Hadronic Substructure

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Hadronic Substructure Dalitz Analyses at CLEO
Mats Selen, University of IllinoisHEP 2005, July
22, Lisboa, Portugal
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Outline

• Why the interest in charm Dalitz Plot (DP)
  analyses?
• Results from CLEO
• D0 ? KK-p0
• D0 ? pp-p0
• D0 ? Ks?0?0
• 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 siliconwith 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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a3
a1
eif3
a4
a2
eif4
eif1
eif2
eif8
a5
eif7
a6
a7
a8
eif5
eif6

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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 ? KK
• Grossman, Ligeti, Soffer PRD 67 (2003)
• Suprun, Rosner PRD 68 (2003)
• CLEO analysis of D0 ? KK-p0
• D ? 3-body/Dalitz
• Giri, Grossman, Soffer, Zupan PRD 68 (2003)
• CLEO analysis of D0 ? KSpp-, pp-p0

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D0?KK-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 ? KK-p0 will yield dD

d180
d0
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D0?KK-p0
CLEO III (4S) Region 8.965/fb
D ? p D0
?
K K p0
?
g g
K Km p0 signal region
mKp02 (GeV/c2)2
(after selection criteria)
f
Signal Fraction 77.4 Signal Events 565 (in
the signal region)
K
K-
mK-p02 (GeV/c2)2
mKK-p0 (GeV/c2)
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D0?KK-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 Fit Fractions 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-
K
mKp02 (GeV/c2)2
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
favored
suppressed
KS, p0
p
p-
B
K
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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 ? KS?-? BELLE 253/fb
m-
m-
(From B decays)
m
m
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D0?pp-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?pp-p
• Has large S-wave component (FOCUS ref)

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D0?pp-p0
S/(SB) 80 S 1100 9.0/fb
m2(pp0) (GeV2)
m2(pp-) (GeV2)
0 1 2 3
0 1 2 3
m2(pp-) (GeV2)
m2(p-p0) (GeV2)
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Amplitude Phase(o) Fit Fraction
rp- 1 (fixed) 0 (fixed) 76.51.82.5
r0p0 0.560.020.03 1032 23.91.82.1
r-p 0.650.030.02 17632 32.32.11.3
NR 1.030.170.12 7785 2.70.90.2
pp- proj
lt 6.4 _at_ 95 CL
0 1 2 3 GeV2
Amplitude Phase(o) Fit Fraction
rp- 1 (fixed) 0 (fixed) 78.02.1
r0p0 0.560.02 93 24.41.9
r-p 0.660.03 1763 33.92.3
s(500) 0.220.06 35524 0.080.08
lt 0.21 _at_ 95 CL
0 1 2 3 GeV2
Amplitude Phase(o) Fit Fraction
rp- 1 (fixed) 0 (fixed) 76.31.92.5
r0p0 0.570.030.03 1032 24.42.02.1
r-p 0.670.030.02 17832 34.52.41.3
K-matrix 0.700.200.12 2145 0.90.70.2
See Au, Morgan, Pennington PRD 35, 1633 (1987)
lt 1.9 _at_ 95 CL
0 1 2 3 GeV2
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D0?pp-p0

• Only rp contributions plus small non-resonant
  component are required to fit Dalitz plot.
• Very small D0?pp-p0 S-wave fit fraction (lt0.9)
  compared to FOCUS (56) for D?pp-p
• D?pp-p / D0?pp-p0 S-wave ratio gt 36_at_95CL
• Tree level estimate
• Flavor tagged D0 and D0 Dalitz plots also fit
  separately to limit DP integrated CP asymmetry
• ACP

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S/(SB) 70 S 700
D0? Ks?0?0
m2(p0p0) (GeV2)

• 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(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)
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CLEO-c data (165 pb-1)
CLEO-II.V III (15 fb-1)
S/(SB) 70 S 700
S/(SB) 72 S 1500
m2(p0p0) (GeV2)
m2(KSp0)RS (GeV2)
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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.D70072003,2004 hep-ex/0406067
• BaBar ICHEP04 paper hep-ex/0408088

D Decay Model Systematic Uncertainty
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2
S/(SB) 98 S 5300
CLEO-II.V D0? Ks??-
Rather low statistics compared to
m2(p-p) (GeV2)
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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
0
0
3
2
1
m2(KSp)RS (GeV2)
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2.27x108 BB pairs
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 systematicuncertainty !
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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.

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Many other CLEO-c Dalitz plot analyses are in the
works
K-ph
p-pp0
KSKSp0
K-pp0
KSKK-
KSKp
KSpp0
ppp-
etcmany others
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Conclusions

• CLEO has done (and continues to do)
  groundbreaking work on charm Dalitz analyses.
• K-pp0,pp-p0,KSpp-,KS?p0,K-Kp0,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