Hadronic Substructure & Dalitz Analyses at CLEO · Mats Selen, University of Illinois HEP 2005,...
Transcript of Hadronic Substructure & Dalitz Analyses at CLEO · Mats Selen, University of Illinois HEP 2005,...
M. Selen, HEP-05 1
Hadronic Hadronic Substructure Substructure
& Dalitz & Dalitz Analyses at Analyses at
CLEOCLEO
Mats Selen, University of IllinoisHEP 2005, July 22, Lisboa, Portugal
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OutlineWhy the interest in charm Dalitz Plot (DP) analyses?Results from CLEO
D0 → K+K−π0
D0 → π+π−π0
D0 → Ksπ0π0
What CLEO-c will do for CKM angle γ/φ3.
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CLEO II.V (9/fb)
CLEO III (14/fb)
CLEO-c (281/pb)
New RICHNew Drift Chamber
New siliconNew Trigger & DAQ
Replace siliconwith a wire
vertex chamber
CLEO Evolution
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Why bother?Need to understand the brown muck.
Final state interactions are trickyRelative 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 φ3 from B→DK
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The power of the DP approachInterference is a beautiful thing !
Phase sensitivity is a very important handle
Example:D0 → K− π+ π0
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a1 eiφ1 + a2 + a3 + a4
+ a5 + a6 + a7 + a8eiφ5
eiφ2 eiφ3 eiφ4
eiφ6 eiφ7
=
eiφ8
79% ρ(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% ρ(1700)
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Relevance to φ3
There are several schemes to access γ/φ3 by exploiting interference in the decays of charged B mesons to charm: B → DK
D → K*KGrossman, Ligeti, Soffer PRD 67 (2003)Suprun, Rosner PRD 68 (2003)CLEO analysis of D0 → K+K−π0
D → 3-body/Dalitz Giri, Grossman, Soffer, Zupan PRD 68 (2003)CLEO analysis of D0 → KSπ+π−, π+π−π0
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Method for measuring CKM phase φ3 by looking at B± → (K*+ K−)DK ± and B± → (K*− K+)DK ±
Needs a measurement of the strong phase difference δD between D0 → K*+ K– and D0 → K*– K+.Dalitz analysis of D0 → K+K−π0 will yield δD
D0→K+K−π0
δ=0 δ=180
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K*−
K*+
φ
mΚ
+ π02
(GeV
/c2 )
2
mΚ−π02 (GeV/c2)2
Signal Fraction ≈ 77.4%Signal Events ≈ 565565
(in the signal region)
mΚ+Κ−π0 (GeV/c2)
K± Κm π0
signal region(after selection criteria)
D*+ → π+ D0
K+ K– π0
γ γ
→→
D0→K+K−π0CLEO III CLEO III ϒ(4S) Region: : 8.965/fb8.965/fb
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Preliminary FitStatistical errors only
ResonanceResonance amplitude amplitude aa phase phase θθ
KK**(892)(892)++ Fixed to 1 Fixed to 0
K*(892)K*(892)-- 0.4951 ± 0.0530 331.48 ± 10.35
φ φ (1020)(1020) 0.4911 ± 0.0487 99.55 ± 12.94
nonresonantnonresonant 5.6660 ± 0.4035 225.40 ± 6.67
Fit FractionsFit Fractions
ResonanceResonance Fit FractionFit Fraction
KK**(892)(892)++ 45.20% ± 2.97%
K*(892)K*(892)-- 11.01% ± 2.25%
φ φ (1020)(1020) 8.57% ± 1.56%
nonresonantnonresonant 35.91% ± 3.46%
100.69% ± 5.32%
D0→K+K−π0
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mΚ−π02 (GeV/c2)2mΚ+π02 (GeV/c2)2
K*−K*+
Fit projections reveal a feature/problem…
dips → are we missing some physics ??Exploring K-π P-wave K-matrix approach
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*0~ ubcsVVKDB −− →
Access φ3 via interference between B± → D0K± and B± → D0K±
*0 ~ cbusVVKDB −− →
b c
u u
u
sb
su u
cu
KS, π0
π+
π−
K±
B±±D~
φ3 from 3-body final states
( ) 00 3~ DreDD i ϕδ −
− +=( ) 00
3~ DreDD i ϕδ +
+ +=
suppressedfavored
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2±=± πSKmm
Where is the amplitude of the D0 matrix element atthe point on the Dalitz Plot, and
( )yxf ,( )yx,
( ) ( ) ( )±±
±± += mmfremmfDAmp i ,,)~( 3mm
ϕδ
Once has been determined (where we come in) then D+ and D− Dalitz plots can be fit to determine φ3.
( )yxf ,
Amplitude differences willbe sensitive to φ3.
