a CP eigenstate : [ Need info on r D – see later]

12. 12 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Quantum Correlations at y (3770) 6 e+e+ e-e- y ’’ D (f)D (f) D (g)D (g) Generalised double-tagged (DT) rate: Q M = 1 – (x 2 – y 2 )/2 R M = (x 2 + y 2 )/2 To access d K p, consider K p tagged against a CP eigenstate : [ Need info on r D – see later] To access d K pp, consider K pp 0 tagged against a CP eigenstate : To access R Kpp, consider K pp 0 tagged against itself, like-charge Kaons:

13. 13 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Quantum Correlations clearly seen! 7 d K p Measurement [Phys Rev. D 78, 012002 (2008)] [Phys Rev. Lett. 100, 221801 (2008)] Extensive d K p and charm-mixing ( x, y ) measurement Consider both double- (DT) and single-tags (ST) Compare coherent/incoherent B ’s [Phys Rev. D 73, 034024 (2006)] QC rate incoherent rate r Kp+Kp+ e+e+ CP+CP - Kp+Kp+ R M / R WS Kp-Kp- 1+2R WS - 4rcos d ( rcos d  + y) e-e- 1- r ( ycos d  + xcos d ) 1 CP+ 1- ( 2rcos d  + y) / (1 + R WS ) 1+ y0 CP- 1+ ( 2rcos d  + y) / (1 + R WS ) 1+ y20 ST 1111 R WS = r 2 + ry’ + R M Avg.(Yield / No-QC prediction) Single Tags Combine inputs + errors matrices in a c 2 fit External inputs: R WS & R M (to determine r D and extract cos d D ) B ’s ( K p, CP -eigenstates) 0 1 2

14. 14 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg d K p Result (281 pb -1 ) [Phys Rev. D 78, 012002 (2008)] [Phys Rev. Lett. 100, 221801 (2008)] 8 [Phys Rev. D 73, 034024 (2006)] Extended fit with a likelihood scan of the physically allowed region leads to a measurement of: Fit result important component in average of charm mixing Result to be updated using full 818 pb -1 and with additional tags

15. 15 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg R f & d f Measurements [Phys Rev. D 80, 031105(R) (2009)] 9 r K-p+p0K-p+p0 K+p-K+p- K + p - p 0 (OS) [N DD ] K - p + p 0 (LS) K - p + (OS) [N DD ] CP± [ e rec. B (D  CP )] QC rate incoherent rate Multi-body ADS modes considered: f = K ¡ p ± p 0 & K ¡ p ± p + p - NEW y f ’ = ycos d f - xsin d f r D ’ = (r K pp /r K p ) DTs using full 818 pb -1 dataset f tagged against CP, f, f Also, K p tagged against CP (Normaliastion) Double-Tag D  K3p vs DKLp0DKLp0 Bkg

16. 16 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg R f & d f Measurements [Phys Rev. D 80, 031105(R) (2009)] 9 Multi-body ADS modes considered: f = K ¡ p ± p 0 & K ¡ p ± p + p - NEW K pp 0 : K ppp: DTs using full 818 pb -1 dataset f tagged against CP, f, f Also, K p tagged against CP (Normaliastion) Double-Tag D  K3p vs DKLp0DKLp0 Bkg y f ’ = ycos d f - xsin d f r D ’ = (r K pp /r K p ) r K-p+p0K-p+p0 K+p-K+p- K + p - p 0 (OS) [N DD ] K - p + p 0 (LS) K - p + (OS) [N DD ] CP± [ e rec. B (D  CP )] QC rate incoherent rate

17. 17 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg R K pp & d K pp Results 10 [Phys Rev. D 80, 031105(R) (2009)] NEW R K pp = 0.84 ± 0.07 d K pp = (227 )   14  17 Very coherent! Almost at ‘2-body’ limit Good news for g ADS measurement Interference term will be large High sensitivity to g

18. 18 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg R K3 p & d K3 p Results 11 [Phys Rev. D 80, 031105(R) (2009)] NEW R K3 p = 0.33 d K3 p = (114 )   26  23  0.26  0.23 Low coherence preferred Low direct sensitivity to g Paradoxically, also goodnews for ‘global’ g measurement B  D(K3 p )K rates will therefore be highly sensitive to r B, which is a very valuable constraint for sister B  DK analyses Poorly know

