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## Charm Dalitz Analyses at BaBar

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### Charm Dalitz Analyses at BaBar

Marco Pappagallo

Durham IPPP & University of Warwick

On behalf of BaBar Collaboration

Charm06, Beijing June 05-07, 2006

Outline

- BaBar Detector
- D0K0K+K- decay and a0(980) meson
- Partial Wave Analysis
- Dalitz Plot Fit
- D0K0π+π- decay and CKM angle
- Dalitz Plot Fit (Isobar Model)
- Dalitz Plot Fit (K-matrix Model)

Phys.Rev.D72:052008,2005

Phys.Rev.Lett.95:121802,2005

hep-ex/0507101

Marco Pappagallo,

Durham IPPP & University of Warwick

Scalar mesons and D meson decays

- On the experimental side:
- Scalar mesons are difficult to resolve because of their large decay widths.
- On the QCD theory side:
- Scalar meson candidates are too numerous to fit in a single qq nonet. Some of them may be multiquark, KK or other meson-meson bound states.
- Many models expect a glueball with mass in the range 1.5 - 1.8 GeV.

- Large coupling to scalar mesons;
- An initial state which is always defined: JP=0-;
- Spectrum is not constrained by isospin and parity conservation.

- D meson decays:
- Charmed meson decays have unique features, making them a very powerful tool for light quark spectroscopy:

Marco Pappagallo,

Durham IPPP & University of Warwick

a0/f0(980) mesons & D0K0K+K- decay

There are experimental evidences that clearly indicate the existence of non-strange and strange content in f0(980) and in a0(980) mesons. Their quark content mixture is not understood yet.

a0/f0(980) mesons lie close to the KK threshold which can strongly influence the resonance shape. A Flatte’ formula is usually used to parameterize these state but mass and coupling constant are still affected by large uncertainties

The D0K0K+K- decay provides a tool to study these resonances in the final states KK

Marco Pappagallo,

Durham IPPP & University of Warwick

D0K0K+K- decay selection

4σ

Event selection uses:

Sample = 12540 Events

Purity = 97.3%

@ 91.5 fb-1

- D* tagging procedure is two-fold useful:
- Selection of high purity sample
- D0 and K0 flavour set by the charge of the slow pion πs+

Presence of Doubly Cabibbo Suppressed contribution may lead to misidentification of K0 flavour.

Marco Pappagallo,

Durham IPPP & University of Warwick

Partial Wave Analysis

Large Forward-Backward Asymmetry variation with the K+K- mass due to interference between K+K-

S-wave(a0(980)/f0(980)) and K+K-P-wave(Φ(1020))

Contribution due to a0(980)+ doesn’t overlap with the Φ(1020) region. A partial wave analysis in the low mass K+K- region allows the K+K- scalar and vector components to be separated resolving:

S.U. Chung, Phys. Rev. D56, 7299(1997)

Marco Pappagallo,

Durham IPPP & University of Warwick

Partial Wave Analysis

Helicity angle θK

Each event was weighted by the spherical harmonicY0ℓ(cos K) (ℓ=0,1,2) divided by its estimated efficiency.

Marco Pappagallo,

Durham IPPP & University of Warwick

Simultaneous fit to P2, S2, φSP and m(K0K+)

FREE

Fixed to Crystal Barrel measurement A. Abele et al., Phys. Rev. D57, 3860(1998)

- K+K- system: Φ(1020) and a0(980)0
- [No evidence of f0(980) (I=0) comparing K0K+ and K+K- (normalized) S-waves]
- K0K+ system: a0(980)+

Marco Pappagallo,

Durham IPPP & University of Warwick

Result of a Partial Wave Analysis

P2

S2

φSP

gkk= 464 ±29(stat.) (MeV)1/2

Marco Pappagallo,

Durham IPPP & University of Warwick

Isobar model formalism

D0 three-body decay D0ABC decaying through an r=[AB] resonance

S. Kopp et al., Phys.Rev.D63:092001,2001

D0 three-body amplitude

NR term(direct 3 body decay)

a0, δ0, ar, δr : Free parameters of fit

Relativistic Breit-Wigner

a0(980)/f0(980)

