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

2. 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

3. 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

4. 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

5. 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

6. = 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

7. 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

8. 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

9. 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

10. D0K+K-p0 Preliminary Fit Statistical errors only Resonance
amplitude a
phase q
K*(892)+
Fixed to 1
Fixed to 0
K*(892)- ±
± 10.35
f (1020) ±
99.55 ± 12.94
nonresonant ±
± 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 % +/- 2.97% : 0.000E+00% kstarM % +/- 2.25% : 63.5% phi % +/- 1.56% : 36.1% non_res % +/- 3.46% : 9.16%
NEW Values:
Values: Resonance phase amp mass width
kstar+ fixed fixed
kstar
phi0 “ ” - corrected (i.e. NOT E687)
non_res n/a n/a
Statistics: points_used 689
Fit Fractions: kstar+ ( )%
kstar- ( )% phi0
( )%
non_res ( )% %
M. Selen, HEP-05

11. 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

12. 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

13. 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

14. 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

15. 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)
m2(p+p-) (GeV2)
m2(p-p0) (GeV2)
M. Selen, HEP-05

16. 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
< 95% CL
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
< 95% CL
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)
< 95% CL
M. Selen, HEP-05
GeV2

17. 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 >
Tree level estimate =
Flavor tagged D0 and D0 Dalitz plots also fit separately to limit DP integrated CP asymmetry:
ACP =
M. Selen, HEP-05

18. 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
m2(p0p0) (GeV2)
m2(p0p0) (GeV2)
M. Selen, HEP-05

19. 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

20. 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/
BaBar – ICHEP04 paper hep-ex/
D Decay Model
Systematic
Uncertainty
M. Selen, HEP-05

21. 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)
m2(p-p+) (GeV2)
m2(KSp-) (GeV2)
M. Selen, HEP-05

22. 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

23. 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

24. 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

25. 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

26. 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