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

M. Selen, HEP-05 2

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.

M. Selen, HEP-05 3

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

M. Selen, HEP-05 4

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

M. Selen, HEP-05 5

The power of the DP approachInterference is a beautiful thing !

Phase sensitivity is a very important handle

Example:D0 → K− π+ π0

M. Selen, HEP-05 6

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)

M. Selen, HEP-05 7

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

M. Selen, HEP-05 8

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

M. Selen, HEP-05 9

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

M. Selen, HEP-05 10

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

M. Selen, HEP-05 11

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

M. Selen, HEP-05 12

*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

M. Selen, HEP-05 13

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)

M. Selen, HEP-05 14

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

M. Selen, HEP-05 15

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 ±+

−

M. Selen, HEP-05 18

• 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

M. Selen, HEP-05 19

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

M. Selen, HEP-05 20

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

M. Selen, HEP-05 21

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 !

M. Selen, HEP-05 24

( ) ( ) ( )−+−+−+ = 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 ,

M. Selen, HEP-05 25

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

M. Selen, HEP-05 26

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