1. 1 Charm Decays at Threshold Sheldon Stone, Syracuse University

2. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 2 What We Hope to Learn Purely Leptonic Charm Decays D→ + : Check QCD calculations including Lattice (LQCD) Semileptonic decay rates & form-factors: QCD checks and the reverse, use QCD to extract V cq Hadronic Charm Decays Engineering numbers useful for other studies B  Charm is dominant, so knowing lots about charm is useful, e.g. absolute B ’s, resonant substructure, phases on Dalitz plots, especially versus CP eigenstates Learn about Strong Interactions, esp. final state interactions Charm Mixing & CP Violation Can we see new physics? SM mixing & CP violation is small, so new effects don’t have large SM background as in the K or B systems ALL RESULTS SHOWN HERE ARE FROM CLEO-C ALMOST ALL ARE PRELIMINARY. Exceptions will be noted Due to lack of time, many interesting results are omitted

3. 3 Absolute Charm Meson Branching Ratios & Other Hadronic Decays D o, D + & D S

4. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 4 Experimental methods  DD production at threshold: used by Mark III, and more recently by CLEO-c and BES-II.  Unique event properties  Only DD not DDx produced  Large cross sections:  (D o D o ) = 3.72  0.09 nb  (D + D - ) = 2.82  0.09 nb  (D S D S *) = 0.9 nb  Ease of B measurements using "double tags“  B A = # of A/# of D's World Ave Continuum ~14 nb

5. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 5 Charm Cross-Sections

6. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 6 D +  K -  +  + & D -  K +  -  - 2002 events D +  K -  +  + at the  ´´ (CLEO-c) Single tags Double tags D +  K -  +  + or D -  K +  -  -, 80,865 events 281 pb -1 of data at  (3770)

7. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 7 Absolute B Results for D + & D o 57 pb -1 B (D +  K -  +  + ) CLEO-c (not in average) B (D o  K -  + ) World avg 3.3 9.43  0.31 PDG 6.59.2±0.6 CLEO-c 3.9 9.52  0.25  0.27 SourceError(%) B (%) World avg 1.9 3.85  0.07 PDG 2.43.81±0.09 CLEO-c 3.1 3.91  0.08  0.09 SourceError(%) B (%) 2.2% projected error 1.8% projected error For 281pb -1 (systematics limited):

8. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 8 CLEO D S + Results at 4170 MeV Since e + e -  D S *D S, the D S from the D S * will be smeared in beam- constrained mass.  cut on M BC & plot invariant mass (equivalent to a p cut) We use ~200 pb -1 of data M BC from D S * Signal MC

9. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 9 Invariant masses K-K++K-K++ KsK+KsK+    Inv Mass (GeV)  +   K * K * from K s K -    +  Total # of Tags = 19185 ±325 (stat)

10. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 10 Single & Double D S + Tags in 200 pb -1 mass D S - (GeV) mass D S + -mass D S - mass D S + (GeV) Modes: Different selection criteria than other analyses Clean double tag signal

11. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 11 Absolute B Results for D S + 200 pb -1 About ±6% error D S  + is difficult to quote because of interferences in KK  Dalitz plot – K*K, f 0 , etc… 1.50±0.9±0.5 5.57±0.30±0.19 5.62±0.33±0.51 1.12±0.08±0.05 1.47±0.12±0.14 4.02±0.27±0.30 m(K + K - ) in KK  signal Partial branching fraction ±10 MeV around m(  1.98±0.12±0.09 % ±20 MeV around m(  2.25±0.13±0.12 % (need x2 for  →K + K - )

12. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 12 D + →  +  -  + Dalitz Results ModeFit Values Relative Amplitude Phase (degrees) Fit Fraction (%)  (770)  + 1.0020.0±2.3±0.9 f 0 (980)  + 1.4±0.2±0.212±10±54.1±0.9±0.3 f 2 (1270)  + 2.1±0.2±0.1237±6±318.2±2.6±0.7 f 0 (1370)  + 1.3±0.4±0.2-21±15±142.6±1.8±0.6 f 0 (1500)  + 1.1±0.3±0.2-44±13±163.4±1.0±0.8  pole 3.7±0.3±0.2-3±4±241.8±1.4±2.5 Limits on Other Contributing Modes  (1450)  + 0.9±0.551±22<2.4 f 0 (1710)  + 1.0±1.5-17±90<3.5 f 0 (1790)  + 1.0±1.123±58<2.0 Non- resonant 0.17±0.14-17±90<3.5 I=2  +  + S-wave 0.17±0.1423±58<3.7  Consistency with E791 - E791 BW s Fit Fraction = (46.3±9.0±2.1)%   pole provides a good description of the DP Likelihood Fit including: Amplitude, phase, spin-dependent PW (ie. BW), angular distribution, Blatt Weiskopf angular momentum penetration factor. 281pb -1, untagged Signal and background box in  E, m BC Dalitz plot statistics: N (π − π + π + ) ~2600 N (K s π + ) ~2240 N back ~ 2150

13. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 13 Inclusive D (s) Hadronic Decays  Inclusive ss rates expected to be higher for D s + than D 0 /D +.  CLEO-c measurements with 281 pb -1 D 0 /D + (3770 MeV) and 200 pb -1 D s + (4170 MeV).  Fully reconstruct one D (s), search for , ,  on the other side Much larger rates for D S as anticipated  includes feed-down from  ´. DS XDS X DS  XDS  X D s +   X B  (%) D0D0 9.4±0.4±0.6 DD 5.7±0.5±0.5 DSDS 23.7±3.1±1.9 B  ´ (%) D0D0 2.6±0.2±0.2 DD 1.0±0.2±0.1 DSDS 8.7±1.9±0.7 B  (%) D0D0 1.0±0.1±0.1 DD 1.1±0.1±0.2 DSDS 16.1±1.2±0.6 Invariant Mass (GeV) Mass Difference (GeV)  signal sideband Less than ½ of D S decays end up in ss mesons

14. 14 Leptonic & Semileptonic Decays

15. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 15 Leptonic Decays: D (s)  + Introduction: Pseudoscalar decay constants c and q can annihilate, probability is  to wave function overlap Example : _ In general for all pseudoscalars: Calculate, or measure if V Qq is known (s) or cs

16. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 16 Goals in Leptonic Decays Test theoretical calculations in strongly coupled theories in non- perturbative regime f B & f Bs /f B needed to improve constraints from  m d &  m S /  m d. Hard to measure directly (i.e. B    measures V ub f B  but we can determine f D & f Ds using D   and use them to test theoretical models (i.e. Lattice QCD)   Constraints from V ub,  m d,  m s & B  

17. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 17 New Measurements of f Ds Two separate techniques (1) Measure D S + →  + along with D S →  +,  →  +. This requires finding a D S - tag, a  from either D s * - →  D s - or D s * + →  +. Then finding the muon or pion using kinematical constraints (2) Find D S + →  +  → e +  opposite a D s - tag

18. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 18 Measurement of D S + →  + In this analysis we use D S *D S events where we detect the  from the D S *→  D S decay We see all the particles from e + e - → D S *D S,  D S (tag) +  + except for the We use a kinematic fit to (a) improve the resolution & (b) remove ambiguities Constraints include: total p & E, tag D S mass,  m=M(  D S )-M(D S ) [or  m= M(  )-M(  )] = 143.6 MeV, E of D S (or D S *) fixed Lowest  2 solution in each event is kept No  2 cut is applied

19. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 19 Tag Sample using  First we define the tag sample by computing the MM* 2 off of the  & D S tag Total of 11880±399±504 tags, after the selection on MM* 2. All 8 Modes Data

20. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 20 The MM 2 To find the signal events, we compute Signal  Signal  → 

21. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 21 Define Three Classes Class (i), single track deposits 300 MeV. (accepts 99% of muons and 60% of kaons & pions) Class (ii), single track deposits > 300 MeV in calorimeter & no other  > 300 MeV (accepts 1% of muons and 40% of kaons & pions) Class (iii) single track consistent with electron & no other  > 300 MeV

22. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 22 MM 2 Results from 200 pb -1 Clear D S + →  + signal for case (i) Will show that events <0.2 GeV 2 are mostly D S →  +,  →  + in cases (i) & (ii) No D S →e + seen, case (iii) Electron Sample DATA 200/pb <0.3GeV in CC DATA 200/pb >0.3GeV in CC 64 events 24 events 12 events Case (i) Case (ii)

23. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 23 Sum of D S + →  +  +,  →  + Two sources of background A) Backgrounds under invariant mass peaks – Use sidebands to estimate In  +  signal region 2 background (64 signal) Sideband bkgrnd 5.5±1.9 B) Backgrounds from real D S decays, e.g.  +  o  o, or D S →  +,  →  +  o  < 0.2 GeV 2, none in  signal region. Total of 1.3 additional events. B(D S →     ) < 1.1x10 -3 &  energy cut yields <0.1 evts Total background < 0.2 GeV 2 is 6.8 events, out of the 100 100 events Sum of case (i) & case (ii) K0+K0+  signal line shape

24. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 24 Branching Ratio & Decay Constant D S + →  + 64  signal events, 2 background, use SM to calculate  yield near 0 MM 2 based on known  ratio B(D S + →  +  (0.657±0.090±0.028)% D S + →  +  + →  + Sum case (i) 0.2 > MM 2 > 0.05 GeV 2 & case (ii) MM 2 < 0.2 GeV 2. Total of 36 signal and 4.8 bkgrnd B(D S + →  +  (7.1±1.4±0.03)% By summing both cases above, find B eff (D S + →  +  (0.664±0.076±0.028)%  f Ds =282 ± 16 ± 7 MeV B(D S + →e +  3.1x10 -4

25. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 25 Measuring D S + →  +  + → e + B(D S + →  +  B  + → e +  1.3%  is “large” compared with expected B(D S + →Xe +  Technique is to find  events with an e + opposite  D S - tags & no other tracks,  with  calorimeter energy < 400 MeV No need to find  from D S * B(D S + →  +    (6.29±0.78±0.52)%  f Ds =278 ± 17 ± 12 MeV 400 MeV Xe +

26. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 26 & Weighted Average: f Ds =280.1±11.6±6.0 MeV, the systematic error is mostly uncorrelated between the measurements (More data is on the way & systematic errors are being addressed) Previously CLEO-c measured M. Artuso et al., Phys.Rev. Lett. 95 (2005) 251801 Thus f Ds /f D + =1.26±0.11±0.03  (D S + →  +  (D S + →  +  9.9±1.7±0.7, SM=9.72, consistent with lepton universality D + →   K0+K0+  

27. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 27 Comparisons with Theory We are consistent with most models, more precision needed Using Lattice ratio find |V cd /V cs |= 0.22±0.03

28. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 28 Comparison with Previous Experiments CLEO-c is most precise result to date for both f Ds & f D + ? ? 280.1±11.6±6.0

29. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 29 Goals in Semileptonic Decays Either take V cq from other information and test theory, or use theory and measure V cq V cs use D  K  K*   to  measure form-factor shapes to distinguish among models & test lattice QCD predictions V cd use D  V cd & V cs with precise unquenched lattice predictions, + V cb would provide an important unitarity check V ub use D   to get form-factor for B , at same vv point using HQET (&  

30. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 30 Exclusive Semileptonic Decays u Best way to determine magnitudes of CKM elements, in principle is to use semileptonic decays. Decay rate  |V QiQf | 2  This is how V us ( ) and V cb (A) have been determined u Kinematics:  Matrix element in terms of form-factors (for D  Pseudoscalar +  For = e, f  (q 2 )  0: V QiQf

31. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 31 Form-Factor Parameterizations In general Modified Pole Series Expansion Hill & Becher, Phys. Lett. B 633, 61 (2006)

32. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 32 Untagged D  K(or  ) e  (281/pb)

33. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 33 New Tagged Results for 281 pb -1 Use U  E miss -|p miss | Branching Ratios ModeTagged (%)Untagged(%) DoDo K - e + 3.58±0.05±0.053.56±0.03±0.10  - e + 0.31±0.01±0.010.30±0.01±0.01 D+D+ K o e + 8.86±0.17±0.208.70±0.13±0.27  o e + 0.40±0.03±0.030.38±0.03±0.02

34. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 34 Form Factors: Tagged D→K e + D→  e + 0.22±0.05±0.02 0.17±0.10±0.05

35. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 35 Form-Factors Compared to Lattice Lattice predictions* D  e f + (0)=0.64±0.03±0.06   =0.44±0.04±0.07 D  Ke f + (0)=0.73±0.03±0.07   =0.50±0.04±0.07 * C. Aubin et al., PRL 94 011601 (2005) DATA FIT (tagged) LQCD DATA FIT (tagged) LQCD Assume V cd = 0.2238 Assume V cs = 0.9745

36. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 36 Discovery of D o →K  e + B(D o →K 1 (1270)e + )*B(K 1 (1270) →K -     ) = consistent with ISGW2 prediction

37. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 37 TCQA: The Quantum Correlation Analysis Because of quantum correlation between D 0 and D 0, not all final states allowed. This affects: total rate apparent branching fractions Two entangled causes: Interf. between CF and DCSD D mixing: single tag rates depend on y = B (CP+)  B (CP-). Can exploit coherence to measure DCSD and mixing. e  e    *  D 0 D 0 C =  1 KK KK KK KK KK KK KK K  l  CP+ K  l  CP- K  l  K  l  K  l  CP+CP- CP+ CP- interference forbidden by CP conservation forbidden by Bose symmetry maximal constructive interference From D. Asner & W. Sun [hep-ph/0507238]

38. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 38 Sensitivity with 1 fb -1 Sensitivities are comparable with present experiments Statistical errors dominate y, but are the ~= to systematic errors for x Can also use D o D o * events at higher energies

39. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 39 Sensitivities versus Increased Statistics Decay constants: statistics limited D + 7.5% for 281 pb -1 at 3770. Ultimate systematic limit may be ~1% D S 4.1% for 200 pb -1 at 4170. Ultimate systematic limit may be ~2% Dalitz analyses e.g. D o →CP vs. D o →K S     Statistics starved until at least~10 fb -1 Semileptonic Decays Branching ratios of Cabibbo favored & suppressed modes will be well known with 1 fb -1 Form-factors will need 10 fb -1 Rare modes will be statistics starved for a long time The Quantum Correlation Analysis will give some results with 1 fb -1, needs 100x

40. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 40 Conclusions Beginning to see accurate absolute B B(D o →K -  + )=(3.85±0.0.07)% not preliminary B(D + →K -  +  + )=(9.43±0.31)% not preliminary B(D S →K + K -  + )=(5.57±0.36)% preliminary not preliminary f Ds =280.1±11.6±6.0 MeV preliminary f Ds /f D + =1.26±0.11±0.03 preliminary Accurate semi-leptonic form-factors confronting QCD Much much more to do – Best wishes to BES

41. 41 The End

42. ITEP Meeting on the Future of Heavy Flavor Physics, July 24-25, 2006 42 Simp. Pole Mod. Pole Untagged: Form-Factor Results