1. 1 Review of Charm Hadronic Decays and Lifetimes Werner Sun, Cornell University (and CLEO-c) 7 th International Conference on Hyperons, Charm, and Beauty Hadrons 2-8 July 2006, Lancaster University, Lancaster, UK D 0, D , D s  only Branching fractions Amplitude analyses D s  lifetime

2. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 2 Introduction  Topics covered reflect personal bias and new developments in past year or so.  Branching fractions for D 0, D , D s  decays:  Important engineering numbers for B and B s decays.  Overall normalization for |V cb |.  Amplitude analyses of D 0 and D  decays:  Probes of strong phases.  Probes of D 0 -D 0 mixing (not discussed).  Lifetimes  Tests of theory.  Probes of D 0 -D 0 mixing (not discussed).  Topics not covered (sorry!)  Charmed baryons  Belle’s recent observation of orbitally excited  cx (2980) ,  cx (3077) , and  cx (3077) 0 decaying to  c  K    and  c  K 0 S   [hep-ex/0606051].  D sJ  (2317) , D sJ (2463) , and D sJ  (2632) 

3. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 3 The Experiments  B factories: BABAR & Belle  E cm ~ 10.6 GeV.  Copious charm production in continuum and B decays, many states available.  Initial state unknown (no absolute B s).  Slow pion from D  tags flavor of D 0 daughter.  Charm factories: CLEO-c & BES  E cm ~ 3.773 GeV and above: DD pair production.  Charm cross section higher, but L much lower.  Known initial state, low-multiplicity, low background.  Fixed target experiments: FOCUS & SELEX  Huge charm cross sections, but high backgrounds.  Limited  0 and K 0 S reconstruction efficiency.  CDF and D0—see P. Karchin’s talk  Different sources of uncertainties make for complementary analyses.  Many thanks to spokespersons and analysis coordinators.

4. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 4 Cabibbo-Favored Decays

5. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 5 D 0 /D + Absolute Branching Fractions  MARK III double tag technique using  (3770) → DD, 55.8 pb -1 [PRL 95, 121801 (2005)].  Single tag (ST): n i = N DD B i  i  Double tag (DT) : n ij = N DD B i B j  ij  Independent of L and cross sections.  Scale of statistical error set by sum of DT yields.  Combine ST and DT yields in  2 fit for B and N DD.  Many D B s measured relative to B (K   + ) or B (K   +  + ).  To be updated soon with 281 pb -1. All D 0 DT 2484 ± 51 All D + DT 1650 ± 42 DD Xi DD ji NDDNDD (2.01±0.04±0.02)x10 5 B(K+)B(K+) (3.91±0.08±0.09)% B(K+)B(K+) (14.9±0.3±0.5)% B(K++)B(K++) (8.3±0.2±0.3)% ND+D-ND+D- (1.56±0.04±0.01)x10 5 B(K++)B(K++) (9.5±0.2±0.3)% B(K++0)B(K++0) (6.0±0.2±0.2)% B(KS+)B(KS+) (1.55±0.05±0.06)% B(K0S+0)B(K0S+0) (7.2±0.2±0.4)% B(K0S+-+)B(K0S+-+) (3.2±0.1±0.2)% B(K+K+)B(K+K+) (0.97±0.04±0.04)% (D0D0)(D0D0) (3.60±0.07 +0.07 -0.05 ) nb (D+D-)(D+D-) (2.79±0.07 +0.10 -0.04 ) nb  (+-)/  (00) 0.776±0.024 +0.014 -0.008 Overall C.L 25.9%

6. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 6  Same basic technique as for D 0 /D +.  Fall 2005: energy scan of 12 points in E cm ~ 4 GeV region (60 pb -1 ).  B s use 76 pb -1, mostly taken at E cm = 4.17 GeV; use D s  D s  instead of D s  D s .  Current precision:  B = 11%.   B < 4% with full CLEO-c dataset.  D s  →   is one component of K  K   .  Previous measurements ignored f 0   (not high enough precision to matter).  Now, need Dalitz analysis to disentangle contributions. D s + Absolute Branching Fractions Maximal D s + yield. Peak structure in D s D s Mode B (%) (CLEO-c) B (%) (PDG) K0SK+K0SK+ 1.28 +0.13 -0.12 ±0.071.80±0.55 K+K-+K+K-+ 4.54 +0.44 -0.42 ±0.254.3±1.2 K+K-+0K+K-+0 4.83 +0.49 -0.47 ±0.46--- ++-++- 1.02 +0.11 -0.10 ±0.051.00±0.28 PRELIMINARY All D s + DT 118 ± 12

7. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 7 Inclusive D → K (*) X  Probe relative strength of CF D → K (*) and CS D → K (*).  33 pb -1 near  (3770).  Tag one side, reconstruct K (*) on other side, subtract M BC sidebands. Mode B (%) (BES) B (%) (PDG) D 0 → K  X 8.7 ± 4.0 ± 1.2 D  → K  X 23.2 ± 4.5 ± 3.0 D 0 → K  X 2.8 ± 1.2 ± 0.4 D  → K  X < 6.6 (90% CL) D 0 → K  X 15.3 ± 8.3 ± 1.9 D  → K  X 5.7 ± 5.2 ± 0.1 D 0 → K  X < 3.6 (90% CL) D  → K  X < 20.3 (90% CL) D0 → K0/K0XD0 → K0/K0X 47.6 ± 4.8 ± 3.042 ± 5 D → K0/K0XD → K0/K0X 62.5 ± 5.6 ± 3.459 ± 7 [PLB 625, 196 (2005)] [PRELIMINARY] D0→D0→ K  K  signal sideband K 0 S sideband

8. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 8 Inclusive D (s) → { ,  ’,  }X  Inclusive ss rates expected to be higher for D s  than D 0 /D .  B s help determine B s 0 production rate at  (5S).  CLEO-c measurements with 281 pb -1 D 0 /D  and 71 pb -1 D s .  Tag one side, reconstruct ,  ’,  on other side, subtract sidebands.   includes feeddown from  ’.  Saturated by exclusive modes for D s . B  (%)  ’ (%)  (%) D0D0 9.4 ± 0.4 ± 0.6 2.6 ± 0.2 ± 0.2 1.0 ± 0.1 ± 0.1 DD 5.7 ± 0.5 ± 0.5 1.0 ± 0.2 ± 0.1 1.1 ± 0.1 ± 0.2 DsDs 32.0 ± 5.6 ± 4.711.9 ± 3.3 ± 1.215.1 ± 2.1 ±1.5 PRELIMINARY D s  →  ’X :  -  ’ mass difference (GeV) signal sideband

9. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 9 D 0 → Three Kaons + X  D 0,D 0 → K 0 S K 0 S K     First observation.  Two CF modes: D 0 → K 0 K 0 K     K 0 K 0 K     Distinguished with D  tag, both observed.  Assuming no contribution from CS mode K 0 K 0 K   .  B (K 0 S K 0 S K    ) = (6.1 ± 1.1 ± 0.7) x 10 -4  No evidence for substructure.  D 0 → K 0 S K 0 S K 0 S  Only proceeds via W-exchange or final state interactions.  B (K 0 S K 0 S K 0 S ) = (10.4 ± 1.6 ± 1.7) x 10 -4  [PDG = (9.2 ± 1.6) x 10 -4 ]  No evidence for substructure. [PLB 607, 56 (2005)]

10. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 10 Cabibbo-Suppressed Decays

11. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 11 D 0/+ : Pionic Modes  Many new B measurements, rich resonant substructure. B (10 -3 ) CLEO-cBABARBESPDG04  1.39 ± 0.04 ± 0.031.31 ± 0.27 ± 0.041.38 ± 0.05  0.79 ± 0.05 ± 0.040.84 ± 0.22  13.2 ± 0.2 ± 0.511 ± 4  < 0.35 (90% CL)---         7.3 ± 0.1 ± 0.36.4 ± 1.5 ± 0.47.3 ± 0.5         9.9 ± 0.6 ± 0.7---           4.1 ± 0.5 ± 0.2---  1.25 ± 0.06 ± 0.081.22 ± 0.10 ± 0.111.33 ± 0.22  3.35 ± 0.10 ± 0.203.9 ± 1.0 ± 0.33.1 ± 0.4  4.8 ± 0.3 ± 0.4---  11.6 ± 0.4 ± 0.7---           1.60 ± 0.18 ± 0.171.82 ± 0.25 CLEO-c isospin analysis of  : A 2 /A 0 = 0.420 ± 0.014 ± 0.010 cos  = 0.062 ± 0.048 ± 0.058 Evidence for final state interactions. [PRL 96, 081802 (2006)] [hep-ex/0605044] [PLB 622, 6 (2005)]

12. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 12 Substructure in D → n(  + ) m(  0 )  Also search for ,  contributions [PRL 96, 081802 (2006)]  Compare M(  +  -  0 ) in  E = E cand  E beam signal and sideband regions. D + →  +  +  -  0 Mode B (x10 -3 ) PDG (x10 -3 )     1.7 ± 0.5 ± 0.2---   0.62 ± 0.14 ± 0.05---  < 0.35 (90% CL)---   < 0.26 (90% CL)---     < 1.9 (90% CL)---   3.61 ± 0.25 ± 0.263.0 ± 0.6   < 0.34 (90% CL)---    

13. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 13 D 0/+ : Kaonic Modes  No SU(3) triangle for KK:  K 0 K 0 vanishes in SU(3) limit—contributions only from SU(3) breaking and final state interactions. B (10 -3 ) FOCUSBESCLEO-cPDG04 KKKK 4.68±0.42±0.183.90±0.12 K0K0K0K0 0.84±0.19±0.110.74±0.14 K  K      2.39±0.09±0.093.6±1.5±0.42.49±0.23 K0SK0SK0SK0S 1.2±0.2±0.21.27±0.24 KKKK 6.64±1.11±0.415.7±0.5 KKKK 11.0±1.2±0.79.7±0.4±0.48.9±0.8 [PLB 610, 225 (2005)] [PLB 607, 56 (2005)] [PLB 622, 6 (2005)] [PRL 95, 121801 (2005)]

14. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 14 Doubly-Cabibbo-Suppressed Decays

15. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 15 D 0 Decays  For D 0, DCS final state is “wrong-sign” relative to CF decay.  R D = DCS/CF rate ratio ~ O(tan 4  C )  BUT, possible contribution from mixing  x =  M/ , y =  /2   {x’,y’} are {x,y} rotated by DCS/CF relative strong phase.  Phase can be measured via quantum correlations at  (3770).  For K , CLEO-c finds cos  = 1.09 ± 0.66 [Preliminary, hep-ex/0603031]  Quoted values of R D assume no mixing or CP violation. R D (10 -3 ) KK K0K0 KK Belle 3.77 ± 0.08 ± 0.052.29 ± 0.15 ± +0.13 -0.09 3.20 ± 0.18 ± +0.18 -0.13 BABAR 2.14 ± 0.08 ± 0.08 FOCUS 4.29 +0.63 -0.61 ± 0.27 CDF 4.05 ± 0.21 ± 0.11 PDG 3.62 ± 0.294.3 +1.1 -1.0 ± 0.74.2 ± 1.3 [PLB 618, 23 (2005)] [hep-ex/0605027] [PRL 96, 151801 (2006)] [PRL 95, 231801 (2005)] [hep-ex/0605046] DCS mostly K    CF mostly K   

16. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 16 D + Decays  The DCS decay D  → K   0 has no CF counterpart.  Recently observed by BABAR, confirmed by CLEO-c.  Last uncertainty from reference B (D  → K      ). B (10 -4 ) BABAR [hep-ex/0605044] CLEO-c K0K0 2.46 ± 0.46 ± 0.24 ± 0.162.14 ± 0.34 ± 0.11 ± 0.07 PRELIMINARY

17. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 17 Amplitude Analyses

18. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 18 D →  Dalitz Analyses  Decay amplitudes parametrized as sum of interfering Breit-Wigners.  D →      0 (CLEO II.V) [PRD 72, 031102 (2005)]  Also used K-matrix parametrization of     S-wave—no evidence found.  D →       (CLEO-c)  Results agree with E791 [PRL 86, 770 (2001)] and FOCUS [PLB 585, 200 (2004)]  In particular,  fit fraction = (41.8 ± 1.4 ± 2.5)%  Parametrized by complex pole: A = 1/[ (0.47-0.22i)GeV 2 – m 2 (     )]. PRELIMINARY

19. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 19 D → KK  (  ) Dalitz Analyses  D → K  K   0 (CLEO III) [hep-ex/0606045, submitted to PRD]  K  and K  strong phase needed to extraction CKM parameter  /  3 [Grossman, Ligeti, Soffer, PRD 67, 071301 (2003)].  Measured to be (332 ± 8 ± 11) o → nearly maximal destructive interference.  r D = 0.52 ± 0.05 ± 0.04  D → K  K      (FOCUS) [PLB 610, 225 (2005)]  Dominated by AP: K 1 (1270)  K  (33%), K 1 (1400)  K  (22%), VV:  0  (29%).  In K  K  spectrum,  line shape distorted by f 0 (980).

20. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 20 D + → K 0 S,L  +  CF/DCS interference switches sign between K 0 L and K 0 S → B asymmetry.  Could be O(10%) [Bigi & Yamamoto, PLB 349 (1995) 363-366].  Depends on relative strong phases between amplitudes.  Reconstruct K 0 s + K 0 L inclusively in missing mass recoiling against  +.  B (D + → K 0 S  + ) + B (D + → K 0 L  + ) = (3.06 ± 0.06 ± 0.16)%  Asymmetry = (K 0 L  K 0 S )/(K 0 L + K 0 S ) =  0.01 ± 0.04 ± 0.07 c d w+w+ s d u d D+D+ ++ K0K0 Cabibbo-favored c d s d u d D+D+ ++ K0K0 w+w+ Color-suppressed c d d s u d D+D+ ++ K0K0 w+w+ DCS, color-suppressed D + → K 0  + (3879 ± 71 events) D + →  +  D + →  0  + (176 ± 13 events) (Missing mass) 2 (GeV 2 ) DATA PRELIMINARY D + →  + (487 ± 38 events) S,L tag side signal side inferred from missing mass fully reconstructed

21. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 21 D s + Lifetime  Need lifetimes to convert B s into partial widths.  Extract CKM matrix elements.  Test isospin invariance.  FOCUS dominates D 0, D +, D s  lifetimes.  [D CP lifetimes also limit mixing.]  New FOCUS measurement for D s  [PRL 95, 052003 (2005)].   (D s  )/  (D  ) = 1.239 ± 0.017  Probes weak annihilation contribution. (fs)FOCUSPDG04 (Ds)(Ds) 507.4 ± 5.5 ± 5.1490 ± 9 D s  →   Ds → KKDs → KK Ds → KKDs → KK

22. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 22 Summary & Outlook  Much recent activity in study of charm hadronic decays.  High-precision branching fractions.  Complex resonant substructure in multibody decays.  Interesting interference effects.  Much more to come:  B factories and Tevatron are still collecting large incoherent charm datasets.  CLEO-c runs through March 2008; will significantly increase coherent charm datasets.  BES III to turn on in the next few years; expected to collect 25x CLEO-c sample!  Next generation fixed target experiments: LHCb & PANDA.  Charm physics will continue to be a rich area of exploration!

23. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 23 Backup Slides

24. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 24 Effect of Quantum Correlations  |D 1,2 > = p|D 0 > ± q|D 0 >  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 = (  2 -  1 )/2  .  Semileptonic decays tag flavor unambiguously (if no mixing)  If one D is SL, the other D decays as if isolated/incoherent.  Exploit coherence to probe DCSD and mixing—shows up in time- integrated rates. 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 in absence of mixing maximal constructive interference

25. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 25 Introduction  In the Standard Model, D mixing strongly suppressed (CKM and GIM).  Previous searches:  Double semileptonic rates give R M.  Time-dependent K  : x and y rotated by   Current analysis:  Uses time-independent yields.  Sensitive to y at first order.  No sensitivity to p/q≠1; neglect CPV in decay.  References:  Goldhaber, Rosner: PRD 15, 1254 (1977).  Xing: PRD 55, 196 (1997).  Gronau, Grossman, Rosner: hep-ph/0103110.  Atwood, Petrov: PRD 71, 054032 (2005).  Asner, Sun: hep-ph/0507238. Definition Current knowledge y (  2 -  1 )/2  = B (CP+)  B (CP-)   B f r f z f 0.008 ± 0.005 x (M 2 -M 1 )/  sensitive to NP x’ < 0.018 RMRM (x 2 +y 2 )/2< ~1 x 10 -3 r K  DCS-to-CF rel. amplitude 0.061 ± 0.001  K  DCS-to-CF relative phase  (weak) + ? (strong) z 2cos  None w 2sin  None

26. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 26 Single and Double Tag Rates  Hadronic rates (flavored and CP eigenstates) depend on mixing/DCSD.  Semileptonic modes (r =  = 0) resolve mixing and DCSD.  Rate enhancement factors, to leading order in x, y and r 2 :  With C=+1 D 0 D 0  at higher energy, sensitivity to wx at first order. Not much info if w is small. fl+l+CP+CP- fR M /r 2 f1+r 2 (2-z 2 ) l-l-11 CP+1+rz10 CP-1-rz120 X1+rzy11-y1+y DD Single tag: X i DD Double tag: j i

27. BEACH06, 2-8 July 2006, Lancaster University, Lancaster, EnglandWerner Sun, Cornell University 27 Results  Fit inputs: 6 ST, 14 hadronic DT, 10 semileptonic DT, efficiencies, crossfeeds, background branching fractions and efficiencies.   2 = 17.0 for 19 d.o.f. (C.L. = 59%). ParameterValuePDG or CLEO-c NDDNDD (1.09 ± 0.04 ± ?)x10 6 (1.01 ± 0.02)x10 6 y-0.057 ± 0.066 ± ? r2r2 -0.028 ± 0.069 ± ? (3.74 ± 0.18)x10 -3 PDG + Belle + FOCUS rz0.130 ± 0.082 ± ? RMRM (1.74 ± 1.47 ± ?)x10 -3 < ~1x10 -3 B (K    ) (3.80 ± 0.29 ± ?)%(3.91 ± 0.12)% B(KK)B(KK)(0.357 ± 0.029 ± ?)%(0.389 ± 0.012)% B()B() (0.125 ± 0.011 ± ?)%(0.138 ± 0.005)% B(K0S00)B(K0S00) (0.932 ± 0.087 ± ?)%(0.89 ± 0.41)% B(K0S0)B(K0S0) (1.27 ± 0.09 ± ?)%(1.55 ± 0.12)% B (X  e  ) (6.21 ± 0.42 ± ?)%(6.87 ± 0.28)% PRELIMINARY  Fitted r 2 unphysical. If constrain to WA, cos  = 1.09 ± 0.66 ± ?.  Limit on C=+1 contamination:  Fit each yield to sum of C=-1 & C=+1 contribs.  Include CP+/CP+ and CP-/CP- DTs in fit.  No significant shifts in fit parameters.  C=+1 fraction = 0.06 ± 0.05 ± ?.  Some branching fracs competitive with PDG. Uncertainties are statistical only