Hadronic Substructure & Dalitz Analyses at CLEO Mats Selen, University of Illinois HEP 2005, July 22, Lisboa, Portugal M. Selen, HEP-05

Outline Why the interest in charm Dalitz Plot (DP) analyses? Results from CLEO D0 → K+K-p0 D0  p+p-p0 D0  Ks00 What CLEO-c will do for CKM angle g/f3. M. Selen, HEP-05

CLEO Evolution CLEO II.V (9/fb) CLEO III (14/fb) CLEO-c (281/pb) New RICH New Drift Chamber New silicon New Trigger & DAQ CLEO III (14/fb) Replace silicon with a wire vertex chamber CLEO-c (281/pb) M. Selen, HEP-05

Why bother? Need to understand the brown muck. Final state interactions are tricky Relative amplitudes and phases hard to calculate – must measure. Need to sort out the best way to model ≥ 3 body decays Isobar, K-matrix, … People have not always agreed on best approach  Important engineering measurement for getting the most out of b-factory data. For example, extracting f3 from BDK M. Selen, HEP-05

The power of the DP approach Interference is a beautiful thing ! Phase sensitivity is a very important handle Example: D0  K- p+ p0 M. Selen, HEP-05

= a1 eif1 + a2 + a3 eif3 + a4 eif2 eif4 + a5 eif5 + a6 eif6 + a7 eif7 79% r(770) 13% K*(892)0 7.5% non-res 16% K*(892)- 4.1% K*(1430)0 3.3% K*(1430)- 1.3% K*(1680)- 5.7% r(1700) a1 eif1 + a2 + a3 eif3 + a4 eif2 eif4 + a5 eif5 + a6 eif6 + a7 eif7 + a8 eif8 = M. Selen, HEP-05

Relevance to f3 There are several schemes to access g/f3 by exploiting interference in the decays of charged B mesons to charm: B  DK D  K*K Grossman, Ligeti, Soffer PRD 67 (2003) Suprun, Rosner PRD 68 (2003) CLEO analysis of D0  K+K-p0 D  3-body/Dalitz Giri, Grossman, Soffer, Zupan PRD 68 (2003) CLEO analysis of D0  KSp+p-, p+p-p0 M. Selen, HEP-05

D0K+K-p0 Method for measuring CKM phase f3 by looking at B± → (K*+ K-)DK ± and B± → (K*- K+)DK ± Needs a measurement of the strong phase difference dD between D0 → K*+ K– and D0 → K*– K+. Dalitz analysis of D0 → K+K-p0 will yield dD d=0 d=180 M. Selen, HEP-05

D0K+K-p0 K± Km p0 signal region mK+p02 (GeV/c2)2 f K*+ K*- CLEO III ¡(4S) Region: 8.965/fb D*+ → p+ D0 → K+ K– p0 → g g K± Km p0 signal region mK+p02 (GeV/c2)2 (after selection criteria) f Signal Fraction » 77.4% Signal Events » 565 (in the signal region) K*+ K*- mK+K-p0 (GeV/c2) mK-p02 (GeV/c2)2 M. Selen, HEP-05

D0K+K-p0 Preliminary Fit Statistical errors only Resonance amplitude a phase q K*(892)+ Fixed to 1 Fixed to 0 K*(892)- 0.4951 ± 0.0530 331.48 ± 10.35 f (1020) 0.4911 ± 0.0487 99.55 ± 12.94 nonresonant 5.6660 ± 0.4035 225.40 ± 6.67 Fit Fractions Resonance Fit Fraction K*(892)+ 45.20% ± 2.97% K*(892)- 11.01% ± 2.25% f (1020) 8.57% ± 1.56% nonresonant 35.91% ± 3.46% 100.69% ± 5.32% kstarP 1.001 45.20% +/- 2.97% : 0.000E+00% kstarM 1.003 11.01% +/- 2.25% : 63.5% phi0 1.001 8.57% +/- 1.56% : 36.1% non_res 1.000 35.91% +/- 3.46% : 9.16% NEW Values: Values: Resonance phase amp mass width --------- --------------- --------------- ---------------- -------- kstar+ fixed fixed 0.8917 0.0508 kstar- -28.52 +- 10.35 0.4951 +- 0.0530 0.8917 0.0508 phi0 “-260.45 +- 12.94” 0.4911 +- 0.0487 1.0190 0.0043 - corrected (i.e. NOT E687) non_res -134.60 +- 6.67 5.6660 +- 0.4035 n/a n/a Statistics: points_used 689 Fit Fractions: kstar+ (45.087 +- 0.000)% kstar- (11.052 +- 2.366)% phi0 ( 8.708 +- 1.727)% non_res (35.841 +- 5.105)% --------- -------- 100.688% M. Selen, HEP-05

