1. 1 Measurement of f D + via D +   + Sheldon Stone, Syracuse University  D o D o, D o  K -  + K-K- K+K+ ++  K-K- K+K+ “I charm you, by my once-commended beauty” Julius Cæsar, Act II, Scene I

2. 2 Importance of Measuring f D + and f D u We can compare theoretical calculations of f D to our measurements and gain confidence in theory to predict f B u f B is necessary to translate measurement of B o -B o mixing into value for |V td |.  If we B +  +  was measured, then we would have a measurement of the product of |V ub | f B. Knowing f B gives V ub u Similarly, can check f Ds /f D to learn about f Bs /f B _ + s

3. 3 Leptonic Decays: D  + Introduction: Pseudoscalar decay constants Q and q can annihilate, probability is  to wave function overlap Example  - : _ In general for all pseudoscalars: Calculate, or measure if V Qq is known V Qq

4. 4 Expected B for P +  +  decays u We know: f  = 131.73±0.15 MeV f K = 160.6±1.3 MeV u The D s has the largest B, the µ + rate is ~0.5% u f Ds Measured by several groups, best CLEO II, but still poorly known  For D + also use µ + +

5. 5 CLEO-c Detector u Upgrade of CLEO II. Kept CsI EM calorimeter, magnet & muon system u New charged particle tracking u New particle id via RICH u New inner wire chamber u B now 1 T, lowered from 1.5T ¼ section vertex wire chamber

6. 6 Kinematical Niceties  Ease of B measurements using "double tags“ B A = # of A/# of D's u Possible because  relatively large B (many %), u multiplicities typically small = ~2.5, ~ 1.2, u enough luminosity u Reconstruct D mesons using: System is over constrained if all particles are observed:  p i  3, E tot  1, m D =m D  1

7. 7 D +  K -  +  + & D -  K +  -  - 377 events D+K-++D+K-++ Single tags Double Tags D +  K -  +  + or D -  K +  -  -, 15,120 events 57 pb -1 of data, we now have 280 pb -1

8. 8 Leptonic Decays u Ease of leptonic decays using double tags & MM 2 technique We know E D =E beam, p D = - p D u Search for peak near MM 2 =0  Since resolution ~ M  o, reject extra particles with calorimeter & tracking u Note that this method is used to evaluate systematic errors on the tracking efficiency, simply by using double tags with one missing track   2

9. 9 Technique for D +   + u Fully reconstruct one D  Seek events with only one additional charged track and no additional photons > 250 MeV to veto D +   +  o u Charged track must deposit only minimum ionization in calorimeter u Compute MM 2  If close to zero then almost certainly we have a   decay. u Can identify electrons to check background level  Expect resolution of ~M  o  If MM 2 > 0, candidate for  , but this is difficult 2 ±

10. 10 Single Tag Sample u From 280 pb -1

11. 11 Problem: how many events? u Fits to Asymmetric signal function (Crystal Ball shape) plus smooth background shape (ARGUS function) – error in tags ±0.3%

12. 12 MM 2 resolution  MM 2 from K S  - from data & MC  =0.0222±0.0005 GeV 2  =0.0233±0.0009 GeV 2 Consistent now, for 1 st analysis data was 15% larger

13. 13 Backgrounds: D +  +  o u We don’t specifically identify muons, only reject hadronic interactions in the crystals.  This mode has a B =(0.13±0.02)%  Eliminate by requiring muon candidate be in good barrel region & reject events with an extra  with E > 250 MeV. Residual effect is 0.3 events in 57 pb -1 and 1.4 events for 280 pb -1.

14. 14 Backgrounds: D +  +  +  +  Because D + is nearly at rest can get some very fast  +.  B is 2.65 x B (D +  +  u Background is calculated via MC with small error, 0.2 events for 57 pb -1 and 1.08 events for 280 pb -1

15. 15 Backgrounds: tail of D +  K o  + u Two methods u Monte Carlo: Simulation gives 0.44±0.22 events for 280 fb -1 u Measurement using double tag events with one D o  K -  + gives 0.44±0.44 events for 280 fb -1 1 bkgrd

16. 16 Other Backgrounds u Simulate: u Continuum sample 540 pb -1 gives 0 events u D o D o sample 540 pb -1 gives 0 events u D + D - 1700 pb -1 gives 0 events, other than the 3 modes we have already considered.

17. 17 One D +   +  Candidate

18. 18 Measurement of f D + MC Expectations from 1.7 fb -1, 30 X this sample Data show 8 events in the signal region in 57 pb -1

19. 19 Deriving a Value for f D + u  Tags are 28,575 events,  = 69.9%  B ( D +   +  =(3.5±1.4±0.6)x10 -4 u f D + = (202±41±17) MeV  No D +  e +  events seen Backgrounds Mode B (%) # Events +0+0 0.13±0.020.31±0.04 ++ 2.77±0.180.06±0.05        2.64* B (D +   + ) 0.30 ±0.07  0   0.25 ±0.15negligible Continuum(old estimate) 0.33 ± 0.23 Total 1.00±0.25 For 57 pb -1

20. 20 Comparison to Theory u CLEO-c measurement – 8 events u BES measurement based on 2.67±1.74 events u Current Lattice measurement (unquenched light flavors) is consistent u But errors on theory & data are still large

21. 21 Systematic Errors (Current) Much smaller than statistical errors

22. 22 New Data u Now have ~50 events in peak around MM 2 =0 u New value will be announced at Lepton- Photon conference in Artuso’s talk. Error will be ±16 MeV u New Unquenched Lattice result to also appear u Thus we will have an interesting comparison +9 -7