19. 19 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Impact of CLEO-c at LHCb [LHCb-2008-31] 12 Expected g precision at LHCb with 2 fb -1 of data (1 year) for ADS modes alone: Significant improvements in sensitivity when using CLEO-c results Using R K3 p & d K3 p results - equivalent to a doubling of LHCb data! Precision including K pp 0 yet to be studied

20. ‘Dalitz’ Type Measurements

21. 21 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg g from B  D(K S pp )K Dalitz Three ingredients to measurement: D flavour Amplitude Model + + Current best constraints on g from Dalitz plot analyses at B A B AR & Belle Belle: arXiv:0804.2089 With enough statistics (LHCb), measurement becomes systematically limited Need an alternative, model-free, method… B A B AR (383M bb) B ELLE (657M bb) D 0  K S pp B   D(K S pp )K  13

22. 22 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Model-Independent Method [Phys Rev. D 68, 054018 (2003)] [Euro. Phys. J. C 55 (2008) 51] [Euro. Phys. J. C 47 (2006) 347] 14 T i known from flavour-tagged D sample ( D * ) Dd D = strong phase-difference between D & D c i = i s i = i Counting experiment proposed by Giri et al., developed by Bondar & Poluektov Consider B ± events in bin i of Dalitz plot:

23. 23 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Model-Independent Method [Phys Rev. D 68, 054018 (2003)] [Euro. Phys. J. C 55 (2008) 51] [Euro. Phys. J. C 47 (2006) 347] s 12 [GeV 2 ] s 13 [GeV 2 ] Bin Number 14 T i known from flavour-tagged D sample ( D * ) Dd D = strong phase-difference between D & D Choosing bins of ‘expected’ similar Dd D maximises statistical precision to g Small loss in statistical sensitivity w.r.t. unbinned method… but no model error! [Model = B A B AR PRL 95 121802 (2005)] Dd D = 180° Dd D = 0° c i = i s i = i Counting experiment proposed by Giri et al., developed by Bondar & Poluektov Consider B ± events in bin i of Dalitz plot:

24. 24 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Model-Independent Method [Phys Rev. D 68, 054018 (2003)] [Euro. Phys. J. C 55 (2008) 51] [Euro. Phys. J. C 47 (2006) 347] Counting experiment proposed by Giri et al., developed by Bondar & Poluektov Consider B ± events in bin i of Dalitz plot: s 12 [GeV 2 ] s 13 [GeV 2 ] Dd D = 180° Dd D = 0° Bin Number Can be measured directly in quantum correlated decays at y (3770) 14 T i known from flavour-tagged D sample ( D * ) Dd D = strong phase-difference between D & D Choosing bins of ‘expected’ similar Dd D maximises statistical precision to g Small loss in statistical sensitivity w.r.t. unbinned method… but no model error! [Model = B A B AR PRL 95 121802 (2005)] c i = i s i = i

25. 25 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg CLEO-c K S,L pp Analysis 15 As shown previously, cos ( Dd ) accessible from CP -tagged decays: sin ( Dd ) accessible from ‘double-Dalitz’ plot: Use all 818 pb -1 of y (3770) Flavour Tags ( T i ): ~ 20k CP Tags ( c i ): ~ 1,600 Double K 0 pp ( c i & s i ) : ~ 1,300 [Phys Rev. D 80, 032002 (2009)] NEW S/B ~ 10 – 100 depending on tag mode

26. 26 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg On Using K L pp [Phys Rev. D 80, 032002 (2009)] NEW 16 CP  K S pp  CP + K L pp Source of additional statistics! Approx. equality seen in data However, a correction term: O ( tan 2 q C ) c i  c i ’ c i, s i from K S pp c i ’ s i ’ from K L pp Events / 0.05 GeV 2 M 2 ( pp ) [GeV 2 ] Events / 0.05 GeV 2 M 2 ( pp ) [GeV 2 ] Events / 0.05 GeV 2 M 2 ( pp ) [GeV 2 ] K L pp K S pp CP  tags CP  tags Determine D c i = c i -c i ’, D s i = s i -s i ’ Introduces small model dep. D c i / D s i floated as a c 2 term in fit