Fit projections reveal a feature/problem… K*- K*+ mK+p02 (GeV/c2)2 mK-p02 (GeV/c2)2 dips  are we missing some physics ?? Exploring K-p P-wave K-matrix approach M. Selen, HEP-05

f3 from 3-body final states Access f3 via interference between B±  D0K± and B±  D0K± b c u s b s u c favored suppressed KS, p0 p+ B± p- K± M. Selen, HEP-05

Where is the amplitude of the D0 matrix element at Amplitude differences will be sensitive to f3. Where is the amplitude of the D0 matrix element at the point on the Dalitz Plot, and Once has been determined (where we come in) then D+ and D- Dalitz plots can be fit to determine f3. ~ ~ D+ ~ D- ~ ~ D  KS-+ BELLE 253/fb m- m- (From B± decays) m+ m+ M. Selen, HEP-05

D0p+p-p0 Useful for studying f3 in charged B decays. Like D0KSp-p+ (discussed later) Good system for CP violation search. Some predictions as high as 0.1% (ref) Compare to D+p+p-p+ Has large S-wave component (FOCUS ref) M. Selen, HEP-05

D0p+p-p0 m2(p+p0) (GeV2) m2(p+p-) (GeV2) S/(S+B) ~ 80% S ~ 1100 9.0/fb m2(p+p0) (GeV2) m2(p+p-) (GeV2) m2(p+p0) (GeV2) 0 1 2 3 0 1 2 3 0 1 2 3 m2(p+p-) (GeV2) m2(p-p0) (GeV2) M. Selen, HEP-05

p+p- proj Amplitude Phase(o) Fit Fraction % r+p- 1 (fixed) 0 (fixed) 76.5±1.8±2.5 r0p0 0.56±0.02±0.03 10±3±2 23.9±1.8±2.1 r-p+ 0.65±0.03±0.02 176±3±2 32.3±2.1±1.3 NR 1.03±0.17±0.12 77±8±5 2.7±0.9±0.2 p+p- proj < 6.4 @ 95% CL 0 1 2 3 GeV2 Amplitude Phase(o) Fit Fraction % r+p- 1 (fixed) 0 (fixed) 78.0±2.1 r0p0 0.56±0.02 9±3 24.4±1.9 r-p+ 0.66±0.03 176±3 33.9±2.3 s(500) 0.22±0.06 355±24 0.08±0.08 < 0.21 @ 95% CL 0 1 2 3 GeV2 Amplitude Phase(o) Fit Fraction % r+p- 1 (fixed) 0 (fixed) 76.3±1.9±2.5 r0p0 0.57±0.03±0.03 10±3±2 24.4±2.0±2.1 r-p+ 0.67±0.03±0.02 178±3±2 34.5±2.4±1.3 K-matrix 0.70±0.20±0.12 2±14±5 0.9±0.7±0.2 See Au, Morgan, Pennington PRD 35, 1633 (1987) < 1.9 @ 95% CL M. Selen, HEP-05 0 1 2 3 GeV2

