1. D sJ mesons Jolanta Brodzicka (KEK) for Belle QWG5, DESY 17-20 October 2007

2. Outline Introduction to cs multipletsIntroduction to cs multiplets Observation of new D sJ (2700) → D 0 K + in B + → D 0 D 0 K +Observation of new D sJ (2700) → D 0 K + in B + → D 0 D 0 K + Observation of D s1 (2536) → D + π - K +Observation of D s1 (2536) → D + π - K + Partial Wave Analysis of D s1 (2536) → D* + K 0 sPartial Wave Analysis of D s1 (2536) → D* + K 0 s SummarySummary J. Brodzicka for Belle @ QWG5

3. cs multiplets Theory:  HQS based potential model predictions: (Godfrey-Isgur ‘85) two doublets for orbitally excited L=1 cs states: two doublets for orbitally excited L=1 cs states: 0 +, 1 + (j q =1/2) and 1 +, 2 + (j q =3/2) 0 +, 1 + (j q =1/2) and 1 +, 2 + (j q =3/2) M(j q =1/2), M(j q =3/2) > M D +M K M(j q =1/2), M(j q =3/2) > M D +M K Γ(j q =1/2) >> Γ(j q =3/2) Γ(j q =1/2) >> Γ(j q =3/2) J. Brodzicka for Belle @ QWG5 spin-orbittensor s-o spin-spin L = 2 ….. j q = s q + L, J = j q + s QExperiment: j q =1/2 doublet j q =1/2 doublet 0 + : D * s 0 (2317) → D s π 0 1 + : D s 1 (2460) → D * s π 0 j q =3/2 doublet j q =3/2 doublet 1 + : D s 1 (2536) → D * K (Argus ‘89) 2 + : D s J (2573) → DK (CLEO ‘94) their properties need to be measured higher orbital/radial excitations? higher orbital/radial excitations? very narrow, masses below D ( * ) K → don’t match the model predictions → how to accommodate them within current models? BaBar CLEO ‘03 Belle L = 0 j q = 1/2 1-1- 0-0- Ds* Ds* Ds Ds mix? 0+0+ 1+1+ 1+1+ 2+2+ JPJP D*K D K D* s0 (2317) D s1 (2460) D s1 (2536) D sJ (2573) j q = 3/2 j q = 1/2 L = 1

4. b → ccs tree process; cs → D 0 K + and cc → D 0 D 0 states can contributeb → ccs tree process; cs → D 0 K + and cc → D 0 D 0 states can contribute B + → D 0 D 0 K + signal identified using:B + → D 0 D 0 K + signal identified using: ΔE=E B -E beam, E beam =√s/2 : cms energy difference ΔE=E B -E beam, E beam =√s/2 : cms energy difference M bc = √E 2 beam -p 2 B : beam-constrained mass M bc = √E 2 beam -p 2 B : beam-constrained mass S=399±40 for 449M BB usedS=399±40 for 449M BB used BF(B + → D 0 D 0 K + )=(22.2±2.2 +2.6 -2.4 ) x 10 -4BF(B + → D 0 D 0 K + )=(22.2±2.2 +2.6 -2.4 ) x 10 -4 Dalitz plot and mass projections Dalitz plot and mass projections different from 3-body Ph. Space different from 3-body Ph. Space New D sJ meson in B + → D 0 D 0 K + points: events from 1.5σ ΔE-Mbc signal box ■ :background from sidebands points: events from 1.5σ ΔE-Mbc signal box ■ :background from sidebands ΔEΔEΔEΔE M bc J. Brodzicka for Belle @ QWG5 hep-ex/0707.3491 (submitted to PRL)  (4160)  (3770) new D sJ