Angular distribution

D and r Blatt-Weisskopfform factors

Marco Pappagallo,

Durham IPPP & University of Warwick

Dalitz Plot Fit of D0K0K+K-

Results of an unbinned maximum likelihood fit

- Decay is dominated by D0K0a0(980)0, D0K0(1020) and D0K- a0(980)+
- DCS and f0(980) contributions consistent with zero
- Presence of tail of a broad resonance (f0(1400)?)

gkk= 473 ±29(stat.) ±40(syst.) (MeV)1/2

f0(980) parameters M. Ablikim et al., Phys.Lett.B607:243-253,2005

Marco Pappagallo,

Durham IPPP & University of Warwick

D0K0+-decay & CKM angle γ

bc transition

bu transition

i δB

-i γ

e

e

Vub

Vcb

γ can be measured from the interference between decays with bcus and bucs transitions

Interference occurs when some final state is accessible by both D0 and D0Giri-Grossman-Soffer-Zupan: PRD68, 054018 (2003): Final state = Ks0π+π- Dalitz Plot Analysis

2

Schematic

view of the

interference

|A-|2 =

Simultaneous fit to the |A_(m-2, m+2)|2 and |A+(m-2, m+2)|2distributions to determine the CP parameters rB, δB and γfor each decay mode(B± D(*)0 K(*)±).

Marco Pappagallo,

Durham IPPP & University of Warwick

D0K0π+π- decay selection

Event selection uses:

D0’s are required to result from a D* meson decay

+

Sample = 81496 Events

Purity = 97%

@ 91.5 fb-1

Analysis will be updated to the full data set

Marco Pappagallo,

Durham IPPP & University of Warwick

Dalitz plot fit(Isobar Model)

Isobar model resonances + Non resonant term

DCS

DCS

DCS

Fit requires two additional BW amplitudes but…

…in this analysis the Dalitz amplitude is only a means to extract the CP parameters

Total fit fraction = 1.24

χ2/dof3824/3022=1.27

γ systematic errors include a fit without ’s

Marco Pappagallo,

Durham IPPP & University of Warwick

K-Matrix Model in ππS-wave

K-Matrix formalism overcomes the main limitation of the BW model to parameterize large and overlapping S -wave ππ resonances.

D0K0π+π-amplitude

+

+

I.J.R. Aitchison, Nucl. Phys. A189, 417 (1972)

+ …

Initial production vector

Pj

[I-iKρ]1j-1

Provided by scattering experiment

5 channels: 1=pp2=KK 3=multi-meson 4= hh5= hh´

V.V. Anisovitch, A.V Sarantev Eur. Phys. Jour. A16, 229 (2003)

Marco Pappagallo,

Durham IPPP & University of Warwick

Dalitz plot fit (K-Matrix Model)

K-Matrix model resonances + pp S-wave term

DCS

DCS

DCS

pp S-wave term

Value of 2 compatible with nominal model

since it is dominate by the P-wave components,

which are identical between the two model

Total fit fraction = 1.16

Marco Pappagallo,

Durham IPPP & University of Warwick

Influence of Dalitz model on γ

γ=(67 ± 28stat ± 13syst ± 11Dalitz)0

- Remove combinations of higher K* and ρ resonances (with low fit fraction)
- Change the functional form of the resonance shapes
- Fit without the σ and σ’
- ππ S-wave described by K-matrix model

Small effect: 30

Marco Pappagallo,

Durham IPPP & University of Warwick

Summary

D0K0K+K- anda0(980) parameters

- Partial Wave Analysis
- Dalitz Plot Fit
- Measurement of the coupling gKK of a0(980) to the KK system
- Small contribution of DCS and f0(980)KK decays

D0K0π+π- and CKM angle γ

- Dalitz Plot Fit with an Isobar model
- Dalitz Plot Fit with a K-matrix model
- Small effect on γmeasurement due to IsobarK-matrix model

Charm Dalitz plot analyses will continue to play an important rule: measurement of resonances parameters, investigation of controversial scalar mesons, D0-D0 mixing,…

Marco Pappagallo,

Durham IPPP & University of Warwick

PEP II and BaBar

(e+e-cc) = 1.3 nb

450M cc pairs!

Marco Pappagallo,

Durham IPPP & University of Warwick

Partial Wave Analysis

S.U. Chung, Phys. Rev. D56, 7299(1997):

Marco Pappagallo,

Durham IPPP & University of Warwick

Partial Wave Analysis

Dalitz Plot Projection

(1020) reflection

Marco Pappagallo,

Durham IPPP & University of Warwick

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