DsJ mesons
Jolanta Brodzicka (KEK) for Belle
QWG5, DESY
17-20 October 2007
J. Brodzicka for Belle @ QWG5
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Introduction to cs multiplets
Observation of new DsJ(2700) →D0K+ in B+→D0D0K+
Observation of Ds1(2536)→D+π-K+
Partial Wave Analysis of Ds1(2536)→D*+K0s
• Summary
Outline
J. Brodzicka for Belle @ QWG5
cs multiplets
Theory:

HQS based potential model predictions:
(Godfrey-Isgur ‘85)
two doublets for orbitally excited L=1 cs states:
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0+, 1+ (jq=1/2) and 1+, 2+ (jq=3/2)
M(jq=1/2), M(jq=3/2) > MD+MK
Γ(jq=1/2) >> Γ(jq=3/2)
Experiment:
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L=2
jq = sq + L,
…..
L=1
0+ : D*s0(2317)→Dsπ0
1+ : Ds1(2460)→D*sπ0
J = jq + s Q
JP
jq = 3/2
2+
DsJ(2573)
1+ Ds1(2536)
jq = 1/2
mix? +
1
D*K
Ds1(2460)
DK
L=0
tensor s-o
spin-spin
jq = 1/2
1- Ds*
0- Ds
BaBar
CLEO ‘03
Belle
very narrow, masses below D(*)K
→ don’t match the model predictions
→ how to accommodate them within
current models?
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0+ D* (2317)
s0
spin-orbit
jq=1/2 doublet
jq=3/2 doublet
1+: Ds1(2536)→D*K (Argus ‘89)
2+: DsJ(2573)→DK
(CLEO ‘94)
their properties need to be measured
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higher orbital/radial
excitations?
J. Brodzicka for Belle @ QWG5
New DsJ meson in B+→D0D0K+
hep-ex/0707.3491
(submitted to PRL)
• b→ccs tree process; cs→D0K+ and cc→D0D0 states can contribute
• B+→D0D0K+ signal identified using:
ΔE=EB-Ebeam , Ebeam=√s/2 : cms energy difference
Mbc= √E2beam-p2B : beam-constrained mass
• S=399±40 for 449M BB used
• BF(B+→D0D0K+)=(22.2±2.2+2.6-2.4) x10-4
Mbc
ΔE
• Dalitz plot and mass projections
different from 3-body Ph. Space
new DsJ
(4160)
(3770)
points: events from 1.5σ ΔE-Mbc signal box
■:background from sidebands
J. Brodzicka for Belle @ QWG5
Decomposition of B+→D0D0K+ Dalitz plot
• 2D ΔE-Mbc fits in invariant mass bins → B signal extracted
• Obtained background-free mass spectra used to estimate the
resonance contributions:
ψ(4160) in
½ helicity distr.
ψ(3770)
fitted B signal yield
DsJ(2700)
M(D0K+) for M(D0D0)>3.85 GeV
fitted with: Breit-Wigner
+ ψ(4160) reflection + Ph. Space (shapes from MC)
+ exponential function (to describe the threshold
enhancement (?) )
• Non-coherent approach; possible interference
effects included in syst. errors
J. Brodzicka for Belle @ QWG5
DsJ(2700) →D0K+ in B+→D0D0K+
fitted B signal yield
• Helicity angle distribution of DsJ(2700):
(background free and efficiency corrected;
reflections from threshold and ψ(4160) subtracted)
• J=1 preferred; 1→0-0- decay implies P=-1
• Contributions to the observed mass spectra
J=0 2/ndf=112/5
J=1 2/ndf= 11/5
J=2 2/ndf=146/5
■DsJ(2700) ■ψ(3770) ■ψ(4160) ■3body ■threshold component
(MC predicted shapes)
• Most observed features well described
J. Brodzicka for Belle @ QWG5
DsJ(2700) interpretation
• DsJ(2700)→D0K+ 1- state can be:
• radial excitation 23S1
(predicted by potential models at M~2720GeV)
• chiral doubler state
1-
to
1+
Ds1(2536)
(predicted from chiral symmetry considerations
at M=2721±10 MeV)
Godfrey, Isgur
PRD 32, 189 (1985)
Close, Swanson
PLB 647, 159 (2007)
Nowak, Rho, Zahed
Acta Phys. Polon. B
35, 2377 (2004)
• BaBaR observed structure at M(DK)~2.69GeV produced
in e+e- continuum. Is that due to DsJ(2700)?
• DsJ(2860) observed by BaBar not seen in our data.
Its production in B decays suppressed by its high spin?