5. 2D ΔE-M bc fits in invariant mass bins → B signal extracted2D ΔE-M bc fits in invariant mass bins → B signal extracted Obtained background-free mass spectra used to estimate the resonance contributions:Obtained background-free mass spectra used to estimate the resonance contributions: fitted B signal yield M(D 0 K + ) for M(D 0 D 0 )>3.85 GeV fitted with: Breit-Wigner ψ(4160) reflection + Ph. Space (shapes from MC) + ψ(4160) reflection + Ph. Space (shapes from MC) + exponential function (to describe the threshold enhancement (? ) ) Decomposition of B + → D 0 D 0 K + Dalitz plot D sJ (2700) J. Brodzicka for Belle @ QWG5 ψ(4160) in ½ helicity distr. ψ(3770) Non-coherent approach; possible interference effects included in syst. errors

6. D sJ (2700) → D 0 K + in B + → D 0 D 0 K + Helicity angle distribution of D sJ (2700):Helicity angle distribution of D sJ (2700): ( background free and efficiency corrected; ( background free and efficiency corrected; reflections from threshold and ψ(4160) subtracted) reflections from threshold and ψ(4160) subtracted) J=1 preferred; 1 → 0 - 0 - decay implies P=-1J=1 preferred; 1 → 0 - 0 - decay implies P=-1 Contributions to the observed mass spectraContributions to the observed mass spectra Most observed features well describedMost observed features well described ■ D sJ (2700) ■ ψ(3770) ■ ψ(4160) ■ 3body ■ threshold component (MC predicted shapes) (MC predicted shapes) fitted B signal yield J. Brodzicka for Belle @ QWG5 J=0  2 /ndf=112/5 J=1  2 /ndf= 11/5 J=2  2 /ndf=146/5

7. D sJ (2700) interpretation D sJ (2700) → D 0 K + 1 - state can be:D sJ (2700) → D 0 K + 1 - state can be: radial excitation 2 3 S 1radial excitation 2 3 S 1 (predicted by potential models at M~2720GeV) (predicted by potential models at M~2720GeV) chiral doubler state 1 - to 1 + D s1 (2536) (predicted from chiral symmetry considerationschiral doubler state 1 - to 1 + D s1 (2536) (predicted from chiral symmetry considerations at M=2721±10 MeV) at M=2721±10 MeV) BaBaR observed structure at M(DK)~2.69GeV producedBaBaR observed structure at M(DK)~2.69GeV produced in e + e - continuum. Is that due to D sJ (2700)? in e + e - continuum. Is that due to D sJ (2700)? D sJ (2860) observed by BaBar not seen in our data.D sJ (2860) observed by BaBar not seen in our data. Its production in B decays suppressed by its high spin? Its production in B decays suppressed by its high spin? BaBar Coll. PRL 97, 222001 (2006) BaBar Coll. PRL 97, 222001 (2006) J. Brodzicka for Belle @ QWG5 Godfrey, Isgur PRD 32, 189 (1985) Close, Swanson PLB 647, 159 (2007) Nowak, Rho, Zahed Acta Phys. Polon. B 35, 2377 (2004)

8. Observation of D s1 (2536) → D + π - K + J. Brodzicka for Belle @ QWG5 hep-ex/0709.4184 (submitted to PRD) angular analysis performed for D s1 (2536) → D* + K s sample Known decay modes of D s1 (2536): D* + K s, D* 0 K +, D s π + π - (evidence)Known decay modes of D s1 (2536): D* + K s, D* 0 K +, D s π + π - (evidence) Study of e + e - → D s1 (2536)X using 462 fb -1,Study of e + e - → D s1 (2536)X using 462 fb -1, D s1 (2536) → D + π - K + and D s1 (2536) → D* + K s (normalization mode) D s1 (2536) → D + π - K + and D s1 (2536) → D* + K s (normalization mode) x P =p Ds1 / p max >0.8 in e + e - cms p max =√E 2 beam -M 2 Ds1x P =p Ds1 / p max >0.8 in e + e - cms p max =√E 2 beam -M 2 Ds1 Two-body mass spectra consistent with Phase SpaceTwo-body mass spectra consistent with Phase Space

