Cabibbo-Allowed and Doubly-Cabibbo Suppressed D  K  Decays Steven Blusk Syracuse University on behalf of the CLEO Collaboration XXXIII International Conference on High Energy Physics July 26 – August 2, 2006, Moscow, Russia Other CLEO-c charm talks Leptonic Charm decays Sheldon Stone, 10-2 Semileptonic Charm decays Yongsheng Gao, Session 10-3 Charm Hadronic Decays S. Blusk, Session 10-2 Y(4260) at CLEO Ian Shipsey, Session 9-3 Charmonium decays at CLEO Tomasz Skwarnicki, Session 9-4

Introduction D  K  decay plays a “special role” in CLEO –“Large” BF, high efficiency, <1% background Many reasons to study this mode –D 0  K -  + normalization for most D 0 BF’s and hence many B decays –ADS method for extracting  needs strong phase shift between CF D 0  K -  + and DCSD D 0  K +  - Can be measured using quantum coherence of  (3770)  DD decay –Limits on mixing But other K  modes are also of interest, such as: –K L  0, K S  0 –K L    K S  + –K +  0 (DCSD) Understand/test strong dynamics of D decays, phases

Cleo-c Overview e + e -   (3770)  DD  Pure DD final state, no additional particles (E D = E beam ).  Low particle multiplicity  ~ 5-6 charged particles/event  Excellent coverage  infer & “reconstruct” in (semi)leptonic decays  Pure J PC = initial state  Quantum correlations D tag D sig K   e+e+ e-e-  CLEO Analysis Untagged Analysis Tagged Analysis  Reconstruct one D (“tag”): Single tags  In “D-tagged” events, count yield of events in a particular signal decay mode: Double tags  Absolute BF’s can be computed, independent of , L  Needn’t fully reconstruct D sig. If 1 particle is missing from decay, missing mass (MM) is the signal.  Used extensively for analyses involving ’s ! e.g. For D sig   +X Neglect mixing  10 -3

Quantum Coherence in  (3770)  D 0 D 0  Diagonalization gives the masses (M 1 & M 2 ) and widths (  1 &  2 ) of the weakly decaying eigenstates.  Convenient to define normalized differences: 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 btw CF & DCSD forbidden by CP conservation forbidden by Bose symmetry e  e    *  D 0 D 0 C =  1 maximal constructive interference “unchanged” MixingNo Mixing CF/DCSD Interfere

Expected and Some Observed rates (C = -1) f l + CP+CP- fRmRm f 1+r 2 (2-(2cos  ) 2 ) l - 11 CP+ 1+r (2cos  ) 10 CP- 1-r (2cos  ) 120 X 1+ ry (2cos  ) 11-y1+y - Fit for BF’s, R m, y, r 2 and 2rcos(  ) States (non-CP) accessible to both D 0 and D 0. Leptonic No QC Data K-K+K-K+ -+-+ Ks00Ks00 Ks0Ks0 K-K+K-K+ 5.2± ± ± ± ± ± ± ±6.3 -+-+ 1.1± ± ± ± ± ±3.7 Ks00Ks00 1.2± ± ± ±4.4 Ks0Ks0 9.7± ±1.7 CP+CP- CP+CP+ Double Tag Rates in units of B i B j Maximal Interference

Results, based on 281 pb -1 ParameterCLEO-c TQCAPDG or CLEO-c y-0.057± ±0.005 r ±0.069(3.74±0.18)X10 -3 r (2cos  D  K  ) 0.130±0.082 RMRM (1.74±1.47)x10 -3 < ~1x10 -3 B(D  K  ) (3.80±0.029)%(3.91±0.12)% B(D  K + K - ) (0.357±0.029)%(0.389±0.012)% B(D  +  - ) (0.125±0.011)%(0.138±0.005)% B(D  K s  0  0 ) (0.932±0.087)%(0.89±0.41)% B(D  K s  0 ) (1.27±0.09)%(1.55±0.12)% B(D 0  Xe ) (6.21±0.42)%(6.46±0.21)% See talk by David Asner, CHARM 2006, also D. Asner, W. Sun, Phys. Rev. D73, (2006)  Fitted r 2 unphysical. If constrained to WA, cos  K  = 1.08 ± 0.66(stat)  With 3-4X more data MeV data, expect  (cos  K   ~ 0.15 TQCA errors are stat. only.

But no phase info D  K  Isospin Decomposition Cabibbo-favored A 1/2 : I=1/2 CF Amplitude A 3/2 : I=3/2 CF Amplitude  I = CF strong phase shift Doubly Cabibbo suppressed B 1/2 : I=1/2 DCS Amplitude B 3/2 : I=3/2 DCS Amplitude C 1/2 : I=1/2 DCS Amplitude Assume  I same for CF & DCS for now (although this assumption will eventually be dropped) 3 observables, 3 unknowns.. Find: A 3/2 ~ (¼)A 1/2,  I ~ 90 0 What can we learn from this ? Access to  K  via CF and DCSD D  K  BF’s

Analysis Overview Measure the asymmetry: Plug in: Interference between K 0 and K 0 diagrams  BF(D  K s  )≠BF(D  K L  ) c d d d ++ K0K0 D+D+ u s DCS c d s d ++ K0K0 D+D+ c d s d ++ K0K0 D+D+ u d CF Then: ~tan 2  C But, need to measure BF(D +  K L  + ) & BF(D 0  K L  0 ) !!  r K ,  K   R(D 0 ), R(D + ) are each functions of the Isospin amplitudes and phase  After some algebra…