BaBar Coll. PRL 97, 222001 (2006)
J. Brodzicka for Belle @ QWG5
Observation of Ds1(2536)→D+π-K+
hep-ex/0709.4184
(submitted to PRD)
• Known decay modes of Ds1(2536): D*+Ks, D*0K+, Dsπ+π-(evidence)
• Study of e+e-→Ds1(2536)X using 462 fb-1,
Ds1(2536)→D+π-K+ and Ds1(2536)→D*+Ks (normalization mode)
• xP=pDs1/pmax>0.8 in e+e-cms pmax=√E2beam-M2Ds1
• Two-body mass spectra consistent with Phase Space
angular analysis performed for
Ds1(2536)→D*+Ks sample
J. Brodzicka for Belle @ QWG5
Mixing of jq=1/2 and jq=3/2 states
• HQET prediction for P-wave cs states:
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1+(jq=3/2)→D*K pure D-wave decay: Ds1(2536)→D*K
1+(jq=1/2)→D*K pure S-wave decay: but Ds1(2460)→D*K forbidden
• If HQET not exact: mixing of S-D waves possible
(by LS interaction, common decay channels, …)
• Exp. knowledge on the mixing:
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from BF’s ratio of Ds1(2460) radiative decays: D*sγ/Dsγ=0.31 ± 0.14
switch from |jq> to |2S+1LJ > basis
(from combined B decays
θ
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θ0
and e+e- study by Belle)
tan2(θ+θ0)=0.8 ± 0.4 where tan2θ0=2 (no-mixing case)
• Measurement of mixing angle: test of HQS, way to understand
unusual properties of jq=1/2 cs doublet
J. Brodzicka for Belle @ QWG5
Partial Wave Analysis of Ds1(2536)→D*+K0s
hep-ex/0709.4184
(submitted to PRD)
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The decay described by α, β, γ angels
Prediction for 1+ state
in the helicity formalism:
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ρ: helicity density matrix ρ00: longitudinal polarization ρ11= ρ-1-1=(1-ρ00)/2
z=√RΛ exp(iξ)=A10/A00
A10 , A00: ampl. of D*‘s helicity= ±1, 0
A10=(S+D/√2)/√3 A00=(S-√2D)/√3)
D, S: partial-wave ampl. in Ds1 decay
D/S= √2(z-1)/(1+2z) =√ΓD/ΓS exp(iη)
• If no angle integrated → ξ-dependent term survives
J. Brodzicka for Belle @ QWG5
Fit to angular distribution of
• 3D maximum-likelihood fit with PDF:
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Ds1(2536)→D*+K0s
Background PDF: from M(D*+Ks) sidebands, normalized
fbck: background fraction in M(D*+Ks) signal region: ~9%
ε(α,β,γ)/<ε> → efficiency correction
Fit result projections (bckgd subtracted and efficiency corrected):
• From χ2 of the fit: goodness-of-fit probability: 60%
J. Brodzicka for Belle @ QWG5
Results of Ds1(2536)→D*+K0s PWA
• Fit results (include systematic errors):
ΓS/ΓTOT = 0.72 ± 0.05
(η=43.9 ± 1.7°)
• S-wave dominates in Ds1(2536)→D*K, contradicts HQET
• Ds1(2460) and Ds1(2536) mix
• How to calculate the mixing angle θ? Help from theorists
needed to translate measurement to the jq=1/2, 3/2 states
Ds1’s helicity=0 preferred
Aligned production of jq=3/2 states is predicted by HQET (ρ00~0.497).
• First full analysis for P-wave cs mesons
CLEO integrated over β in PWA of D1(2420)→D*π PLB 331, 236; PLB 340, 194.
D1’-D1 mixing angle measured from B→D*ππ Dalitz plot analysis by Belle
(-0.10±0.03±0.02±0.02 rad)
PRD 69, 112002
J. Brodzicka for Belle @ QWG5
Summary
• New info to cs multiplets:
• new DsJ(2700)→D0K+ meson observed:
M=2708±9+11-10MeV Γ=108±26+36-31MeV JP=1It opens a box of higher radial/orbital excitations of cs states
• new decay mode: Ds1(2536)→D+π-K+ observed
• from PWA of Ds1(2536)→D*+Ks (first full analysis for cs mesons):
• S-wave dominates: ΓS/ΓTOT = 0.72 ± 0.05
• Ds1(2460) and Ds1(2536) mix
• longitudinal polarization: ρ00 = 0.490±0.013
→ Falk-Peskin HQET parameter: w3/2 = 0.266 ± 0.019
• …and to cc
• Ψ(3770)[→D0D0] production in B decays confirmed
• Ψ(4160)[→D0D0] production in B decays not significant
J. Brodzicka for Belle @ QWG5
Backup
J. Brodzicka for Belle @ QWG5
Ds1 recoil mass study
• Ds1(2536) recoil mass:
• Mrec spectrum indicates 2-body reactions:
e+e-→Ds1(2536)X, where X=Ds , D*s , higher D**s’s
• Mrec resolution: ~70MeV at 2GeV, 1/Mrec dependence
• 3D fits to angular distribution
in bins of Mrec (RΛ and ξ fixed)
• Polarization at low Mrec:
show structures expected for:
e+e-→Ds1(2536)Ds , Ds1(2536)D*s
• HQET Falk-Peskin parameter w3/2 (prob. of light quark’s helicities)
• ρ00=2/3(1- w3/2)
w3/2 = 0.266 ± 0.019
(w3/2 <0.24 @90%CL from D2*(2460)→Dπ by ARGUS)
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