9. Mixing of jq=1/2 and jq=3/2 states HQET prediction for P-wave cs states:HQET prediction for P-wave cs states: 1 + (j q =3/2) → D*K pure D-wave decay: D s1 (2536) → D*K 1 + (j q =3/2) → D*K pure D-wave decay: D s1 (2536) → D*K 1 + (j q =1/2) → D*K pure S-wave decay: but D s1 (2460) → D*K forbidden 1 + (j q =1/2) → D*K pure S-wave decay: but D s1 (2460) → D*K forbidden If HQET not exact: mixing of S-D waves possibleIf HQET not exact: mixing of S-D waves possible (by LS interaction, common decay channels, …) (by LS interaction, common decay channels, …) Exp. knowledge on the mixing:Exp. knowledge on the mixing: from BF’s ratio of D s1 (2460) radiative decays: D* s γ/D s γ=0.31 ± 0.14 from BF’s ratio of D s1 (2460) radiative decays: D* s γ/D s γ=0.31 ± 0.14 switch from |j q > to | 2S+1 L J > basis (from combined B decays switch from |j q > to | 2S+1 L J > basis (from combined B decays and e + e - study by Belle) and e + e - study by Belle) tan 2 (θ+θ 0 )=0.8 ± 0.4 where tan 2 θ 0 =2 (no-mixing case) tan 2 (θ+θ 0 )=0.8 ± 0.4 where tan 2 θ 0 =2 (no-mixing case) J. Brodzicka for Belle @ QWG5 θθ0θ0 Measurement of mixing angle: test of HQS, way to understand jq=1/2 cs doublet unusual properties of jq=1/2 cs doublet

10. The decay described by α, β, γ angelsThe decay described by α, β, γ angels Prediction for 1 + statePrediction for 1 + state in the helicity formalism: in the helicity formalism: ρ: helicity density matrix ρ 00 : longitudinal polarization ρ 11 = ρ -1-1 =(1- ρ 00 )/2ρ: helicity density matrix ρ 00 : longitudinal polarization ρ 11 = ρ -1-1 =(1- ρ 00 )/2 z=√R Λ exp(iξ)=A 10 /A 00 A 10, A 00 : ampl. of D*‘s helicity= ±1, 0z=√R Λ exp(iξ)=A 10 /A 00 A 10, A 00 : ampl. of D*‘s helicity= ±1, 0 A 10 =(S+D/√2)/√3 A 00 =(S-√2D)/√3)A 10 =(S+D/√2)/√3 A 00 =(S-√2D)/√3) D, S : partial-wave ampl. in D s1 decay D, S : partial-wave ampl. in D s1 decay D/S= √2(z-1)/(1+2z) =√Γ D /Γ S exp(iη) D/S= √2(z-1)/(1+2z) =√Γ D /Γ S exp(iη) Partial Wave Analysis of D s1 (2536) → D* + K 0 s J. Brodzicka for Belle @ QWG5 hep-ex/0709.4184 (submitted to PRD) If no angle integrated → ξ-dependent term survives If no angle integrated → ξ-dependent term survives

11. Fit to angular distribution of D s1 (2536) → D* + K 0 s 3D maximum-likelihood fit with PDF: Background PDF: from M(D* + K s ) sidebands, normalized f bck : background fraction in M(D* + K s ) signal region: ~9% ε(α,β,γ)/ → efficiency correction Fit result projections (bckgd subtracted and efficiency corrected) : From χ 2 of the fit: goodness-of-fit probability: 60% J. Brodzicka for Belle @ QWG5

