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

Outline Why the interest in charm Dalitz Plot (DP) analyses? Results from CLEO

D0 → K+K0 D0

D0 Ks0

What CLEO-c will do for CKM angle /3.

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 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 3 from BDK

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

M. Selen, HEP-05 6

a1 ei1 + a2+ a3 + a4

+ a5 + a6 + a7 + a8ei5

ei2 ei3 ei4

ei6 ei7

=

ei8

79% (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% (1700)

M. Selen, HEP-05 7

Relevance to 3

There are several schemes to access /3 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 D KK

D 3-body/Dalitz Giri, Grossman, Soffer, Zupan PRD 68 (2003) CLEO analysis of D KS,

M. Selen, HEP-05 8

Method for measuring CKM phase by looking at B± → (K*+ K)DK ± and B± → (K* K)DK ±

Needs a measurement of the strong phase difference D between D0 → K*+ K– and D0 → K*– K+.

Dalitz analysis of D0 → K+K0 will yield D

D0KK

=0 =180

M. Selen, HEP-05 9

K*

K*

m

2 (G

eV/c

2 )2

m2 (GeV/c2)2

Signal Fraction 77.4%

Signal Events 565565(in the signal region)

m (GeV/c2)

K 0

signal region(after selection criteria)

D*+ → + D0

K+ K– 0

→

→

D0KKCLEO III CLEO III (4S) Region: : 8.965/fb8.965/fb

M. Selen, HEP-05 10

Preliminary FitStatistical errors only

ResonanceResonance amplitude amplitude aa phase phase

KK**(892)(892)++ Fixed to 1 Fixed to 0

K*(892)K*(892)-- 0.4951 0.0530 331.48 10.35

(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%

(1020)(1020) 8.57% 1.56%

nonresonantnonresonant 35.91% 3.46%

100.69% 5.32%

D0KK

M. Selen, HEP-05 11

m2 (GeV/c2)2m

2 (GeV/c2)2

K*K*

Fit projections reveal a feature/problem…

dips are we missing some physics ??Exploring K- P-wave K-matrix approach

M. Selen, HEP-05 12

*0~ ubcsVVKDB

Access 3 via interference between B± D0K± and B± D0K±

*0 ~ cbusVVKDB

b c

u u

u

sb

su u

cu

KS, 0

K±

B±D

~

3 from 3-body final states

00 3~

DreDD i

003

~DreDD i

suppressedfavored

M. Selen, HEP-05 13

2 SK

mmWhere is the amplitude of the D0 matrix element atthe point on the Dalitz Plot, and

yxf , yx,

mmfremmfDAmp i ,,)

~( 3

Once has been determined (where we come in) then

D+ and D Dalitz plots can be fit to determine 3. yxf ,

Amplitude differences willbe sensitive to 3.

~ ~

D+

~D

~

m+ m+

mm

D KS+

BELLE253/fb

~

(From B± decays)

M. Selen, HEP-05 14

Useful for studying 3 in charged B decays.

Like D0KS(discussed later)

Good system for CP violation search. Some predictions as high as 0.1% (ref)

Compare to D+ Has large S-wave component (FOCUS ref)

D0

M. Selen, HEP-05 15

m2() (GeV2)

m2 (

) (G

eV2 )

S/(S+B) ~ 80% S ~ 1100

9.0/fb

m2() (GeV2)

0 1 2 3m2() (GeV2)

0 1 2 3m2() (GeV2)

0 1 2 3

D0

M. Selen, HEP-05 16

Amplitude Phase(o) Fit Fraction %

+ 1 (fixed) 0 (fixed) 76.5±1.8±2.5

0 0.56±0.02±0.03 10±3±2 23.9±1.8±2.1

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

Amplitude Phase(o) Fit Fraction %

+ 1 (fixed) 0 (fixed) 78.0±2.1

0 0.56±0.02 9±3 24.4±1.9

0.66±0.03 176±3 33.9±2.3

(500) 0.22±0.06 355±24 0.08±0.08

< 0.21 @ 95% CL

< 6.4 @ 95% CL

Amplitude Phase(o) Fit Fraction %

+ 1 (fixed) 0 (fixed) 76.3±1.9±2.5

0 0.57±0.03±0.03 10±3±2 24.4±2.0±2.1

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

< 1.9 @ 95% CL

proj

0 1 2 3 GeV2

0 1 2 3 GeV2

0 1 2 3 GeV2

See Au, Morgan, Pennington PRD 35, 1633 (1987)

M. Selen, HEP-05 17

D0

Only contributions plus small non-resonant component are required to fit Dalitz plot.

Very small D0 S-wave fit fraction (<0.9%) compared to FOCUS (56%) for D+ D+ / D0 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 KSanalyses• Good place to search for low mass

• No 00 to get in the way!

m2() (GeV2)

0 1 2

K*(890) + K0(1430) + f0 + NR

m2() (GeV2)

0 1 2

D0 Ks0S/(S+B) ~ 70% S ~ 700

m2 (

) (G

eV2 )

m2(S)RS (GeV2)

K*(890) + K0(1430) + f0 + NR +

M. Selen, HEP-05 19

S/(S+B) ~ 70% S ~ 700

m2 (

) (G

eV2 )

m2(S)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 for3

mmfremmfDAmp i ,,)

~( 3

The determination of is presently the limiting systematic yxf ,

Belle and BaBar have studied the dependence of on

the D decay model (analysis used D0 Ks)

Belle - Phys.Rev.D70:072003,2004 hep-ex/0406067

BaBar – ICHEP04 paper hep-ex/0408088

o111377 17

193

o10102670

D Decay Model

Systematic

Uncertainty

M. Selen, HEP-05 21

Fit Fraction (%) (stat err shown)

0.34 ± 0.13

65.7 ± 1.3

26.4 ± 0.9

0.72 ± 0.18

f 4.3 ± 0.5

f 0.27 ± 0.15

f 9.9 ± 1.1

7.3 ± 0.7

1.1 ± 0.2

2.2 ± 0.4

NR 0.9 ± 0.4

m2(S) (GeV2) 0 1 2 3

m2() (GeV2) 0 1 2 3

m2(S) (GeV2) 0 1 2 3

m2 (

) (G

eV2 )

m2(S)RS (GeV2)

S/(S+B) ~ 98% S ~ 5300

0

1

2

0 1 2 3

CLEO-II.V D0 Ks

Rather low statistics compared to…

M. Selen, HEP-05 22

BaBar data with“CLEO” model

not so good

2.27x108 BB pairs

BELLE fits look like BaBar

M. Selen, HEP-05 23

Fit with additionalresonances muchbetter.

This includes BW

1 and 2 with ~10% fit fractions.

Causes big systematicuncertainty !

M. Selen, HEP-05 24

mmiemmfmmf ,,,

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 3 analyses need.

mmmm ,,cos mmf ,

M. Selen, HEP-05 25

Many other CLEO-c Dalitz plot analyses are in the works:

SS

S S S

etc…many others

M. Selen, HEP-05 26

Conclusions CLEO has done (and continues to do) groundbreaking

work on charm Dalitz analyses. SSS, 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

3, mixing, CP violation, … Double correlated Dalitz analyses (i.e. DP vs DP)

Stay tuned