1. 1 CLEO-c Measurements of Purely Leptonic Decays of Charmed Mesons & other Wonders Sheldon Stone, Syracuse University

2. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 2 Leptonic Decays: D  + 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

3. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 3 New Physics Possibilities Besides the obvious interest in comparing with Lattice & other calculations of f P there are NP possibilities Another Gauge Boson could mediate decay Or leptoquarks (see Kronfeld’s talk) Ratio of leptonic decays could be modified e.g. in Standard Model If H ± couples to M 2  no effect See Hewett [hep- ph/9505246] & Hou, PRD 48, 2342 (1993).

4. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 4 New Physics Possibilities II Leptonic decay rate is modified by H ± Can calculate in SUSY as function of m q /m c, In 2HDM predicted decay width is x by Since m d is ~0, effect can be seen only in D S From Akeroyd See Akeryod [hep-ph/0308260] = meas rate/SM rate tan  /M H

5. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 5 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 Continuum ~12 nb  Ease of B measurements using "double tags“  B A = # of A/# of D's World Ave

6. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 6 Technique for D +   + Fully reconstruct a D -, and count total # of tags Seek events with only one additional oppositely charged track and no additional photons > 250 MeV (to veto D +   +  o ) Charged track must deposit only minimum ionization in calorimeter (< 300 MeV case 1) Compute MM 2. If close to zero then almost certainly we have a   decay. We know E D + =E beam, p D + = - p D -

7. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 7 D - Candidates (in 281 pb -1 ) # of tags = 158,354±496, includes charge-conjugate modes

8. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 8 The Missing Mass Squared To find signal events, we compute Monte Carlo Signal  Monte Carlo Signal  → 

9. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 9 Measurement of f D + Data: 50 events in the signal region in 281 pb -1 Mode# Events +0+0 1.40±0.18±0.22 ++ 0.33±0.19±0.02        1.08±0.15±0.16 Other D +, D o <0.4, <0.4 @ 90% c.l. Continuum <1.2 @ 90% c.l. Total Backgrounds B (D +  e +  <2.4x10 -5 @ 90% c.l. |V cd |=.2238

10. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 10 Systematic Errors Source of Error % Finding the   track 0.7 Minimum ionization of   in EM cal 1.0 Particle identification of   1.0 MM 2 width 1.0 Extra showers in event > 250 MeV 0.5 Background 0.6 Number of single tag D + 0.6 Monte Carlo statistics 0.4 Total 2.1

11. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 11 Upper limit on D + →  + By using intermediate MM 2 region B (D + →  + )<2.1x10 -3 where 2.65 is SM expectation both at 90% c.l E cal < 300 MeV E cal > 300 MeV

12. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 12 Measurements of f Ds Two separate techniques. [Here expect in SM:  (D S →  +  D S →  +  (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 find the muon or pion & apply kinematical constraints (mass & energy) to resolve this ambiguity & improve resolution (use 314 pb -1, results are published) (2) Find D S + →  +  → e +  opposite a D S - tag (use 298 pb -1, results are final arXiv:0712.1175 )

13. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 13 Invariant masses D S studies done at E cm =4170 MeV To choose tag candidates: Fit distributions & determine  Cut at ±2.5  Define sidebands to measure backgrounds 5-7.5  Total # of Tags = 31,302± 472 (stat) K * K * from K s K     

14. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 14 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

15. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 15 The MM 2 To find the signal events, we compute Monte Carlo Signal  Monte Carlo Signal  → 

16. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 16 MM 2 In Data Clear D S + →  + signal for case (i) Most events <0.2 GeV 2 are D S →  +,  →  + in cases (i) & (ii) No D S →e + seen, case (iii) Electron Sample < 0.3GeV in CC > 0.3GeV in CC 92 events 31 events 25 events mK o2

17. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 17 Branching Ratio & Decay Constant D S + →  + 92  signal events, 3.5 background, use SM to calculate  yield near 0 MM 2 based on known  ratio B(D S + →  +  (0.597±0.067±0.039)% D S + →  +  + →  + Sum case (i) 0.2 > MM 2 > 0.05 GeV 2 & case (ii) MM 2 < 0.2 GeV 2. Total of 56 signal and 8.6 bkgrnd B(D S + →  +  (8.0±1.3±0.4)% By summing both cases above, find B eff (D S + →  +  (0.638±0.059±0.033)%  f Ds =274 ± 13 ± 7 MeV, for |V cs | =0.9737 B(D S + →e +  x10 -4

18. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 18 B (D S + →  +  Systematic errors

19. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 19 Measuring D S + →  +  + → e + B(D S + →  +  B  + → e +  1.3%  is “large” compared with expected B(D S + →Xe +  We will be searching for events opposite a tag with one electron and not much other energy Opt to use only a subset of the cleanest tags

20. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 20 Measuring D S + →  +  + → e + 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 + →  +    (6.17±0.71±0.36)%  f Ds =273 ± 16 ± 8 MeV 400 MeV

21. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 21 & Weighted Average: f Ds =274±10±5 MeV, the systematic error is mostly uncorrelated between the measurements Using M. Artuso et al., Phys.Rev. Lett. 95 (2005) 251801 f Ds /f D + =1.23±0.10±0.03  (D S + →  +  (D S + →  +  11.0±1.4±0.6, SM=9.72, consistent with lepton universality Radiative corrections i.e. D S + →  +  not included, estimated to be ~1% (see Burdman et al., PRD 51, 11 (1995)

22. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 22 Comparison with Other Experiments CLEO-c is most precise result to date for both f Ds & f D + preliminary Manchester EPS

23. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 23 Comparisons with Theory We are ~3  above Follana et al. Either: Calculation is wrong There is new physics that interferes constructively with SM Note: No value of M H is allowed in 2HDM at 99.5% c.. Comparing measured f D S /f D + with Follana prediction we find m H >2.2 GeV tan  Using Follana ratio find |V cd /V cs |=0.217±0.019 (exp) ±0.002(theory)

24. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 24 Projections We will almost triple the D + sample, including some improvements in technique, error in f D + should decrease to ~9 MeV We doubled the D S sample, improved the technique, expect error in f Ds to decrease to ~7 MeV

25. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 25 Discover of D S +  pn Use same technique as for  , but plot MM from a detected proton No background First example of a charm meson decaying into baryons neutron mass

26. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 26 Semileptonic Decays Precise B (D o  K - e + ) & B (D o  - e + )

27. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 27 Form Factors: D o  K - e +

28. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 28 D o  - e +

29. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 29

30. 30 The End

31. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 31 Check: B (D S + →K + K o ) Do almost the same analysis but consider MM 2 off of an identified K + Allow extra charged tracks and showers so not to veto K o decays or interactions in EM Signal verifies expected MM 2 resolution Find (2.90±0.19±0.18)%, compared with result from double tags (3.00±0.19±0.10)%

32. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 32 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 314 pb -1 of data M BC from D S * Signal MC Beam Constrained Mass (GeV)

33. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 33 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

34. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 34 Combining Semileptonics & Leptonics Semileptonic decay rate into Pseudoscalar: Note that the ratio below depends only on QCD:

35. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 35 Background Samples Two sources of background A) Backgrounds under invariant mass peaks – Use sidebands to estimate In  +  signal region 3.5 background (92 total) bkgrnd MM 2 <0.20 GeV 2 = 9.0±2.3 B) Backgrounds from real D S decays, e.g.      , or D S →  +,  →  +  o  < 0.2 GeV 2, none in  signal region B(D S →     ) < 1.1x10 -3 &  energy cut yields <0.2 evts Signal region High SB region Low SB region Backgrounds from real D S +

36. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 36 Sum of D S + →  +  +,  →  + As we will see, there is very little background present in any sub-sample for MM 2 <0.2 GeV 2 148 events Sum of case (i) & case (ii) K0+K0+  signal line shape

37. QCD & High Energy Hadronic Interactions, Moriond, March 8 – 15, 2008 37 Radiative Corrections Not just final state radiation which is already corrected for. Includes D → D* →  D→    Based on calculations of Burdman et al.  (D (S) + →   )  (D (S) + →   )  ~ 1/40 – 1/100 Burdman etal ~1% Using narrow MM 2 region makes this much smaller Other authors in general agreement, see Hwang Eur. Phys. J. C46, 379 (2006), except Korchemsky, Pirjol & Yan PRD 61, 114510 (2000)