D  K L  Analysis Technique Tagged analysis: D tag K   e+e+ e-e-  Peak at M K0 2 for D  (K s,K L )  Isolate K L contribution by  Vetoing extra tracks and  0 ’s  Correct for K s leak-through (small) & loss of K L signal from veto (small) D+KL+D+KL+ D+KL+D+KL+ D0KL0D0KL0 D0KL0D0KL0  Measure D +  K L  + using MM method.  Use CLEO-c BF measurement of D +  K S  + (57 pb -1, to be updated to 281 pb -1 soon )  Compute R(D + )  Because of D 0 -D 0 mixing & DCSD, what we measure in D 0 decays are:  ST: BF(D 0  K L,S  0 ) (1±y)  DT: BF(D 0  K L,S  0 ) (1±2r f cos  +r f 2 )  Measure B(D 0  K S,  0 ) in both ST and DT  Since y<1%, compute 1-2r f cos  +r 2 by comparing ST and DT BF’s  Correct DT BF(D 0  K L  0 ) using 1+2r f cos  +r f 2 from K s analysis and PDG values for r f  Compute R(D 0 ) K L = + K S = -

D+KL+D+KL+ YieldEfficencyBF (%) K S,L  ±7985.2± ±0.056 KL+KL+ 2023±5481.8± ±0.040 Single Tags: 165,000 after selection on M bc No Veto Extra trk/  0 Veto (removes most K s ) Missing Mass Squared Dominant systematics: Signal fit and D   +  -  + BG (K S,L  + only) K-++K-++ K-++0K-++0 KS+KS+ KS+0KS+0 KS+-+KS+-+ K-K++K-K++ Summing over all modes

D 0  K S,L  0 Single Tag B(D 0  K S  0 ):  Inclusive search, reconstruct K s   +  - and  0.  Yield=7487, determined from M bc by  E and M(  +  - ) sideband subtraction  N(D 0 ) ~ 2.02x10 6,  B(D 0  K S  0 ) = (1.212±0.016±0.039)% DD cross-section dominant uncertainty (2.75%) Double Tag B(D 0  K S  0 ):  3 tag modes, K -  +, K -  +  0 K  +  -  +.  Reconstruct D 0  K S  0 -  E and M(  +  - ) sideband subtraction  N tag = 182,000, Yield = 614,  ~32% M bc K -  + tagK -  +  0 tagK -  +  -  + tag B(D 0  K S  0 )*(1-2rcos  +r 2 ) = (1.032±0.047±0.016)% Double Tag B(D 0  K L  0 ):  Follows K S  0 DT analysis, except use MM 2.  Veto candidates with extra tracks/  0 ’s  N tag = 182,000, Yield = 1115,  ~55% MM 2 B(D 0  K L  0 )*(1+2rcos  +r 2 ) = (1.077±0.036±0.023)% M bc

Corrections to for Interference Corrections to D 0  K L  0 for Interference K s  0 corr. factor K L  0 corr. factor B(D 0  K L  0 ) = (0.940±0.046±0.032)% B(D 0  K S  0 ) = (1.212±0.016±0.039)% Significant effect here ! Strategy: Determine 2rcos  from K S    apply correction to K L  

D  K L,S  Results R(D 0 ) R(D + ) r K  = ± (PDG04)  (R(D 0 ),R(D + )) measurement    ± 6 ± 7) o Preliminary Strong phase between CF and DCS D 0  K  is close to 0 Assumptions:  Zero phase between B 1/2 and C 1/2  Zero phase between A 1/2 and B 1/2 Systematics associated with these assumptions are being studied

D+ K+0D+ K+0D+ K+0D+ K+0 Very few DCSD measurement in D + decays Provide a useful handle on understanding strong dynamics and tests of SU(3) symmetry Recent BaBar measurement:  124 fb -1 at/just below Y(4S)   cc events,  ~6%  B(D +  K +  0 ) = (2.46±0.46±0.24±0.16)x10 -4 CLEO-c excels in reconstructing decays such as these. –~0.8 M D + D - events,  ~45% BaBar

D+ K+0D+ K+0D+ K+0D+ K+0 Reconstruct K + using RICH (some dE/dx),  0  . Require -40<E cand -E beam <35 MeV  Fit M bc spectrum Yield = 148±23  = 44.5% B(D +  K +  0 )= (2.25 ± 0.36 ± 0.15 ± 0.07) x 10 -4

More on Isospin Amplitudes Using Isospin Amplitudes (Small) Taking  2 small: Using measured B(D +  K +  0 ), R(D + ),R(D 0 )  ~ 0 or  ~1 So, either: C 1/2 << B 1/2 C 1/2 >> B 1/2 Need additional information to distinguish between the two possibilities

Acknowledgements Thanks to CLEO collaborators who have made this talk possible.. –Ed Thorndike, Dave Asner, Anders Ryd, Werner Sun, Steve Stroiney, Qing He, Fan Yang –Hanna Mahlke-Krueger for coordinating

Summary Probing mixing and DCSD through time-integrated ST and DT BF’s. By the end of the CLEO-c program, expect: –  y) ~ 0.012,  x 2 )~0.0006,  cos  K  ) ~0.15, R M < O(10 -4 ) –  x*sin  K  ) ~0.024 (Needs C=+1 initial state from DD  & DD  0 from 4170 MeV) The K  system is a very nice laboratory to study and extract important hadronic parameters. –Isospin decomposition relating observed rates to amplitudes & phases –CLEO’s ability to measure D  K L  germaine to carrying out these measurements. –D  K L,S  asymmetries consistent with r K  from BF(D 0  K -  + )/ BF(D 0  K +  ) –Preliminary results indicate  K  near zero, systematic errors from assumptions still being investigated. –Full fit for amplitudes and strong phases in progress, expect results soon Lots of beautiful results still pouring out of CLEO ! Stay tuned for more