D0p+p-p0 Only rp contributions plus small non-resonant component are required to fit Dalitz plot. Very small D0p+p-p0 S-wave fit fraction (<0.9%) compared to FOCUS (56%) for D+p+p-p+ D+p+p-p+ / D0p+p-p0 S-wave ratio > 36@95%CL Tree level estimate = Flavor tagged D0 and D0 Dalitz plots also fit separately to limit DP integrated CP asymmetry: ACP = M. Selen, HEP-05

D0 Ks00 Lots of brown muck Complement KSp-p+ analyses S/(S+B) ~ 70% S ~ 700 D0 Ks00 Lots of brown muck Complement KSp-p+ analyses Good place to search for low mass pp No r 00 to get in the way! m2(p0p0) (GeV2) m2(KSp0)RS (GeV2) K*(890) + K0(1430) + f0 + NR K*(890) + K0(1430) + f0 + NR + s 0 1 2 0 1 2 m2(p0p0) (GeV2) m2(p0p0) (GeV2) M. Selen, HEP-05

CLEO-c data CLEO-II.V & III (165 pb-1) (~15 fb-1) m2(p0p0) (GeV2) S/(S+B) ~ 70% S ~ 700 S/(S+B) ~ 72% S ~ 1500 m2(p0p0) (GeV2) m2(KSp0)RS (GeV2) M. Selen, HEP-05

What CLEO-c will do for f3 The determination of is presently the limiting systematic Belle and BaBar have studied the dependence of f3 on the D decay model (analysis used D0  Ks+-) Belle - Phys.Rev.D70:072003,2004 hep-ex/0406067 BaBar – ICHEP04 paper hep-ex/0408088 D Decay Model Systematic Uncertainty M. Selen, HEP-05

Fit Fraction (%) (stat err shown) 2 S/(S+B) ~ 98% S ~ 5300 CLEO-II.V D0 Ks+- Rather low statistics compared to… m2(p-p+) (GeV2) Fit Fraction (%) (stat err shown) K*(892)+p- 0.34 ± 0.13 K*(892)-p+ 65.7 ± 1.3 K0r0 26.4 ± 0.9 K0w 0.72 ± 0.18 K0f0(980) 4.3 ± 0.5 K0f2(1270) 0.27 ± 0.15 K0f0(1370) 9.9 ± 1.1 K0*(1430)-p+ 7.3 ± 0.7 K2*(1430)-p+ 1.1 ± 0.2 K*(1680)-p+ 2.2 ± 0.4 NR 0.9 ± 0.4 1 1 2 3 m2(KSp)RS (GeV2) m2(KSp+) (GeV2) 0 1 2 3 m2(p-p+) (GeV2) 0 1 2 3 m2(KSp-) (GeV2) 0 1 2 3 M. Selen, HEP-05

BaBar data with “CLEO” model not so good 2.27x108 BB pairs BaBar data with “CLEO” model not so good BELLE fits look like BaBar M. Selen, HEP-05

Causes big systematic uncertainty ! Fit with additional resonances much better. This includes BW s1 and s2 with ~10% fit fractions. Causes big systematic uncertainty ! M. Selen, HEP-05

CLEO-c can help Do simultaneous CP tagged and flavor tagged analysis of D0  Ks+- [only at ’’(3770)] Suppose we write We will extract as well as in a model independent way. This is exactly what the f3 analyses need. M. Selen, HEP-05

Many other CLEO-c Dalitz plot analyses are in the works: K-p+p0 K-p+h p-p+p0 KSKSp0 KSK+K- KSKp p+p+p- KSp+p0 etc…many others M. Selen, HEP-05

Conclusions CLEO has done (and continues to do) groundbreaking work on charm Dalitz analyses. K-p+p0,p+p-p0,KSp+p-,KSp0,K-K+p0,KSp0p0, ... Implementation of K-Matrix amplitudes in fits CLEO-c will open a new window on the charm sector by exploiting quantum correlations: CP tagged Dalitz Plot analyses f3, mixing, CP violation, … Double correlated Dalitz analyses (i.e. DP vs DP) Stay tuned M. Selen, HEP-05