Transcript HEP-2005

Hadronic
Substructure
& Dalitz
Analyses at
CLEO
Mats Selen, University of Illinois
HEP 2005, July 22, Lisboa, Portugal
M. Selen, HEP-05
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Outline



Why the interest in charm Dalitz Plot (DP) analyses?
Results from CLEO
0
+ - 0
D → K K p
 D0  p+p-p0
 D0  Ksp0p0
What CLEO-c will do for CKM angle g/f3.
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CLEO Evolution
CLEO II.V (9/fb)
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)
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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
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The power of the DP approach

Interference is a beautiful thing !
 Phase sensitivity is a very important handle
Example:
D0  K- p+ p0
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79% r(770)
a1
eif1 + a2
3.3% K*(1430)-
+ a5
13% K*(892)0
eif2
1.3% K*(1680)-
eif5 + a6
eif6
16% K*(892)-
+ a3
eif3 + a4
5.7% r(1700)
+ a7
4.1% K*(1430)0
eif4
7.5% non-res
eif7 + a8
eif8
=
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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)
0
+ - 0
 CLEO analysis of D  K K p


D  3-body/Dalitz
Giri, Grossman, Soffer, Zupan PRD 68 (2003)
0
+ + - 0
 CLEO analysis of D  KSp p , p p p

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0
+
0
D K K p



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
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d=180
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0
+
0
D K K p
D*+ → p+ D0
CLEO III (4S) Region: 8.965/fb
K+ K– p0
K Km p0
signal region
(after selection criteria)
Signal Fraction  77.4%
Signal Events  565
(in the signal region)
mK+p02 (GeV/c2)2
gg
f
K*+
K*-
mK+K-p0 (GeV/c2)
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mK-p02 (GeV/c2)2
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0
+
0
D K K p
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%
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Fit projections reveal a feature/problem…
K*+
mK+p02 (GeV/c2)2
K*-
mK-p02 (GeV/c2)2
dips  are we missing some physics ??
Exploring K-p P-wave K-matrix approach
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f3 from 3-body final states
Access f3 via interference between B±  D0K± and B±  D0K±
s
u
c
b
favored
u
-
-
u
B  D K ~V V
B±
u
c
b
0
~
D
*
us cb
KS, p0
p+
pK±
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suppressed
u
-
0
s
u
B  D K - ~ VcsVub*
0
~
i d -3 
0
D-  D + re
D
0
~
D+  D + rei d +3  D 0
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Amplitude differences will
be sensitive to f3.
~
i d 3 
Amp( D )  f m , mm  + re
f mm , m 
Where f x, y  is the amplitude of the D0 matrix element at
the point x, y  on the Dalitz Plot, and m  m 2 
K Sp
Once f x, y  has been determined (where we come in) then
~
~
D+ and D- Dalitz plots can be fit to determine f3.
~
D-
~
D+
~
D  KSp-p+
BELLE
m253/fb
m-
(From B± decays)
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m+
m+
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0
+
0
D p p p



Useful for studying f3 in charged B decays.
0
- +
 Like D 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)
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S/(S+B) ~ 80%
S ~ 1100
9.0/fb
m2(p+p0) (GeV2)
D0p+p-p0
m2(p+p-) (GeV2)
0
1
2
m2(p+p-) (GeV2)
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0
1
m2(p+p0)
2
(GeV2)
3
0
1
m2(p-p0)
2
(GeV2)
3
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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
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
1
2
3 GeV2
< 0.21 @ 95% CL
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)
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1
2
3 GeV2
0
1
2
3 GeV216
< 1.9 @ 95% CL
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+
+
+ - +
0
+ - 0
 D p p p / D p p p S-wave
ratio > 36@95%CL


 
Tree level estimate = 3 2
2
 18
Flavor tagged D0 and D0 Dalitz plots also fit separately to
limit DP integrated CP asymmetry:
+0.09
 ACP = 0.01- 0.07  0.05
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D0 Ksp0p0
• Lots of brown muck
• Complement KSp-p+ analyses
• Good place to search for low mass pp
• No r p0p0 to get in the way!
K*(890) + K0(1430) + f0 + NR
0
1
m2(p0p0) (GeV2)
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m2(p0p0) (GeV2)
S/(S+B) ~ 70%
S ~ 700
K*(890) + K0(1430) + f0 + NR + s
0
1
m2(p0p0) (GeV2)
m2(KSp0)RS (GeV2)
2
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CLEO-II.V & III
(~15 fb-1)
S/(S+B) ~ 72%
S ~ 1500
m2(p0p0) (GeV2)
S/(S+B) ~ 70%
S ~ 700
CLEO-c data
(165 pb-1)
m2(KSp0)RS (GeV2)
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What CLEO-c will do for f3
~
i d 3 
Amp( D )  f m , mm  + re
f mm , m 
The determination of f x, y  is presently the limiting systematic

Belle and BaBar have studied the dependence of f3 on
the D decay model (analysis used D0  Ksp+p-)


Belle - Phys.Rev.D70:072003,2004 hep-ex/0406067
o
+17
f3  77 -19  13  11


BaBar – ICHEP04 paper hep-ex/0408088
g   70  26  10  10 o
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D Decay Model
Systematic
Uncertainty
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CLEO-II.V
Fit Fraction (%)
(stat err shown)
K*892+p-
0.34 ± 0.13
K*892-p+
65.7 ± 1.3
K0r0
26.4 ± 0.9
K0 w
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
S/(S+B) ~ 98%
S ~ 5300
m2(p-p+) (GeV2)
D0 Ksp+p-
2
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0
0
Rather low
statistics
compared
to…
0
1
1
2
3
2
m2(KSp)RS (GeV2)
m2(KSp+) (GeV2)
30
1
2
m2(p-p+) (GeV2)
30
1
2
3
m2(KSp-) (GeV2) 21
2.27x108 BB pairs
BaBar data with
“CLEO” model
not so good
BELLE fits
look like BaBar
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Fit with additional
resonances much
better.
This includes BW
s1 and s2 with
~10% fit fractions.
Causes big
systematic
uncertainty !
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CLEO-c can help

Do simultaneous CP tagged and flavor tagged
analysis of D0  Ksp+p- [only at ’’(3770)]

Suppose we write f m+ , m-   f m+ , m-  eif m+ ,m- 

We will extract cos m+ , m-  -  m- , m+ 
as well as f m+ , m-  in a model independent way.

This is exactly what
the f3 analyses need.
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Many other CLEO-c Dalitz plot analyses are in the works:
K-p+p0
K SK + K -
K-p+h
KSKp
p-p+p0
p+p+p-
KSKSp0
KSp+p0
etc…many others
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Conclusions

CLEO has done (and continues to do) groundbreaking
work on charm Dalitz analyses.
 K-p+p0,p+p-p0,KSp+p-,KShp0,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
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