12. Results of D s1 (2536) → D* + K 0 s PWA Results of D s1 (2536) → D* + K 0 s PWA Fit results (include systematic errors) :Fit results (include systematic errors) : Γ S /Γ TOT = 0.72 ± 0.05 (η=43.9 ± 1.7°) Γ S /Γ TOT = 0.72 ± 0.05 (η=43.9 ± 1.7°) S-wave dominates in D s1 (2536) → D * K, contradicts HQETS-wave dominates in D s1 (2536) → D * K, contradicts HQET D s1 (2460) and D s1 (2536) mixD s1 (2460) and D s1 (2536) mix How to calculate the mixing angle θ? Help from theoristsHow to calculate the mixing angle θ? Help from theorists needed to translate measurement to the j q =1/2, 3/2 states needed to translate measurement to the j q =1/2, 3/2 states D s1 ’s helicity=0 preferred D s1 ’s helicity=0 preferred A ligned production of j q =3/2 states is predicted by HQET (ρ 00 ~0.497). A ligned production of j q =3/2 states is predicted by HQET (ρ 00 ~0.497). First full analysis for P-wave cs mesonsFirst full analysis for P-wave cs mesons CLEO integrated over β in PWA of D 1 (2420) →D* π PLB 331, 236; PLB 340, 194. CLEO integrated over β in PWA of D 1 (2420) →D* π PLB 331, 236; PLB 340, 194. D 1 ’-D 1 mixing angle measured from B →D* ππ Dalitz plot analysis by Belle D 1 ’-D 1 mixing angle measured from B →D* ππ Dalitz plot analysis by Belle (-0.10±0.03±0.02±0.02 rad) PRD 69, 112002 (-0.10±0.03±0.02±0.02 rad) PRD 69, 112002 J. Brodzicka for Belle @ QWG5

13. Summary New info to cs multiplets: New info to cs multiplets: new D sJ (2700) → D 0 K + meson observed:new D sJ (2700) → D 0 K + meson observed: M=2708±9 +11 -10 MeV Γ=108±26 +36 -31 MeV J P =1 - M=2708±9 +11 -10 MeV Γ=108±26 +36 -31 MeV J P =1 - It opens a box of higher radial/orbital excitations of cs states It opens a box of higher radial/orbital excitations of cs states new decay mode: D s1 (2536) → D + π - K + observednew decay mode: D s1 (2536) → D + π - K + observed from PWA of D s1 (2536) → D *+ Ks (first full analysis for cs mesons):from PWA of D s1 (2536) → D *+ Ks (first full analysis for cs mesons): S-wave dominates: Γ S /Γ TOT = 0.72 ± 0.05S-wave dominates: Γ S /Γ TOT = 0.72 ± 0.05 D s1 (2460) and D s1 (2536) mixD s1 (2460) and D s1 (2536) mix longitudinal polarization: ρ 00 = 0.490±0.013longitudinal polarization: ρ 00 = 0.490±0.013 → Falk-Peskin HQET parameter: w 3/2 = 0.266 ± 0.019 → Falk-Peskin HQET parameter: w 3/2 = 0.266 ± 0.019 …and to cc …and to cc Ψ(3770)[ → D 0 D 0 ] production in B decays confirmed Ψ(3770)[ → D 0 D 0 ] production in B decays confirmed Ψ(4160)[ → D 0 D 0 ] production in B decays not significant Ψ(4160)[ → D 0 D 0 ] production in B decays not significant J. Brodzicka for Belle @ QWG5

14. Backup J. Brodzicka for Belle @ QWG5 J. Brodzicka for Belle @ QWG5

15. D s1 recoil mass study D s1 (2536) recoil mass: M rec spectrum indicates 2-body reactions: e + e - → D s1 (2536)X, where X=D s, D* s, higher D** s ’s M rec resolution: ~70MeV at 2GeV, 1/M rec dependence 3D fits to angular distribution in bins of M rec (R Λ and ξ fixed) Polarization at low M rec : show structures expected for: e + e - → D s1 (2536)D s, D s1 (2536)D* s J. Brodzicka for Belle @ QWG5

16. 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)