~ ~
D+~ D−
~
m+ m+
m−m−
D → KSπ−π+
BELLE253/fb
~
(From B± decays)
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Useful for studying φ3 in charged B decays.Like D0→KSπ−π+ (discussed later)
Good system for CP violation search.Some predictions as high as 0.1% (ref)
Compare to D+→π+π−π+
Has large S-wave component (FOCUS ref)
D0→π+π−π0
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m2(π+π−) (GeV2)
m2 (
π+ π0 )
(GeV
2 ) S/(S+B) ~ 80%
S ~ 11009.0/fb
m2(π+π−) (GeV2) 0 1 2 3
m2(π+π0) (GeV2) 0 1 2 3
m2(π−π0) (GeV2) 0 1 2 3
D0→π+π−π0
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Amplitude Phase(o) Fit Fraction %ρ+π− 1 (fixed) 0 (fixed) 76.5±1.8±2.5
ρ0π0 0.56±0.02±0.03 10±3±2 23.9±1.8±2.1
ρ−π+ 0.65±0.03±0.02 176±3±2 32.3±2.1±1.3NR 1.03±0.17±0.12 77±8±5 2.7±0.9±0.2
Amplitude Phase(o) Fit Fraction %ρ+π− 1 (fixed) 0 (fixed) 78.0±2.1
ρ0π0 0.56±0.02 9±3 24.4±1.9
ρ−π+ 0.66±0.03 176±3 33.9±2.3
σ(500) 0.22±0.06 355±24 0.08±0.08< 0.21 @ 95% CL
< 6.4 @ 95% CL
Amplitude Phase(o) Fit Fraction %ρ+π− 1 (fixed) 0 (fixed) 76.3±1.9±2.5
ρ0π0 0.57±0.03±0.03 10±3±2 24.4±2.0±2.1
ρ−π+ 0.67±0.03±0.02 178±3±2 34.5±2.4±1.3K-matrix 0.70±0.20±0.12 2±14±5 0.9±0.7±0.2
< 1.9 @ 95% CL
π+π− proj
0 1 2 3 GeV2
0 1 2 3 GeV2
0 1 2 3 GeV2See Au, Morgan, Pennington PRD 35, 1633 (1987)
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D0→π+π−π0
Only ρπ contributions plus small non-resonant component are required to fit Dalitz plot.
Very small D0→π+π−π0 S-wave fit fraction (<0.9%) compared to FOCUS (56%) for D+→π+π−π+
D+→π+π−π+ / D0→π+π−π0 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 =
( ) 18232
=
05.001.0 09.007.0 ±+
−
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• Lots of brown muck • Complement KSπ−π+ analyses• Good place to search for low mass ππ
• No ρ →π0π0 to get in the way!
m2(π0π0) (GeV2)0 1 2
K*(890) + K0(1430) + f0 + NR
m2(π0π0) (GeV2)0 1 2
D0→ Ksπ0π0S/(S+B) ~ 70%
S ~ 700
m2 (
π0 π0 )
(GeV
2 )
m2(ΚSπ0)RS (GeV2) K*(890) + K0(1430) + f0 + NR + σ
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S/(S+B) ~ 70%S ~ 700
m2 (
π0 π0 )
(GeV
2 )
m2(ΚSπ0)RS (GeV2)
CLEO-II.V & III(~15 fb-1)
CLEO-c data(165 pb-1)
S/(S+B) ~ 72%S ~ 1500
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What CLEO-c will do for φ3
( ) ( ) ( )±±
±± += mmfremmfDAmp i ,,)~( 3mm
ϕδ
The determination of is presently the limiting systematic( )yxf ,
Belle and BaBar have studied the dependence of φ3 on the D decay model (analysis used D0 → Ksπ+π−)
Belle - Phys.Rev.D70:072003,2004 hep-ex/0406067
BaBar – ICHEP04 paper hep-ex/0408088
( )o111377 17193 ±±= +
−φ
( )o10102670 ±±±=γ
D Decay ModelSystematic Uncertainty
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Fit Fraction (%)(stat err shown)
Κ∗(892)+π− 0.34 ± 0.13
Κ∗(892)−π+ 65.7 ± 1.3
Κ0ρ0 26.4 ± 0.9
Κ0ω 0.72 ± 0.18
Κ0f0(980) 4.3 ± 0.5
Κ0f2(1270) 0.27 ± 0.15
Κ0f0(1370) 9.9 ± 1.1
Κ0∗(1430)−π+ 7.3 ± 0.7
Κ2∗(1430)−π+ 1.1 ± 0.2
Κ∗(1680)−π+ 2.2 ± 0.4
NR 0.9 ± 0.4
m2(ΚSπ+) (GeV2) 0 1 2 3
m2(π−π+) (GeV2) 0 1 2 3
m2(ΚSπ−) (GeV2) 0 1 2 3
m2 (
π− π+ )
(GeV
2 )
m2(ΚSπ)RS (GeV2)
S/(S+B) ~ 98%S ~ 5300
0
1
2
0 1 2 3
CLEO-II.V D0→ Ksπ+π− Rather low
statistics compared to…
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BaBar data with“CLEO” model
not so good
2.27x108 BB pairs
BELLE fits look like BaBar
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Fit with additionalresonances muchbetter.
This includes BWσ1 and σ2 with ~10% fit fractions.
Causes big systematicuncertainty !
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( ) ( ) ( )−+−+−+ = mmiemmfmmf ,,, φ
Do simultaneous CP tagged and flavor tagged analysis of D0 → Ksπ+π− [only at ψ’’(3770)]
Suppose we write
CLEO-c can help
We will extract as well as in a model independent way.
This is exactly what the φ3 analyses need.
( ) ( )[ ]+−−+ − mmmm ,,cos ϕϕ( )−+ mmf ,
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Many other CLEO-c Dalitz plot analyses are in the works:
Κ−π+π0 Κ−π+η π−π+π0 ΚSΚSπ0
ΚSΚ+Κ− π+π+π−ΚSΚπ ΚSπ+π0
etc…many others
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ConclusionsCLEO has done (and continues to do) groundbreaking work on charm Dalitz analyses.
Κ−π+π0,π+π−π0,ΚSπ+π−,ΚSηπ0,Κ−Κ+π0,ΚSπ0π0, ...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 analysesφ3, mixing, CP violation, …
Double correlated Dalitz analyses (i.e. DP vs DP)
Stay tuned