27. 27 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg On Using K L pp [Phys Rev. D 80, 032002 (2009)] NEW 16 M 2 (K L p + ) [GeV 2 ] M 2 (K L p - ) [GeV 2 ] M 2 (K S p + ) [GeV 2 ] M 2 (K L p - ) [GeV 2 ] M 2 (K L p + ) [GeV 2 ] M 2 (K S p - ) [GeV 2 ] M 2 (K S p + ) [GeV 2 ] CP  K S pp  CP + K L pp Source of additional statistics! Approx. equality seen in data However, a correction term: O ( tan 2 q C ) c i  c i ’ c i, s i from K S pp c i ’ s i ’ from K L pp Determine D c i = c i -c i ’, D s i = s i -s i ’ Introduces small model dep. D c i / D s i floated as a c 2 term in fit K L pp CP  tags K S pp CP  tags CP  tags CP  tags

28. 28 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg CLEO-c Results: c i & s i [Phys Rev. D 80, 032002 (2009)] NEW 17 Result  stat  sys  ( K L pp K S pp syst) Statistical uncertainties dominant c i better determined than s i Results also available for c i ’ & s i ’ Broad agreement with model predictions [Model = B A B AR PRL 95 121802 (2005)] g Uncertainty: s CLEO-input ( g ) = 1.7  (recall model error = 7  )

29. 29 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Conclusions & Outlook 18 Several CLEO-c results available applicable to g -type analyses D  K p : strong phase difference [~1/3 of total y (3770) data used] D  K pp o, Kppp : coherence factors & strong phase differences D  K S(L) pp : c i (‘) & s i (‘) in 8 bins of equal Dd D width All y (3770) data used These results provide invaluable input to the g measurement See LHCb- g talk [S. Ricciardi] More yet to come! D  K p : full 818 pb -1 result D  K S(L) pp : optimal binning for maximal g -sensitivity D  K S(L) KK : c i (‘) & s i (‘) measurements D  K S(L) ppp 0 : possible analysis

30. Backup

31. 31 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg External Inputs to Fit [Phys Rev. D 78, 012002 (2008)] [Phys Rev. Lett. 100, 221801 (2008)] [Phys Rev. D 73, 034024 (2006)] External inputs improve y and d K p precision All correlations amongst measurements included in fit Standard fit includes: Info needed to obtain cos d : R WS = r 2 + ry’ + R M R M = (x 2 + y 2 )/2 xsin d = 0  y’~ ycos d K p and CP -eigenstate B s Extended fit averages y and y ’ CP+ lifetimes ( y ) K S p + p - Dalitz analysis ( x, y ) K p CP -conserving fits ( y, r 2, R M ):

32. 32 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg External Fit Likelihoods [Phys Rev. D 78, 012002 (2008)] [Phys Rev. Lett. 100, 221801 (2008)] [Phys Rev. D 73, 034024 (2006)]

33. 33 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg r -Observable Results [Phys Rev. D 80, 031105(R) (2009)] NEW Systematic for r CP dominated by internal uncertainty associated w/ the e rec x B (D  CP ) normalisation Finite CP -tagged K p statistics Systematic for all other observables are small, and dominated by knowledge of B s Extracted from PDG Observables dependent on x, y, d K p, r D in addition to parameters of interest Perform c 2 fit, placing external constraints on x, y, d K p parameters Constraints taken from HFAG Correlations included

34. 34 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg K pp 0 Likelihood Scans [Phys Rev. D 80, 031105(R) (2009)] NEW r CP r LS r Kp, LS All Constraints

35. 35 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg K3 p Likelihood Scans [Phys Rev. D 80, 031105(R) (2009)] NEW r CP r LS r Kp, LS All Constraints

36. 36 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg Colour Suppressed r B ~ 0.1 Extraction through interference between b  u and b  c transitions Comparison of B - and B + rates allow g to be extracted D 0 specific parameters also contribute to B - and B + rates e.g. strong-phase differences, d D Can be accessed via Quantum-Correlated D-decays r D & d D analogous to r B & d B. For multi-body final states these parameters vary over phase space g from B ±  DK ± Require both D 0 and D 0 to decay to a common final state, f(D) f(D) = K p, K ppp, K pp 0, K S pp, …

37. 37 Andrew Powell, University of Oxford 7 th -11 th September 2009, Beauty ‘09, Heidelberg CLEO-c Detector